cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

improved approximation algorithms for the uncapacitated facility location problem we consider the uncapacitated facility location problem in this problem there is a set of locations at which facilities can be built a fixed cost fi is incurred if a facility is opened at location i furthermore there is a set of demand locations to be serviced by the opened facilities if the demand location j is assigned to a facility at location i then there is an associated service cost proportional to the distance between i and j cij the objective is to determine which facilities to open and an assignment of demand points to the opened facilities so as to minimize the total cost we assume that the distance function c is symmetric and satisfies the triangle inequality for this problem we obtain a 1 2 e approximation algorithm where 1 2 e approx 1 736 which is a significant improvement on the previously known approximation guarantees the algorithm works by rounding an optimal fractional solution to a linear programming relaxation our techniques use properties of optimal solutions to the linear program randomized rounding as well as a generalization of the decomposition techniques of shmoys tardos and aardal proceedings of the 29th acm symposium on theory of computing el paso tx 1997 pp 265 274

variance calculations and confidence intervals for estimates of the attributable risk based on logistic models the attributable risk ar defined as ar pr disease pr disease no exposure pr disease measures the proportion of disease risk that is attributable to an exposure recently bruzzi et al 1985 american journal of epidemiology 122 904 914 presented point estimates of ar based on logistic models for case control data to allow for confounding factors and secondary exposures to produce confidence intervals we derived variance estimates for ar under the logistic model and for various designs for sampling controls calculations for discrete exposure and confounding factors require covariances between estimates of the risk parameters of the logistic model and the proportions of cases with given levels of exposure and confounding factors these covariances are estimated from taylor series expansions applied to implicit functions similar calculations for continuous exposures are derived using influence functions simulations indicate that those asymptotic procedures yield reliable variance estimates and confidence intervals with near nominal coverage an example illustrates the usefulness of variance calculations in selecting a logistic model that is neither so simplified as to exhibit systematic lack of fit nor so complicated as to inflate the variance of the estimate of ar

identifying codes and covering problems the identifying code problem for a given graph involves finding a minimum set of vertices whose neighborhoods uniquely overlap at any given graph vertex initially introduced in 1998 this problem has demonstrated its fundamental nature through a wide variety of applications such as fault diagnosis location detection and environmental monitoring in addition to deep connections to information theory superimposed and covering codes and tilings this work establishes efficient reductions between the identifying code problem and the well known set covering problem resulting in a tight hardness of approximation result and novel provably tight polynomial time approximations the main results are also extended to r robust identifying codes and analogous set 2r 1 multicover problems finally empirical support is provided for the effectiveness of the proposed approximations including good constructions for well known topologies such as infinite two dimensional grids

typical approximation performance for maximum coverage problem this study investigated the typical performance of approximation algorithms known as belief propagation the greedy algorithm and linear programming relaxation for maximum coverage problems in sparse biregular random graphs after we used the cavity method for a corresponding hard core lattice gas model results showed that two distinct thresholds of replica symmetry and its breaking exist in the typical performance threshold of belief propagation in the low density region the superiority of three algorithms in terms of a typical performance threshold is obtained by some theoretical analyses although the greedy algorithm and linear programming relaxation have the same approximation ratio in worst case performance their typical performance thresholds are mutually different indicating the importance of typical performance results of numerical simulations validate the theoretical analyses and imply further mutual relations of approximation algorithms

a threshold of ln n for approximating set cover given a collection f of subsets of s 1 n setcover is the problem of selecting as few as possiblesubsets from f such that their union covers s and maxk cover is the problem of selecting k subsets from f such that their union has maximum cardinality both these problems arenp hard we prove that 1 o 1 ln n is a threshold below which setcover cannot be approximated efficiently unless np has slightlysuperpolynomial time algorithms this closes the gap up to low orderterms between the ratio of approximation achievable by the greedyalogorithm which is 1 o 1 lnn and provious results of lund and yanakakis that showed hardness ofapproximation within a ratio of log 2 n 2s0 72 ln n for max k cover we show an approximationthreshold of 1 1 e up tolow order terms under assumption that p np

