worst case analysis of demand point aggregation for the euclidean p median problem abstract solving large scale p median problems is usually time consuming people often aggregate the demand points in a large scale p median problem to reduce its problem size and make it easier to solve most traditional research on demand point aggregation is either experimental or assuming uniformly distributed demand points in analytical studies in this paper we study demand point aggregation for planar p median problem when demand points are arbitrarily distributed efficient demand aggregation approaches are proposed with the corresponding attainable worst case aggregation error bounds measured we demonstrate that these demand aggregation approaches introduce smaller worst case aggregation error bounds than that of the honeycomb heuristic papadimitriou c h 1981 worst case and probabilistic analysis of a geometric location problem siam journal on computing 10 542 557 when demand points are arbitrarily distributed we also conduct numerical experiments to show their effectiveness

using dual approximation algorithms for scheduling problems theoretical and practical results the problem of scheduling a set of n jobs on m identical machines so as to minimize the makespan time is perhaps the most well studied problem in the theory of approximation algorithms for np hard optimization problems in this paper the strongest possible type of result for this problem a polynomial approximation scheme is presented more precisely for each e an algorithm that runs in time o n e 1 e 2 and has relative error at most e is given in addition more practical algorithms for e 1 5 2 k and e 1 6 2 k which have running times o n k log n and o n km 4 log n are presented the techniques of analysis used in proving these results are extremely simple especially in comparison with the baroque weighting techniques used previously the scheme is based on a new approach to constructing approximation algorithms which is called dual approximation algorithms where the aim is to find superoptimal but infeasible solutions and the performance is measured by the degree of infeasibility allowed this notion should find wide applicability in its own right and should be considered for any optimization problem where traditional approximation algorithms have been particularly elusive

scaling of critical connectivity of mobile ad hoc networks in this paper critical global connectivity of mobile ad hoc networks manets is investigated we model the two dimensional plane on which nodes move randomly with a triangular lattice demanding the best communication of the network we account the global connectivity eta as a function of occupancy sigma of sites in the lattice by mobile nodes critical phenomena of the connectivity for different transmission ranges r are revealed by numerical simulations and these results fit well to the analysis based on the assumption of homogeneous mixing scaling behavior of the connectivity is found as eta approximately f r beta sigma where r r r 0 r 0 r 0 is the length unit of the triangular lattice and beta is the scaling index in the universal function f x the model serves as a sort of geometric distance dependent site percolation on dynamic complex networks moreover near each critical sigma c r corresponding to certain transmission range r there exists a cutoff degree k c below which the clustering coefficient of such self organized networks keeps a constant while the averaged nearest neighbor degree exhibits a unique linear variation with the degree k which may be useful to the designation of real manets

capacitated max batching with interval graph compatibilities we consider the problem of partitioning interval graphs into cliques of bounded size each interval has a weight and the weight of a clique is the maximum weight of any interval in the clique the goal is then to find such a partition of minimum total weight this graph problem can also be interpreted as a batch scheduling problem solving a long standing open question we show np hardness even if the bound on the clique sizes is constant moreover we give a ptas for this case

maximizing the minimum load for selfish agents we consider the problem of maximizing the minimum load completion time for machines that are controlled by selfish agents who are only interested in maximizing their own profit unlike the classical load balancing problem this problem has not been considered for selfish agents until now the goal is to design a truthful mechanism i e one in which all users have an incentive to tell the truth about the speeds of their machines this then allows us to find good job assignments it is known that this requires monotone approximation algorithms in which the amount of work assigned to an agent does not increase if its bid claimed cost per unit work increases for a constant number of machines m we show a monotone polynomial time approximation scheme ptas with running time that is linear in the number of jobs it uses a new technique for reducing the number of jobs while remaining close to the optimal solution we use an fptas for the classical problem i e where no selfish agents are involved to give a monotone fptas additionally we give a monotone approximation algorithm with approximation ratio min m email protected s 1 s m where e 0 can be chosen arbitrarily small and s i is the real speed of machine i finally we give improved results for two machines

on point covers of c oriented polygons let s be any family of n c oriented polygons of the two dimensional euclidean plane e2 i e bounded intersection of halfplanes whose normal directions of edges belong to a fixed collection of c distinct directions let s denote the packing number of s that is the maximum number of pairwise disjoint objects of s let s be the transversal number of s that is the minimum number of points required so that each object contains at least one of those points we provide linear time algorithms t n c t nc for a fat c oriented polytopes translates or homothets of ed proving that g 2 c o a d g 2 c dd and g 2 c 3d3 2 d respectively

relationship between juxtaposed overlapping and fractal representations of multimodal spatial variability 1 it has been shown by neuman 1990 di federico and neuman 1997 and di federico et al 1999 that the power variogram of a statistically isotropic or anisotropic fractal field can be constructed as a weighted integral from zero to infinity of exponential or gaussian variograms of overlapping homogeneous random fields modes having mutually uncorrelated increments and variance proportional to a power 2h of the integral spatial correlation scale where h is the hurst coefficient low and high frequency cutoffs are related to length scales of the sampling window domain and data support sample volume respectively intermediate cutoffs account for lacunarity due to gaps in the multiscale hierarchy created by a hiatus of modes associated with discrete ranges of scales alternative mathematical representations of multimodal spatial variability were formulated by various authors in which space is filled by a discrete number of juxtaposed mutually exclusive materials or categories each having its own architecture and attributes the spatial distribution of categories is characterized by indicator random variables and their attributes by random fields this paper focuses on expressions developed by lu and zhang 2002 in which the indicator variables and their attributes are mutually uncorrelated while each is autocorrelated and cross correlated within and between categories upon rewriting their expressions for statistically homogeneous and anisotropic media it is demonstrated mathematically that in the limit as the categories stretch to occupy each point in space overlap in a way that preserves their local architecture their attributes become mutually uncorrelated categories are said to overlap if they are found in fixed proportions within a representative sampling volume centered about any mathematical point throughout space the idea is analogous to the well known dual continuum concept in which two categories most commonly fractures and porous blocks are considered to overlap in reality the categories do not overlap but are considered to preserve their relative architectural arrangement throughout space the variogram of an attribute sampled jointly over overlapping statistically homogeneous and anisotropic categories is the sum of the variograms of statistically homogeneous and anisotropic components of this attribute sampled over individual categories weighted by their volumetric proportions it is further demonstrated that when the overlapping categories represent an infinite or truncated hierarchy of modes whose attributes have exponential or gaussian variograms such that the product of category probability density function pdf and attribute variance is proportional to a power 2h 1 of the attribute integral scale they represent a fractal field characterized by a power or truncated power variogram as in the work of di federico and neuman any category pdf that satisfies this condition and any attribute pdf having a variance that satisfies the same condition are admissible neither of them need to be gaussian to form fractional brownian motion or levy like to approximate fractional levy motion for the attribute to form a random fractal intermediate cutoffs render the latter model discrete as is that of lu and zhang hence the two multimodal models are mutually consistent and complementary

excluded grid minors and efficient polynomial time approximation schemes two of the most widely used approaches to obtain polynomial time approximation schemes ptass on planar graphs are the lipton tarjan separator based approach and baker s approach in 2005 demaine and hajiaghayi strengthened both approaches using bidimensionality and obtained efficient polynomial time approximation schemes eptass for several problems including c onnected d ominating s et and f eedback v ertex s et in this work we unify the two strengthened approaches to combine the best of both worlds we develop a framework allowing the design of eptas on classes of graphs with the subquadratic grid minor sqgm property roughly speaking a class of graphs has the sqgm property if for every graph g from the class the fact that g contains no t t grid as a minor guarantees that the treewidth of g is subquadratic in t for example the class of planar graphs and more generally classes of graphs excluding some fixed graph as a minor have the sqgm property at the heart of our framework is a decomposition lemma stating that for most bidimensional problems on a graph class g with the sqgm property there is a polynomial time algorithm that given a graph g e g as input and an e 0 outputs a vertex set x of size e opt such that the treewidth of g x is f e here opt is the objective function value of the problem in question and f is a function depending only on e this allows us to obtain eptass on apex minor free graphs for all problems covered by the previous framework as well as for a wide range of packing problems partial covering problems and problems that are neither closed under taking minors nor contractions to the best of our knowledge for many of these problems including c ycle p acking f p acking f d eletion m ax l eaf s panning t ree or p artial r d ominating s et no eptass even on planar graphs were previously known we also prove novel excluded grid theorems in unit disk and map graphs without large cliques using these theorems we show that these classes of graphs have the sqgm property based on the developed framework we design eptass and subexponential time parameterized algorithms for various classes of problems on unit disk and map graphs

optimal locations for a class of nonlinear single facility location problems on a network this paper investigates a class of single facility location problems on an arbitrary network necessary and sufficient conditions are obtained for characterizing locally optimal locations with respect to a certain nonlinear objective function this approach produces a number of new results for locating a facility on an arbitrary network and in addition it unifies several known results for the special case of tree networks it also suggests algorithmic procedures for obtaining such optimal locations

on the self affinity of various curves a numerical method is discussed which enables us to scale independently analyze the self affinity of various curves such as noise and topogrophical curves curve length n and standard deviations for two appropriately chosen coordinates x and z of a curve in two dimensions are measured between many arbitrary pairs of points on the curve by using the smallest fixed scale yardstick the self affinity is confirmed by checking the scaling of the form x nv and z nvz with vx vz the method is applied to transect profiles of real mountain topography which is found to be self affine with vx 1 for the horizontal and vz 1 for the vertical coordinate variations the consistency of a scaling relation d 2 h between a self similar contour line with the fractal dimension d and a self affine transect profile with h vz in the same area is also discussed

a 4 31 approximation for the geometric unique coverage problem on unit disks we give an improved approximation algorithm for the unique unit disk coverage problem given a set of points and a set of unit disks both in the plane we wish to find a subset of disks that maximizes the number of points contained in exactly one disk in the subset erlebach and van leeuwen 2008 introduced this problem as the geometric version of the unique coverage problem and gave a polynomial time 18 approximation algorithm in this paper we improve this approximation ratio 18 to 2 4 email protected 0 our algorithm runs in polynomial time which depends exponentially on 1 e the algorithm can be generalized to the budgeted unique unit disk coverage problem in which each point has a profit each disk has a cost and we wish to maximize the total profit of the uniquely covered points under the condition that the total cost is at most a given bound

approximation schemes for scheduling and covering on unrelated machines we examine the problem of assigning n independent jobs to m unrelated parallel machines so that each job is processed without interruption on one of the machines and at any time every machine processes at most one job we focus on the case where m is a fixed constant and present a new rounding approach that yields approximation schemes for multi objective minimum makespan scheduling with a fixed number of linear cost constraints the same approach gives approximation schemes for covering problems like maximizing the minimum load on any machine and for assigning specific or equal loads to the machines

covering moving points with anchored disks consider a set of mobile clients represented by n points in the plane moving at constant speed along n different straight lines we study the problem of covering all mobile clients using a set of k disks centered at k fixed centers each disk exists only at one instant and while it does covers any client within its coverage radius the task is to select an activation time and a radius for each disk such that every mobile client is covered by at least one disk in particular we study the optimization problem of minimizing the maximum coverage radius first we prove that although the static version of the problem is polynomial the kinetic version is np hard moreover we show that the problem is not approximable by a constant factor unless p np we then present a generic framework to solve it for fixed values of k which in turn allows us to solve more general optimization problems our algorithms are efficient for constant values of k

finite dominating sets for network location problems a research theme involving location on networks since its inception has been the identification of a finite dominating set fds or a finite set of points to which an optimal solution must belong we attempt to unify and generalize results of this sort we survey the literature and then prove some theorems that subsume most previous results and that are at the same time more general than previous results the paper is aimed primarily at investigators who wish to know whether an fds exists for a specific problem

the within strip discrete unit disk cover problem we present a study of the within strip discrete unit disk cover wsdudc problem which is a restricted version of the discrete unit disk cover dudc problem for the wsdudc problem there exists a set of points and a set of unit disks in the plane and the points and disk centres are conned to a strip of xed height an optimal solution to the wsdudc problem is a set of disks of minimum cardinality that covers all points in the input set we describe a range of approximation algorithms for the problem including 4 and 3 approximate algorithms which apply for strips of height 2 p 2 3 0 94 and 0 8 units respectively as well as a general scheme for any strip with less than unit height we prove that the wsdudc problem is np complete on strips of any xed height which is our most interesting result from a theoretical standpoint the result is also quite surprising since a number of similar problems are tractable on strips of xed height finally we discuss how these results may be applied to known dudc approximation algorithms

optimal cover of points by disks in a simple polygon let p be a simple polygon and let q be a set of points in p we present an almost linear time algorithm for computing a minimum cover of q by disks that are contained in p we then generalize the algorithm so that it can compute a minimum cover of q by homothets of any fixed compact convex set cal o of constant description complexity that are contained in p this improves previous results of katz and morgenstern lecture notes in comput sci 5664 2009 pp 447 458 we also consider the minimum disk cover problem when q is contained in a sufficiently narrow annulus and present a nearly linear algorithm for this case too

locating tree shaped facilities using the ordered median objective in this paper we consider the location of a tree shaped facility s on a tree network using the ordered median function of the weighted distances to represent the total transportation cost objective this function unifies and generalizes the most common criteria used in location modeling e g median and center if there are n demand points at the nodes of the tree t v e this function is characterized by a sequence of reals 1 n satisfying 1 2 n 0 for a given subtree s let x s x1 xn be the set of weighted distances of the n demand points from s the value of the ordered median objective at s is obtained as follows sort the n elements in x s in nonincreasing order and then compute the scalar product of the sorted list with the sequence two models are discussed in the tactical model there is an explicit bound l on the length of the subtree and the goal is to select a subtree of size l which minimizes the above transportation cost function in the strategic model the length of the subtree is variable and the objective is to minimize the sum of the transportation cost and the length of the subtree we consider both discrete and continuous versions of the tactical and the strategic models we note that the discrete tactical problem is np hard and we solve the continuous tactical problem in polynomial time using a linear programming lp approach we also prove submodularity properties for the strategic problem these properties allow us to solve the discrete strategic version in strongly polynomial time moreover the continuous version is also solved via lp for the special case of the k centrum objective we obtain improved algorithmic results using a dynamic programming dp algorithm and discretization and nestedness results