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

a best possible heuristic for the k center problem in this paper we present a 2 approximation algorithm for the k center problem with triangle inequality this result is best possible since for any 2 the existence of approximation algorithm would imply that p np it should be noted that no approximation algorithm for any constant has been reported to date linear programming duality theory provides interesting insight to the problem and enables us to derive in o e log e time a solution with value no more than twice the k center optimal value a by product of the analysis is an o e algorithm that identifies a dominating set in g2 the square of a graph g the size of which is no larger than the size of the minimum dominating set in the graph g the key combinatorial object used is called a strong stable set and we prove the np completeness of the corresponding decision problem

on the hardness of approximating minimization problems we prove results indicating that it is hard to compute efficiently good approximate solutions to the graph coloring set covering and other related minimization problems specifically there is an e 0 such that graph coloring cannot be approximated with ratio n e unless p np set covering cannot be approximated with ratio c log n for any c 1 4 unless np is contained in dtime n poly log n similar results follow for related problems such as clique cover fractional chromatic number dominating set and others

on estimation of time dependent attributable fraction from population based case control studies summary population attributable fraction paf is widely used to quantify the disease burden associated with a modifiable exposure in a population it has been extended to a time varying measure that provides additional information on when and how the exposure s impact varies over time for cohort studies however there is no estimation procedure for paf using data that are collected from population based case control studies which because of time and cost efficiency are commonly used for studying genetic and environmental risk factors of disease incidences in this article we show that time varying paf is identifiable from a case control study and develop a novel estimator of paf our estimator combines odds ratio estimates from logistic regression models and density estimates of the risk factor distribution conditional on failure times in cases from a kernel smoother the proposed estimator is shown to be consistent and asymptotically normal with asymptotic variance that can be estimated empirically from the data simulation studies demonstrate that the proposed estimator performs well in finite sample sizes finally the method is illustrated by a population based case control study of colorectal cancer

finding minimum weight connected dominating set in stochastic graph based on learning automata finding the minimum weight connected dominating set mcds in an arbitrary graph is an np hard problem and several heuristics and approximation methods have been proposed to solve it forwarding the messages along the virtual backbone induced by the connected dominating set cds significantly reduces the routing overhead as well as the power consumption by reducing the routing nodes to the backbone nodes this paper first defines the stochastic mcds problem where the probability distribution function pdf of the random weight associated with the graph vertices is unknown then it presents several learning automata based algorithms algorithms 1 6 to solve the stochastic mcds problem taking advantage of learning automata the proposed algorithms significantly reduce the number of samples that must be taken from the graph to construct the mcds it is proved that by the proper choice of the learning rate the probability of finding the mcds is close enough to unity the standard sampling method ssm is the baseline with which we compare the performance of the proposed algorithms experimental results show that algorithm 6 significantly outperforms the ssm and the other proposed algorithms in terms of the sampling rate

toward synchronization in networks with nonlinear dynamics a submodular optimization framework synchronization underlies phenomena including memory and perception in the brain coordinated motion of animal flocks and stability of the power grid these synchronization phenomena are often modeled through networks of phase coupled oscillating nodes heterogeneity in the node dynamics however may prevent such networks from achieving the required level of synchronization in order to guarantee synchronization external inputs can be used to pin a subset of nodes to a reference frequency while the remaining nodes are steered toward synchronization via local coupling in this paper we present a submodular optimization framework for selecting a set of nodes to act as external inputs in order to achieve synchronization from a desired set of initial states we derive threshold based sufficient conditions for synchronization and then prove that these conditions are equivalent to constraints on monotone submodular functions over partition matroids based on this connection we map the sufficient conditions for synchronization to constraints on submodular functions leading to efficient algorithms with provable optimality bounds for selecting input nodes we illustrate our approach via numerical studies of synchronization in power systems

an optimal time algorithm for minimum linear arrangement of chord graphs a linear arrangement f of an undirected graph g v e with v n nodes is a bijective function f v 0 n 1 the cost function is cost g f email protected u v e f u email protected v and opt g min fcost g f the problem of finding opt g is called minimum linear arrangement minla the minimum linear arrangement is an np hard problem in general but there are some classes of graphs optimally solvable in polynomial time in this paper we show that the label of each node equals to the reverse of binary representation of its id in the optimal arrangement then we design an o n algorithm to solve the minimum linear arrangement problem of chord graphs

self improved gaps almost everywhere for the agnostic approximation of monomials given a learning sample we focus on the hardness of finding monomials having low error inside the interval bounded below by the smallest error achieved by a monomial the best rule and bounded above by the error of the default class the poorest rule it is well known that when its lower bound is zero it is an easy task to find in linear time a monomial with zero error what we prove is that when this bound is not zero regardless of the location of the default class in 0 1 2 it becomes a huge complexity burden to beat significantly the default class in fact under some complexity theoretical assumptions it may already be hard to beat the trivial approximation ratios even when relaxing the time complexity constraint to be quasi polynomial or sub exponential our results also hold with uniform weights over the examples