a two stage intelligent search algorithm for the two dimensional strip packing problem this paper presents a two stage intelligent search algorithm for a two dimensional strip packing problem without guillotine constraint in the first stage a heuristic algorithm is proposed which is based on a simple scoring rule that selects one rectangle from all rectangles to be packed for a given space in the second stage a local search and a simulated annealing algorithm are combined to improve solutions of the problem in particular a multi start strategy is designed to enhance the search capability of the simulated annealing algorithm extensive computational experiments on a wide range of benchmark problems from zero waste to non zero waste instances are implemented computational results obtained in less than 60 seconds of computation time show that the proposed algorithm outperforms the supposedly excellent algorithms reported recently on average it performs particularly better for large instances

flow in multiscale log conductivity fields with truncated power variograms in a previous paper we offered an interpretation for the observation that the log hydraulic conductivity of geologic media often appears to be statistically homogeneous but with variance and integral scale which grow with the size of the region window being sampled we did so by demonstrating that such behavior is typical of any random field with a truncated power semi variogram and that this field can be viewed as a truncated hierarchy of mutually uncorrelated homogeneous fields with either exponential or gaussian spatial autocovariance structures the low and high frequency cutoff scales l and u are related to the length scales of the sampling window and data support respectively we showed how this allows the use of truncated power variograms to bridge information about a multiscale random field across windows of different sizes either at a given locale or between different locales in this paper we investigate mean uniform steady state groundwater flow in unbounded domains where the log hydraulic conductivity forms a truncated multiscale hierarchy of gaussian fields each associated with an exponential autocovariance we start by deriving an expression for effective hydraulic conductivity as a function of the hurst coefficient h and the cutoff scales in one two and three dimensional domains which is qualitatively consistent with experimental data we then develop leading order analytical expressions for two and three dimensional autocovariance and cross covariance functions of hydraulic head velocity and log hydraulic conductivity versus h l and u examine their behavior and compare them with those corresponding to an exponential log hydraulic conductivity autocovariance our results suggest that it should be possible to bridge information about hydraulic heads and groundwater velocities across windows of disparate scales in particular when l u the variance of head is infinite in two dimensions and grows in proportion to l2 2h in three dimensions while the variance and longitudinal integral scale of velocity grow in proportion to l2h and l respectively in both cases

new approximations for minimum weighted dominating sets and minimum weighted connected dominating sets on unit disk graphs given a node weighted graph the minimum weighted dominating set mwds problem is to find a minimum weighted vertex subset such that for any vertex it is contained in this subset or it has a neighbor contained in this set and the minimum weighted connected dominating set mwcds problem is to find a mwds such that the graph induced by this subset is connected in this paper we study these two problems on a unit disk graph a 4 e approximation algorithm for an mwds based on a dynamic programming algorithm for a min weight chromatic disk cover is presented meanwhile we also propose a 1 e approximation algorithm for the connecting part by showing a polynomial time approximation scheme for a node weighted steiner tree problem when the given terminal set is c local and thus obtain a 5 e approximation algorithm for an mwcds

simple statistical models for river networks abstract the geometric scaling properties associated with simple river network models have been studied using computer simulations in these models the river networks are comprised of random trajectories which start at randomly selected positions on a square lattice and continue until they either reach an edge of the lattice or join a previous trajectory to form a branched network for those cases where the trajectories are either self avoiding random walks saws or indefinitely growing self avoiding walks igsaws the river basins are compact but have fractal basin boundaries with a dimensionally near to 5 4 for the igsaw model the longest river is a self similar fractal with a fractal dimensionality close to or equal to that of the igsaw itself if the trajectory is a directed walk then the model is very similar to the scheidegger river network model in this case the basin boundary and the longest channel are self affine brownian processes the results obtained from the igsaw and directed walk models can be described in terms of a simple scaling model for the saw models this scaling picture does not apply and it appears that practical simulations are far from the asymptotic large system size limit

online unit covering in euclidean space abstract we revisit the online unit covering problem in higher dimensions given a set of n points in r d that arrive one by one cover the points by balls of unit radius so as to minimize the number of balls used in this paper we work in r d using the euclidean distance i we give an online deterministic algorithm with competitive ratio o 1 321 d thereby improving on the previous record o 2 d d log d due to charikar et al 2004 by an exponential factor in particular the competitive ratios are 5 in the plane and 12 in 3 space the previous ratios were 7 and 21 respectively for d 3 the ratio of our online algorithm matches the ratio of the current best offline algorithm for the same problem due to biniaz et al 2017 which is remarkable and rather unusual ii we show that the competitive ratio of every deterministic online algorithm for unit covering in r d under the l 2 norm is at least d 1 for every d 1 this greatly improves upon the previous best lower bound log d log log log d due to charikar et al 2004 iii we generalize the above result to unit covering in r d under the l c norm where c is a centrally symmetric convex body via the illumination number iv we obtain lower bounds of 4 and 5 for the competitive ratio of any deterministic algorithm for online unit covering in r 2 and r 3 respectively the previous best lower bounds were 3 for both cases v when the input points are from the square or hexagonal lattice in r 2 we give deterministic online algorithms for unit covering with an optimal competitive ratio of 3 for the cubic lattice in r 3 we give a deterministic online algorithm with a competitive ratio of 5

approximation schemes for independent set and sparse subsets of polygons we present a 1 e approximation algorithm with quasi polynomial running time for computing a maximum weight independent set of polygons from a given set of polygons in the plane contrasting this the best known polynomial time algorithm for the problem has an approximation ratio of ne surprisingly we can extend the algorithm to the problem of computing the maximum cardinality subset of the given set of polygons whose intersection graph fulfills some sparsity condition for example we show that one can approximate the maximum subset of polygons such that the intersection graph of the subset is planar or does not contain a cycle of length 4 i e k2 2 our algorithm relies on a recursive partitioning scheme whose backbone is the existence of balanced cuts with small complexity that intersect polygons from the optimal solution of a small total weight for the case of large axis parallel rectangles we provide a polynomial time 1 e approximation for the maximum weight independent set specifically we consider the problem where each rectangle has one edge whose length is at least a constant fraction of the length of the corresponding edge of the bounding box of all the input elements this is now the most general case for which a ptas is known and it requires a new and involved partitioning scheme which should be of independent interest

approximation schemes for covering and packing problems in image processing and vlsi a unified and powerful approach is presented for devising polynomial approximation schemes for many strongly np complete problems such schemes consist of families of approximation algorithms for each desired performance bound on the relative error e o with running time that is polynomial when e is fixed though the polynomiality of these algorithms depends on the degree of approximation e being fixed they cannot be improved owing to a negative result stating that there are no fully polynomial approximation schemes for strongly np complete problems unless np p the unified technique that is introduced here referred to as the shifting strategy is applicable to numerous geometric covering and packing problems the method of using the technique and how it varies with problem parameters are illustrated a similar technique independently devised by b s baker was shown to be applicable for covering and packing problems on planar graphs

a framework for demand point and solution space aggregation analysis for location models abstract many location problems can be formulated as minimizing some location objective function subject to upper bounds on other location constraint functions when such functions are subadditive and nondecreasing in the distances a common occurrence worst case demand point aggregation error bounds are known we show how to solve a relaxation and a restriction of the aggregated problem in such a way as to obtain lower and upper bounds on the optimal value of the original problem we consider some applications to covering and related problems

hortonian scaling and effect of cutoffs on statistics of self affine river networks 1 the planar structure of river networks exhibits fractal properties in particular available data indicate a tendency for drainage areas a to be distributed according to a power law their boundaries and main channels to form self affine curves the characteristic lengths of drainage areas to be independently self affine in the one dimensional space z of total channel length rendering the network elongated and anisotropic the inverse network density a z to be either constant or self affine in z depending on whether or not the network fills the two dimensional space of a and as found in a recent study areas of given size vegetative cover and mean steady state soil moisture weighted by their flow distance from the basin outlet to be self affine in the one dimensional space of this distance various theoretical and semiempirical relationships have been proposed among exponents defining some of these and other scale dependencies expressions have been proposed for ensemble moments of a and some length measures associated with finite size river basins we present a new model that views any self affine basin property y x as belonging to an infinite hierarchy of mutually uncorrelated statistically homogeneous random functions defined on elementary subbasins each of which is characterized by a unique integral spatial correlation scale we cite a mathematically rigorous hydrologic rationale for our model and use it in conjunction with published scaling relations to obtain the probability density function of to derive analytical expressions for ensemble analogs of horton s scaling laws to deduce from them that streams of any horton strahler order are associated with integral scales 1 where the ratio 1 is a constant independent of to develop analytical expressions relating statistical moments of y x to arbitrary lower and upper cutoff scales that may but need not be taken to represent data support and maximum watershed size to describe ways of estimating the corresponding parameters and to provide a theoretical basis for the heretofore unexplained observation that self affine amplitude fluctuations of basin boundaries and main channels as measured by their variance having a common hurst exponent are larger in the former than in the latter

an adaptive multiphase approach for large unconditional and conditional p median problems abstract a multiphase approach that incorporates demand points aggregation variable neighbourhood search vns and an exact method is proposed for the solution of large scale unconditional and conditional p median problems the method consists of four phases in the first phase several aggregated problems are solved with a local search with shaking procedure to generate promising facility sites which are then used to solve a reduced problem in phase 2 using vns or an exact method the new solution is then fed into an iterative learning process which tackles the aggregated problem phase 3 phase 4 is a post optimisation phase applied to the original disaggregated problem for the p median problem the method is tested on three types of datasets which consist of up to 89 600 demand points the first two datasets are the birch and the tsp datasets whereas the third is our newly geometrically constructed dataset that has guaranteed optimal solutions the computational experiments show that the proposed approach produces very competitive results the proposed approach is also adapted to cater for the conditional p median problem with interesting results

an effective quasi human based heuristic for solving the rectangle packing problem abstract in this paper we introduce an effective deterministic heuristic less flexibility first for solving the classical np complete rectangle packing problem many effective heuristics implemented for this problem are cpu intensive and non deterministic in nature others including the polynomial approximation methodology j assoc comput mach 32 1 1985 130 are too laborious for practical problem sizes the technique we propose is inspired and developed by enhancing some rule of thumb guidelines resulting from the generation long work experience of human professionals in ancient days although the less flexibility first heuristic is a deterministic algorithm the results are very encouraging this algorithm can consistently produce packing densities of around 99 on most randomly generated large examples as compared with the recent results of a well known simulated annealing based rectangle packing rp algorithm ieee trans computer aided design integrated circuits systems 17 1 1998 60 the results are much better both in less dead space 2 4 vs 6 7 and much less cpu time 9 57 vs 331 78 seconds experimenting our heuristics on a public rectangle packing data set covering instances of 16 97 rectangles the average unpack ratio is quite satisfactory 0 92 for bounding boxes limited to be optimum and 2 68 for the completed packing while most cases spend only a few minutes in cpu time

range assignment of base stations maximizing coverage area without interference abstract we study the problem of assigning non overlapping geometric objects centered at a given set of points such that the sum of area covered by them is maximized the problem remains open since 2002 as mentioned in a lecture slide of david eppstein in this paper we have performed an exhaustive study on the problem we show that if the points are placed in r 2 then the problem is np hard even for simplest type of covering objects like disks or squares in contrast eppstein 2017 10 proposed a polynomial time algorithm for maximizing the sum of radii or perimeter of non overlapping disks when the points are arbitrarily placed in r 2 we show that eppstein s algorithm for maximizing sum of perimeter of the disks in r 2 gives a 2 approximation solution for the sum of area maximization problem we also propose a ptas for the same problem our results can be extended in higher dimensions as well as for a class of centrally symmetric convex objects

aggregation error bounds for a class of location models many location models involve distances and demand points in their objective function in urban contexts there can be millions of demand points this leads to demand point aggregation which produces error we identify a general model structure that includes most such location models and present a means of obtaining error bounds for all models with this structure the error bounds suggest how to do the demand point aggregation so as to keep the error small

transport in multiscale log conductivity fields with truncated power variograms di federico and neuman this issue investigated mean uniform steady state groundwater flow in an unbounded domain with log hydraulic conductivity that forms a truncated multiscale hierarchy of statistically homogeneous and isotropic gaussian fields each associated with an exponential autocovariance here we present leading order expressions for the displacement covariance and dispersion coefficient of an ensemble of solute particles advected through such a flow field in two or three dimensions both quantities are functions of the mean travel distance s the hurst coefficient h and the low and high frequency cutoff integral scales l and u the latter two are related to the length scales of the sampling window region under investigation and sample volume data support respectively if one considers transport to be affected by a finite domain much larger than the mean travel distance so that s l then an early preasymptotic regime develops during which longitudinal and transverse dispersivities grow linearly with s if one considers transport to be affected by a domain which increases in proportion to s then l and s are of similar order and a preasymptotic regime never develops instead transport occurs under a regime that is perpetually close to asymptotic under the control of an evolving scale l s we show that if additionally u l then the corresponding longitudinal dispersivity grows in proportion to l1 2h or equivalently s1 2h both these preasymptotic and asymptotic theoretical growth rates are shown to be consistent with the observed variation of apparent longitudinal fickian dispersivities with scale we conclude by investigating the effect of variable separations between cutoff scales on dispersion

on self similarity and self affinity of drainage basins an approach is proposed which allows consideration from common positions the self similar and self affine properties of river drainage basins and which introduces respective characteristics of their fractal structure horton s 1945 model has been assumed as the basis of this study it is shown that self similarity of river drainage basins is characterized by the self similarity dimension ds ln rb ln rl in the case of self affinity two scaling indices dl ln rb ln rl and dw ln rb ln ra rl are required the combinations of which determine the hurst h dl dw index characterizing the degree of drainage basins self affinity and the lacunary dimension dg 2dldw dl dw characterizing the degree of lacunarity or noncompactness of drainage basins on the basis of analysis of published data from rivers in the united states italy russia and romania the conclusion is drawn that river drainage basins are generally noncompact dg 2 and self affine h 1 fractal objects besides for a quantitative description of river drainage basins a new parameter is introduced which characterizes the degree to which a large catchment is filled with smaller ones

approximations for steiner trees with minimum number of steiner points abstract given n terminals in the euclidean plane and a positive constant find a steiner tree interconnecting all terminals with the minimum number of steiner points such that the euclidean length of each edge is no more than the given positive constant this problem is np hard with applications in vlsi design wdm optical networks and wireless communications in this paper we show that a the steiner ratio is 1 4 that is the minimum spanning tree yields a polynomial time approximation with performance ratio exactly 4 b there exists a polynomial time approximation with performance ratio 3 and c there exists a polynomial time approximation scheme under certain conditions