approximation algorithms for solving the constrained arc routing problem in mixed graphs abstract given a mixed graph g with vertex set v let e and a denote the sets of edges and arcs respectively we use q and z to denote the sets of positive rational numbers and positive integers respectively for any connected mixed graph g v e a w l u with a length function w e a q and two integer functions l u e a z satisfying l e u e for each e e a we are asked to determine a minimum length tour t traversing each e e a at least l e and at most u e times this new constrained arc routing problem generalizes the mixed chinese postman problem let n v and m e a denote the number of vertices and edges including arcs respectively using network flow techniques we design a 1 1 l 0 approximation algorithm in time o n 2 m 3 log n to solve this constrained arc routing problem such that l e u e holds for each edge e e l e u e holds for each arc e a and l 0 min l e e e in addition we present two optimal combinatorial algorithms in times o n 3 and o nm 2 log n to solve this problem for the cases a and e respectively

intuitionistic fuzzy hypergraphs with applications hypergraphs are considered a useful tool for modeling system architectures and data structures and to represent a partition covering and clustering in the area of circuit design in this paper we apply the concept of intuitionistic fuzzy set theory to generalize results concerning hypergraphs for each intuitionistic fuzzy structure defined we use cut level sets to define an associated sequence of crisp structures we determine what properties of the sequence of crisp structures characterize a given property of the intuitionistic fuzzy structure we also present applications of intuitionistic fuzzy hypergraphs

approximation algorithms for inventory problems with submodular or routing costs we consider the following two deterministic inventory optimization problems with non stationary demands submodular joint replenishment problem this involves multiple item types and a single retailer who faces demands over a finite planning horizon of t periods in each time period any subset of item types can be ordered incurring a joint ordering cost which is submodular moreover items can be held in inventory while incurring a holding cost the objective is to find a sequence of orders that satisfies all demands and minimizes the total ordering and holding costs inventory routing problem this involves a single depot that stocks items and multiple retailer locations facing demands over a finite planning horizon of t periods in each time period any subset of locations can be visited using a vehicle originating from the depot there is also cost incurred for holding items at any retailer the objective here is to satisfy all demands while minimizing the sum of routing and holding costs we present a unified approach that yields mathcal o left frac log t log log t right ologtloglogt factor approximation algorithms for both problems when the holding costs are polynomial functions a special case is the classic linear holding cost model wherein this is the first sub logarithmic approximation ratio for either problem

inapproximability of dominating set on power law graphs we prove the first logarithmic lower bounds for the approximability of the minimum dominating set problem for the case of connected power law graphs for being a size parameter and the power law exponent we give also a best up to now upper approximation bound for this problem in the case of the parameters 2 we develop also a new functional method for proving lower approximation bounds and display a sharp approximation phase transition area between approximability and inapproximability of the underlying problems our results depend on a method which could be also of independent interest

rainbow domination numbers of generalized petersen graphs abstract domination and its variations in graphs are natural models for the location problems in operations research in this paper we investigate the rainbow domination number of graphs which was introduced by bresar henning and rall given a graph g and a positive integer t a t rainbow dominating function of g is a function f from vertex set to the set of all subsets of 1 2 t such that for any vertex v with f v we have u n v f u 1 2 t the t rainbow domination problem is to determine the t rainbow domination number rt g of g that is the minimum value of v v g f v where f runs over all t rainbow dominating functions of g the domination number and its variations of generalized petersen graphs p n k are widely investigated the exact values of r2 p n 1 and r3 p n 1 are already determined in 11 12 in this paper we determine the exact values of rt p n 1 for any t 8 and t 4 and prove that r t p 2 k k 4 k for t 6 where p 2k k is a special graph

approximation algorithms for wavelet transform coding of data streams this paper addresses the problem of finding a b term wavelet representation of a given discrete function fepsirn whose distance from is minimized the problem is well understood when we seek to minimize the euclidean distance between f and its representation the first known algorithms for finding provably approximate representations minimizing general lp distances including linfin under a wide variety of compactly supported wavelet bases are presented in this paper for the haar basis a polynomial time approximation scheme is demonstrated these algorithms are applicable in the one pass sublinear space data stream model of computation they generalize naturally to multiple dimensions and weighted norms a universal representation that provides a provable approximation guarantee under all mu norms simultaneously and the first approximation algorithms for bit budget versions of the problem known as adaptive quantization are also presented further it is shown that the algorithms presented here can be used to select a basis from a tree structured dictionary of bases and find a b term representation of the given function that provably approximates its best dictionary basis representation

dynamic algorithms via the primal dual method abstract we develop a dynamic version of the primal dual method for optimization problems and apply it to obtain the following results 1 for the dynamic set cover problem we maintain an o f 2 approximately optimal solution in o f log m n amortized update time where f is the maximum frequency of an element n is the number of sets and m is the maximum number of elements in the universe at any point in time 2 for the dynamic b matching problem we maintain an o 1 approximately optimal solution in o log 3 n amortized update time where n is the number of nodes in the graph