fractal relation of mainstream length to catchment area in river networks institute of hydraulics university of genoa italymandelbrot s 1982 hypothesis that river length is fractal has been recently substantiated byhjelmfelt 1988 using eight rivers in missouri the fractal dimension of river length d is derived herefrom the horton s laws of network composition this results in a simple function of stream length andstream area ratios that is d max 1 2 log rl og ra three case studies are reported showing thisestimate to be coherent with measurements of d obtained from map analysis the scaling properties ofthe network as a whole are also investigated showing the fractal dimension of river network d todepend upon bifurcation and stream area ratios according to d min 2 2 log rb log ra theseresults provide a linkage between quantitative analysis of drainage network composition and scalingproperties of river networks

hierarchically specified unit disk graphs we characterize the complexity of several basic optimization problems for unit disk graphs specified hierarchically as in lw87a le88 lw92 both pspace hardness results and polynomial time approximations are presented for most of the problems considered these problems include minimum vertex coloring maximum independent set minimum clique cover minimum dominating set and minimum independent dominating set

geometry of river networks i scaling fluctuations and deviations this paper is the first in a series of three papers investigating the detailed geometry of river networks branching networks are a universal structure employed in the distribution and collection of material large scale river networks mark an important class of two dimensional branching networks being not only of intrinsic interest but also a pervasive natural phenomenon in the description of river network structure scaling laws are uniformly observed reported values of scaling exponents vary suggesting that no unique set of scaling exponents exists to improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure here we report a theoretical and empirical study of fluctuations about and deviations from scaling we examine data for continent scale river networks such as the mississippi and the amazon and draw inspiration from a simple model of directed random networks we center our investigations on the scaling of the length of a subbasin s dominant stream with its area a characterization of basin shape known as hack s law we generalize this relationship to a joint probability density and provide observations and explanations of deviations from scaling we show that fluctuations about scaling are substantial and grow with system size we find strong deviations from scaling at small scales which can be explained by the existence of a linear network structure at intermediate scales we find slow drifts in exponent values indicating that scaling is only approximately obeyed and that universality remains indeterminate at large scales we observe a breakdown in scaling due to decreasing sample space and correlations with overall basin shape the extent of approximate scaling is significantly restricted by these deviations and will not be improved by increases in network resolution

the usefulness of optimum experimental designs optimum experimental designs were originally developed by kiefer mainly for response surface models this survey of recent developments emphasizes potential or actual usefulness for linear models the construction of exact designs particularly over irregular design regions is stressed as is the blocking of response surface designs other important areas include systematic designs that are robust against trend and designs for mixtures with irregular design regions several industrial examples are mentioned both d and c optimum designs are found for a non linear model of the economic response of cereal production to fertilizer level the c optimum design being for the conditions of maximum economic return locally optimum and bayesian designs are both described similar results for generalized linear models lead to designs for the ld 95 in a logistic model in which male and female subjects respond differently designs with structure in the variance suggest alternatives to the potentially wasteful product designs of taguchi designs for sequential clinical trials to include random balance are presented the last section outlines some applications including life testing and models in which time is a factor

the p median problem a survey of metaheuristic approaches the p median problem is one of the basic models in discrete location theory as with most location problems it is classified as np hard and so heuristic methods are usually used to solve it metaheuristics are frameworks for building heuristics in this survey we examine the p median with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules

k eccentricity and absolute k centrum of a probabilistic tree abstract the k eccentricity evaluated at a point x of a graph g is the sum of the weighted distances from x to the k vertices farthest from it the k centrum is the set of vertices for which the k eccentricity is a minimum the concept of k centrum includes as a particular case that of center and that of centroid or median of a graph the absolute k centrum is the set of points not necessarily vertices for which the k eccentricity is a minimum in this paper it will be proven that for a weighted tree both deterministic and probabilistic the k eccentricity is a convex function and that the absolute k centrum is a connected set and is contained in an elementary path hints will be given for the construction of an algorithm to find the k centrum and the absolute k centrum

scaling of random fields by means of truncated power variograms and associated spectra an interpretation is offered for the observation that the log hydraulic conductivity of geologic media often appears to be statistically homogeneous but with variance and integral scale which grow with domain size we first demonstrate that the power semi variogram and associated spectra of random fields having homogeneous isotropic increments can be constructed as weighted integrals from zero to infinity an infinite hierarchy of exponential or gaussian variograms and spectra of mutually uncorrelated homogeneous isotropic fields modes we then analyze the effect of filtering out truncating high and low frequency modes from this infinite hierarchy in the real and spectral domains a low frequency cutoff renders the truncated hierarchy homogeneous with an autocovariance function that varies monotonically with separation distance in a manner not too dissimilar than that of its constituent modes the integral scales of the lowest and highest frequency modes cutoffs are related respectively to the length scales of the sampling window domain and data support sample volume taking each relationship to be one of proportionality renders our expressions for the integral scale and variance of a truncated field dependent on window and support scales in a manner consistent with observations the traditional approach of truncating power spectral densities yields autocovariance functions that oscillate about zero with finite in one and two dimensions or vanishing in one dimension integral scales our hierarchical theory allows bridging across scales at a specific locale by calibrating a truncated variogram model to data observed on a given support in one domain and predicting the autocovariance structure of the corresponding multiscale field in domains that are either smaller or larger one may also venture we suspect with less predictive power to bridge across both domain scales and locales by adopting generalized variogram parameters derived on the basis of juxtaposed hydraulic and tracer data from many sites

a ptas for the cardinality constrained covering with unit balls in this paper we address the cardinality constrained covering with unit balls problem given a positive integer l and a set of n points in r d partition them into a minimum number of parts such that each part contains at most l points and it can be covered by a unit ball of the given p metric developing a constant factor approximation algorithm for this problem is an old open problem by proving a structural property in the problem and applying the shifting strategy and dynamic programming we derive the first email protected d approximation n o 1 e d time algorithm for this problem when d is a fixed constant

on hack s law hack s law is reviewed emphasizing its implications for the elongation of river basins as well as its connections with their fractal characteristics the relation between hack s law and the internal structure of river basins is investigated experimentally through digital elevation models it is found that hack s exponent elongation and some relevant fractal characters are closely related the self affine character of basin boundaries is shown to be connected to the power law decay of the probability of total contributing areas at any link and to hack s law an explanation for hack s law is derived from scaling arguments from the results we suggest that a statistical framework referring to the scaling invariance of the entire basin structure should be used in the interpretation of hack s law

dynamics on spatial networks and the effect of distance coarse graining abstract recently spatial networks have attracted much attention the spatial network is constructed from a regular lattice by adding long range edges shortcuts with probability p r r where r is the geographical distance between the two ends of the edge also a cost constraint on the total length of the additional edges is introduced r c it has been pointed out that such networks have optimal exponents for the average shortest path traffic dynamics and navigation however when is large too many generated long range edges will be added to the network in this scenario the total cost constraint cannot be satisfied in this paper we propose a distance coarse graining procedure to solve this problem we find that the optimal exponents for the traffic process navigation and synchronization indeed result from the trade off between the probability density function of long range edges and the total cost constraint but the optimal exponent for percolation is actually due to dissatisfying the total cost constraint on the other hand because the distance coarse graining procedure widely exists in the real world our work is also meaningful in this aspect

integer programming with a fixed number of variables it is shown that the integer linear programming problem with a fixed number of variables is polynomially solvable the proof depends on methods from geometry of numbers

approximating uniform triangular meshes in polygons we consider the problem of triangulating a convex polygon using n steiner points under the following optimality criteria 1 minimizing the overall edge length ratio 2 minimizing the maximum edge length and 3 minimizing the maximum triangle perimeter we establish a relation of these problems to a certain extreme packing problem based on this relationship we develop a heuristic producing constant approximations for all the optimality criteria above provided n is chosen sufficiently large that is the produced triangular mesh is uniform in these respects the method is easy to implement and runs in o n2log n time and o n space the observed runtime is much less moreover for criterion 1 the method works within the same complexity and approximation bounds for arbitrary polygons with possible holes and for criteria 2 and 3 it does so for a large subclass

clustering to minimize the maximum intercluster distance the problem of clustering a set of points so as to minimize the maximum intercluster distance is studied an o kn approximation algorithm where n is the number of points and k is the number of clusters that guarantees solutions with an objective function value within two times the optimal solution value is presented this approximation algorithm succeeds as long as the set of points satisfies the triangular inequality we also show that our approximation algorithm is best possible with respect to the approximation bound if pz np

near optimal sensor placements in gaussian processes theory efficient algorithms and empirical studies when monitoring spatial phenomena which can often be modeled as gaussian processes gps choosing sensor locations is a fundamental task there are several common strategies to address this task for example geometry or disk models placing sensors at the points of highest entropy variance in the gp model and a d or e optimal design in this paper we tackle the combinatorial optimization problem of maximizing the mutual information between the chosen locations and the locations which are not selected we prove that the problem of finding the configuration that maximizes mutual information is np complete to address this issue we describe a polynomial time approximation that is within 1 1 e of the optimum by exploiting the submodularity of mutual information we also show how submodularity can be used to obtain online bounds and design branch and bound search procedures we then extend our algorithm to exploit lazy evaluations and local structure in the gp yielding significant speedups we also extend our approach to find placements which are robust against node failures and uncertainties in the model these extensions are again associated with rigorous theoretical approximation guarantees exploiting the submodularity of the objective function we demonstrate the advantages of our approach towards optimizing mutual information in a very extensive empirical study on two real world data sets

hyperbolic set covering problems with competing ground set elements motivated by a challenging problem arising in wireless network design we investigate a new nonlinear variant of the set covering problem with hyperbolic objective function each ground set element user competes with all its neighbors interfering users for a shared resource the network access time and the goal is to maximize the sum of the resource share assigned to each ground set element the network efficiency while covering all of them the hyperbolic objective function privileges covers with limited overlaps among selected subsets in a sense this variant lies in between the set partitioning problem where overlaps are forbidden and the standard set covering problem where overlaps are not an issue at all we study the complexity and approximability of generic and euclidean versions of the problem present an efficient lagrangean relaxation approach to tackle medium to large scale instances and compare the computational results with those obtained by linearizations

approximation algorithms for the set covering and vertex cover problems we propose a heuristic that delivers in o n 3 steps a solution for the set covering problem the value of which does not exceed the maximum number of sets covering an element times the optimal value

generalized p center problems complexity results and approximation algorithms abstract in an earlier paper two alternative p center problems where the centers serving costumers must be chosen so that exactly one node from each of p prespecified disjoint pairs of nodes is selected were shown to be np complete this paper considers a generalized version of these problems in which the nodes from which the p servers are to be selected are partitioned into k sets and the number of servers selected from each set must be within a prespecified range we refer to these problems as the set p center problems we establish that the triangle inequality inequality versions of these problems in which the edge weights are assumed to satisfy the triangle inequality are also np complete we also provide a polynomial time approximation algorithm for the two inequality set p center problems that is optimal for one of the problems in the sense that no algorithm with polynomial running time can provide a better constant factor performance guarantee unless p np for the special case alternative p center problems which we refer to as the pair p center problems we extend the previous results in several ways for example the results mentioned above for the set p center problems also apply to the pair p center problems furthermore we establish and exploit a correspondence between satisfiability and the dominating set type of problems that naturally arise when considering the decision versions of the pair p center problems

parallel approximation schemes for a class of planar and near planar combinatorial optimization problems define a g almost planar graph to be a graph g v e consisting of vertex set v and a genus g layout with at most v crossover nodes we study a class of combinatorial optimization problems formulated as follows let x x1 x2 xn be a set of variables each of which has a finite domain d 0 1 poly n also let s be a fixed finite set of finite arity relations r1 rq the optimization problem max relation s is the following given a set of terms t1 t2 tm where each term ti is of the form f xi1 xi2 xir for some f s assign values to each xi 1 i n so as to maximize the number of satisfied terms we show that for each fixed finite set s and fixed g 0 there is an nc approximation scheme ncas for the problem max relation s when restricted to instances whose bipartite graphs that represent the variable term relationship are g almost planar this result in conjunction with approximation preserving reductions to max relation s enables us to obtain ncass for a number of graph theoretic and satisfiability problems when restricted to g almost planar instances our results provide a characterization of a class of problems having an ncas and hence a ptas

distribution systems design with role dependent objectives in this paper we introduce flexible models for capacitated discrete location problems we describe three different points of view of a location problem in a logistics system different mathematical programming formulations are presented illustrated by examples and compared using a battery of test problems extensive computational tests are done showing the potentials and limits of this kind of resolution approach

approximation algorithms for maximum two dimensional pattern matching we introduce the following optimization version of the classical pattern matching problem referred to as the maximum pattern matching problem given a two dimensional rectangular text and a two dimensional rectangular pattern find the maximum number of non overlapping occurrences of the pattern in the text unlike the classical two dimensional pattern matching problem the maximum two dimensional pattern matching problem is np complete we devise polynomial time approximation algorithms and approximation schemes for this problem we also briefly discuss how the approximation algorithms can be extended to include a number of other variants of the problem

fast stabbing of boxes in high dimensions abstract we present in this paper a simple yet efficient algorithm for stabbing a set s of n axis parallel boxes in d dimensional space with c s points in output sensitive time o dn log c s and linear space let c s and b s be respectively the minimum number of points required to stab s and the maximum number of pairwise disjoint boxes of s we prove that b s c s c s b s 1 log 2 b s d 1 since finding a minimal set of c s points is np complete as soon as d 1 we obtain a fast precision sensitive heuristic for stabbing s whose quality does not depend on the input size in the case of congruent or constrained isothetic boxes our algorithm reports respectively c s 2 d 1 b s and c s o d b s stabbing points moreover we show that the bounds we get on c s are asymptotically tight and corroborate our results with some experiments we also describe an optimal output sensitive algorithm for finding a minimal size optimal stabbing point set of intervals finally we conclude with insights for further research

stochastic models that separate fractal dimension and the hurst effect fractal behavior and long range dependence have been observed in an astonishing number of physical biological geological and socioeconomic systems time series profiles and surfaces have been characterized by their fractal dimension a measure of roughness and by the hurst coefficient a measure of long memory dependence both phenomena have been modeled and explained by self affine random functions such as fractional gaussian noise and fractional brownian motion the assumption of statistical self affinity implies a linear relationship between fractal dimension and hurst coefficient and thereby links the two phenomena this article introduces stochastic models that allow for any combination of fractal dimension and hurst coefficient associated software for the synthesis of images with arbitrary prespecified fractal properties and power law correlations is available the new models suggest a test for self affinity that assesses coupling and decoupling of local and global behavior

anisotropy lacunarity and upscaled conductivity and its autocovariance in multiscale random fields with truncated power variograms it has been shown by di federico and neuman 1997 1998a b that observed multiscale behaviors of subsurface fluid flow and transport variables can be explained within the context of a unified stochastic framework which views hydraulic conductivity as a random fractal characterized by a power variogram such a random field is statistically nonhomogeneous but possesses homogeneous spatial increments di federico and neuman 1997 have demonstrated that the power variogram and associated spectra of a statistically isotropic fractal field can be constructed as a weighted integral from zero to infinity an infinite hierarchy of exponential or gaussian variograms and spectra of mutually uncorrelated fields modes that are homogeneous and isotropic we show in this paper that the same holds true when the field and its constituent modes are statistically anisotropic provided the ratios between principal integral spatial correlation scales are the same for all modes we then analyze the effect of filtering out truncating modes of low high and intermediate spatial frequency from this infinite hierarchy in the real and spectral domains a low frequency cutoff renders the truncated hierarchy homogeneous the integral scales of the lowest and highest frequency cutoff modes are related to length scales of the sampling window domain and data support sample volume respectively taking the former to be proportional to the latter renders expressions for the integral scale and variance of the truncated field dependent on window and support scale in a manner previously shown to be consistent with observations in the isotropic case it also allows in principle bridging across scales at a specific locale as well as among locales by adopting either site specific or generalized variogram parameters the introduction of intermediate cutoffs allows us to account in a straightforward manner for lacunarity due to gaps in the multiscale hierarchy created by the absence of modes associated with discrete ranges of scales for example where textural and structural features are associated with distinct ranges of scale such as fractures having discrete ranges of trace length and density which dissect the rock into matrix blocks having corresponding ranges of sizes we explore mathematically and graphically the effects that anisotropy and lacunarity have on the integral scale variance covariance and spectra of a truncated fractal field we then develop an expression for the equivalent hydraulic conductivity of a box shaped porous block embedded within a multiscale log hydraulic conductivity field under mean uniform flow the block is larger than the support scale of the field but is smaller than a surrounding sampling window consequently its equivalent hydraulic conductivity is a random variable whose variance and spatial autocorrelation function conditioned on a known mean value of support scale conductivity across the window are given explicitly by our multiscale theory

polynomial time approximation schemes for geometric intersection graphs a disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane for the case that the disk representation is given we present polynomial time approximation schemes ptass for the maximum weight independent set problem selecting disjoint disks of maximum total weight and for the minimum weight vertex cover problem in disk graphs these are the first known ptass for mathcal np hard optimization problems on disk graphs they are based on a novel recursive subdivision of the plane that allows applying a shifting strategy on different levels simultaneously so that a dynamic programming approach becomes feasible the ptass for disk graphs represent a common generalization of previous results for planar graphs and unit disk graphs they can be extended to intersection graphs of other disk like geometric objects such as squares or regular polygons also in higher dimensions

an efficient polynomial time approximation scheme for load balancing on uniformly related machines we consider basic problems of non preemptive scheduling on uniformly related machines for a given schedule defined by a partition of the jobs into m subsets corresponding to the m machines c i c i denotes the completion time of machine i our goal is to find a schedule that minimizes or maximizes sum i 1 m c i p i 1 m c i p for a fixed value of p such that 0 1 p 1 the minimization problem is equivalent to the well known problem of minimizing the ell p l p norm of the vector of the completion times of the machines and for 0 p 1 0 p 1 the maximization problem is of interest our main result is an efficient polynomial time approximation scheme eptas for each one of these problems our schemes use a non standard application of the so called shifting technique we focus on the work total size of jobs assigned to each machine and introduce intervals of work that are forbidden these intervals are defined so that the resulting effect on the goal function is sufficiently small this allows the partition of the problem into sub problems with subsets of machines and jobs whose solutions are combined into the final solution using dynamic programming our results are the first eptas s for this natural class of load balancing problems

the ultimate planar convex hull algorithm we present a new planar convex hull algorithm with worst case time complexity o n log h where n is the size of the input set and h is the size of the output set i e the number of vertices found to be on the hull we also show that this algorithm is asymptotically worst case optimal on a rather realistic model of computation even if the complexity of the problem is measured in terms of input as well as output size the algorithm relies on a variation of the divide and conquer paradigm which we call the marriage before conquest principle and which appears to be interesting in its own right

probabilistic structure of the distance between tributaries of given size in river networks we analyze the distribution of the distances between tributaries of a given size or of sizes larger than a given area draining along either an open boundary or the mainstream of a river network by proposing a description of the distance separating prescribed merging contributing areas we also address related variables like mean or bankfull flow rates and channel and riparian area widths which are derived under a set of reasonable hydrologic assumptions the importance of such distributions lies in their ecological hydrologic and geomorphic implications on the spreading of species along the ecological corridor defined by the river network and on the propagation of infections due to water borne diseases particularly in view of exact theoretical predictions explicitly using the alongstream distribution of confluences carrying a given flow use is made here of real river networks suitably extracted from digital elevation models optimal channel networks and exactly solved tree like constructs like the peano and the scheidegger networks the results obtained redefine theoretically in a coherent and general manner and verify observationally the distribution function of the above distances and thus provide the general probabilistic structure of tributaries in river networks specifically we find that the probability of exceedence of the alongstream distance d of tributaries of size larger than a has the explicit form p d exp cd a h 1 h where c is a constant that depends on the choice of boundary conditions and h 1 is the hurst exponent

a polynomial approximation scheme for scheduling on uniform processors using the dual approximation approach in this paper we present a polynomial approximation scheme for the minimum makespan problem on uniform parallel processors more specifically the problem is to find a schedule for a set of independent jobs on a collection of machines of different speeds so that the last job to finish is completed as quickly as possible we give a family of polynomial time algorithms a such that a delivers a solution that is within a relative error of e of the optimum the technique employed is the dual approximation approach where infeasible but superoptimal solutions for a related dual problem are converted to the desired feasible but possibly suboptimal solution

the complexity of planar counting problems we prove the p hardness of the counting problems associated with various satisfiability graph and combinatorial problems when restricted to planar instances these problems include 3sat 1 3sat 1 ex3sat minimum vertex cover minimum dominating set minimum feedback vertex set x3c partition into triangles and clique cover we also prove the np completeness of the ambiguous satisfiability problems j b saxe two papers on graph embedding problems tech report cmu cs 80 102 dept of computer science carnegie mellon univ pittsburgh pa 1980 and the dp completeness with respect to random polynomial reducibility of the unique satisfiability problems l g valiant and v v vazirani np is as easy as detecting unique solutions in proc 17th acm symp on theory of computing 1985 pp 458 463 associated with several of the above problems when restricted to planar instances previously very few p hardness results no sf np hardness results and no dp completeness results were known for counting problems ambiguous satisfiability problems and unique satisfiability problems respectively when restricted to planar instances assuming sf p neq np one corollary of the above results is that there are no epsilon approximation algorithms for the problems of maximizing or minimizing a linear objective function subject to a planar system of linear inequality constraints over the integers

on the complexity of bandwidth allocation in radio networks we define and study an optimization problem that is motivated by bandwidth allocation in radio networks because radio transmissions are subject to interference constraints in radio networks physical space is a common resource that the nodes have to share in such a way that concurrent transmissions do not interfere the bandwidth allocation problem we study under these constraints is the following given bandwidth traffic demands between the nodes of the network the objective is to schedule the radio transmissions in such a way that the traffic demands are satisfied the problem is similar to a multicommodity flow problem where the capacity constraints are replaced by the more complex notion of non interfering transmissions we provide a formal specification of the problem that we call round weighting by modeling non interfering radio transmissions as independent sets we relate the complexity of round weighting to the complexity of various independent set problems e g maximum weight independent set vertex coloring fractional coloring from this relation we deduce that in general round weighting is hard to approximate within n 1 e n being the size of the radio network we also provide polynomial exact or approximation algorithms e g in the following two cases a when the interference constraints are specific for instance for a network whose vertices belong to the euclidean space or b when the traffic demands are directed towards a unique node in the network also called gathering analogous to single commodity flow

a modified vicsek model for self propelled agents with exponential neighbor weight and restricted visual field abstract large flocks of wild beings can have coordinated motion with neither leading center nor global information the vicsek model and its new versions explained such collective behavior of self propelled agents with the mechanism of un weighted influence of neighbors and global visual field gvf which may not always fit the reality in the present work we take both exponential neighbor weight enw and restricted visual field rvf into account and investigate the combinatory effect of them based on this mechanism in most cases of our simulation stationary direction consensus v a exhibits a maximum or decreases with v f and a minimum convergence time t m i n appears in rvf which demonstrates that gvf is not necessary for coordinated motion while rvf matched enw would be reasonable moreover we simulated various recipes for optimizing v a and t in unfavorable cases and found critical points separating inverse dependent variations of t the present work may be useful in improving the efficiency of direction consensus of large flocks of artificial individuals besides the understanding of biological collective motion in nature

analysis of greedy solutions for a replacement part sequencing problem this paper considers the problem of sequencing the installation of replacement parts for the repeated repair of a machine consisting of two working parts a finite inventory of spares is initially available for each type of part each spare has a known deterministic field life and spares of each type may have different field lives the inventories are eventually depleted since no replacement or repairs of parts occur the primary objective is to obtain a sequencing policy which minimizes the total number of installations replacements this problem is a special case of many opportunistic replacement problems and is called a build problem the motivation for this work is based on the maintenance of modular gas turbine aircraft engines used by domestic airlines and the u s air force we show this build problem is np hard which indicates the necessity of efficient heuristic solution procedures this paper considers several greedy type algorithms based on grouping parts according to exact matching of field lives then a generalization is presented which allows approximate matches the focus of the analysis is to obtain tight worst case bounds on the number of replacements obtained by each of the greedy algorithms

new upper bounds in klee s measure problem new upper bounds for the measure problem of klee are given which significantly improve the previous bounds for dimensions greater than two an o n d 2 log n n time space upper bound is obtained and used to compute the measure of a set of n boxes in euclidean d space the solution is based on a new data structure which is called an orthogonal partition tree this structure has other applications as well

a note on fractal channel networks this paper studies the relation between the structure of river networks and the features of their geomorphologic hydrologic response a mathematical formulation of connectivity of a drainage network is proposed to relate contributing areas and the network geometry in view of the connectivity conjecture horton s bifurcation ratio r b tends for high values of strahler s order omega of the basin to the area ratio r a and horton s length ratio r l equals in the limit the single order contributing area ratio r a the relevance of these arguments is examined by reference to data from real basins well known empirical results from the geomorphological literature melton s law hack s relation moon s conjecture are viewed as a consequence of connectivity it is found that in hortonian networks the time evolution of contributing areas exhibits a multifractal behavior generated by a multiplicative process of parameter 1 r b the application of the method of the most probable distribution in view of connectivity contributes new inroads toward a general formulation of the geomorphologic unit hydrograph in particular generalizing its width function formulation a quantitative example of multifractal hydrologic response of idealized networks based on peano s construct for which r b r a 4 r l 2 closes the paper

river network fractal geometry and its computer simulation the hierarchical ordinal and statistical models of river networks are proposed their investigation has been carried out on the basis of river networks computer simulation as well as on empirical data analysis the simulated river networks display self similar behavior on small scales the fractal dimension d 1 52 and hurst s exponent h 1 0 and self affine behavior on large scales the lacunary dimension dg 1 71 h 0 58 similar behavior is also qualitatively characteristic for natural river networks for catchment areas from 142 to 63 700 km2 we obtained dg 1 87 and h 0 73 thus in both cases one finds a region of scales with self affine behavior h 1 and with dg 2 proceeding from fractal properties of the river networks the theoretical basis of scaling relationships l a and ae widely used in hydrology are given l and a denote the main river length the total length of the river network and catchment area respectively 1 1 h and e dg 2

an improved algorithm for the packing of unequal circles within a larger containing circle abstract this paper describes an approved algorithm for the problems of unequal circle packing the quasi physical quasi human algorithm first the quasi physical approach for the general packing problems is described in solving the pure problems of unequal circle packing the method is an analogy to the physical model in which a number of smooth cylinders are packed inside a container a quasi human strategy is then proposed to trigger a jump for a stuck object in order to get out of local minima our method has been tested in numerical experiments the computational results are presented showing the merits of the proposed method our algorithm can be thought as an adoptive algorithm of the tabu search

on the complexity of some common geometric location problems given n demand points in the plane the p center problem is to find p supply points anywhere in the plane so as to minimize the maximum distance from a demand point to its respective nearest supply point the p median problem is to minimize the sum of distances from demand points to their respective nearest supply points we prove that the p center and the p median problems relative to both the euclidean and the rectilinear metrics are np hard in fact we prove that it is np hard even to approximate the p center problems sufficiently closely the reductions are from 3 satisfiability

robustness of regional matching scheme over global matching scheme analyzing the effect of concentrated noise on a typical decision making process of a simplified two candidate voting model we have demonstrated that a local approach using a regional matching process is more robust and stable than a direct approach using a global matching process by establishing that the former is capable of accommodating a higher level of noise than the latter before the result of the decision overturns to extend the theory to imagery analysis we pose a conjecture that our conclusion on the robustness of the regional matching processes remains valid not only for the simpler vote counting schemes but also for practically more important decision making schemes in image analysis which involve dimension reducing transforms or other features extraction processes such as principal component analysis or gablor transforms two convincing experimental verifications are provided supporting not only the theory by a white black flag recognition problem on a pixel by pixel basis but also the validity of the conjecture by a facial recognition problem in the presence of localized noise typically represented by clutter or occlusion in imagery

a general fractal model of flow and solute transport in randomly heterogeneous porous media 1 one of the challenges of hydrology is modeling flow and solute transport through media that are not uniformly porous this paper proposes a general fractal model of flow and solute transport in randomly heterogeneous porous media we describe the random field using fractional levy motion flm which more effectively represents a field with a high degree of variability understanding flow and solute transport in the flm field expands the applicability of stochastic theory following the work of v di federico and s p neuman 1997 and v di federico et al 1999 we derive truncated isotropic and anisotropic power variograms for the flm fields the results are analogous to but more general than those of fractional brownian motion fbm v di federico and s p neuman 1997 and v di federico et al 1999 for a random field when the levy index in flm is replaced by a constant of 2 fbm is recovered this study employs first order perturbation analyses of flow and solute transport in two dimensional flm fields for the stationary fbm and flm fields macrodispersion coefficients are compared the plume is found to grow slowest in the flm field but will show highest concentration the proposed fractal model is general in the sense that when the levy index of flm equals 2 the results of flow and solute transport for the commonly used fbm model are recovered when the upper cutoff of the truncated power variogram is close to the lower cutoff the results for the stationary exponential or gaussian model can be well approximated since the proposed general fractal model has broader applications than the stationary and fbm models it simulates flow and solute transport in more different scenarios to yield more accurate modeling results