the k tuple twin domination in generalized de bruijn and kautz networks given a digraph network g v a a vertex u in g is said to out dominate itself and all vertices v such that the arc u v a similarly u in dominates both itself and all vertices w such that the arc w u a a set d of vertices of g is a k tuple twin dominating set if every vertex of g is out dominated and in dominated by at least k vertices in d respectively the k tuple twin domination problem is to determine a minimum k tuple twin dominating set for a digraph in this paper we investigate the k tuple twin domination problem in generalized de bruijn networks g b n d and generalized kautz g k n d networks when d divides n we provide construction methods for constructing minimum k tuple twin dominating sets in these networks these results generalize previous results given by araki t araki the k tuple twin domination in de bruijn and kautz digraphs discrete mathematics 308 2008 6406 6413 for de bruijn and kautz networks

design to minimize diameter on building block network this paper proposes a simple algorithm for the graph design of small diameter networks for given nodes n and degree d this algorithm can be used to construct a directed graph with diameter logd n which is at most one larger than the lower bound logd n d 1 1 1 its average distance is also close to the lower bound the algorithm can be used to construct a directed graph with smaller diameter compared with any other conventional methods when n is larger

tight approximation algorithms for maximum separable assignment problems a separable assignment problem sap is defined by a set of bins and a set of items to pack in each bin a value fij for assigning item j to bin i and a separate packing constraint for each bin i e for each bin a family of subsets of items that fit in to that bin the goal is to pack items into bins to maximize the aggregate value this class of problems includes the maximum generalized assignment problem gap 1 and a distributed caching problem dcp described in this paper given a approximation algorithm for finding the highest value packing of a single bin we give a polynomial time lp rounding based 1 1 e approximation algorithm a simple polynomial time local search 1 e approximation algorithm for any e 0 therefore for all examples of sap that admit an approximation scheme for the single bin problem we obtain an lp based algorithm with 1 1 e e approximation and a local search algorithm with e approximation guarantee furthermore for cases in which the subproblem admits a fully polynomial approximation scheme such as for gap the lp based algorithm analysis can be strengthened to give a guarantee of 1 1 e the best previously known approximation algorithm for gap is a approximation by shmoys and tardos and chekuri and khanna our lp algorithm is based on rounding a new linear programming relaxation with a provably better integrality gap to complement these results we show that sap and dcp cannot be approximated within a factor better than 1 1 e unless np dtime no log log n even if there exists a polynomial time exact algorithm for the single bin problem we extend the 1 1 e approximation algorithm to a constant factor approximation algorithms for a nonseparable assignment problem with applications in maximizing revenue for budget constrained combinatorial auctions and the adwords assignment problem we generalize the local search algorithm to yield a e approximation algorithm for the maximum k median problem with hard capacities

almost tight bounds and existence theorems for single commodity confluent flows a flow of a commodity is said to be confluent if at any node all the flow of the commodity leaves along a single edge in this article we study single commodity confluent flow problems where we need to route given node demands to a single destination using a confluent flow single and multi commodity confluent flows arise in a variety of application areas most notably in networking in fact most flows in the internet are multi commodity confluent flows since internet routing is destination based we present near tight approximation algorithms hardness results and existence theorems for minimizing congestion in single commodity confluent flows the maximum edge congestion of a single commodity confluent flow occurs at one of the incoming edges of the destination therefore finding a minimum congestion confluent flow is equivalent to the following problem given a directed graph g with k sinks and non negative demands on all the nodes of g determine a confluent flow that routes every node demand to some sink such that the maximum congestion at a sink is minimized the main result of this article is a polynomial time algorithm for determining a confluent flow with congestion at most 1 p ln k in g if g admits a splittable flow with congestion at most 1 we complement this result in two directions first we present a graph g that admits a splittable flow with congestion at most 1 yet no confluent flow with congestion smaller than hk the kth harmonic number thus establishing tight upper and lower bounds to within an additive constant less than 1 second we show that it is np hard to approximate the congestion of an optimal confluent flow to within a factor of log2k 2 thus resolving the polynomial time approximability to within a multiplicative constant we also consider a demand maximization version of the problem we show that if g admits a splittable flow of congestion at most 1 then a variant of the congestion minimization algorithm yields a confluent flow in g with congestion at most 1 that satisfies 1 3 fraction of total demand we show that the gap between confluent flows and splittable flows is much smaller if the underlying graph is k connected in particular we prove that k connected graphs with k sinks admit confluent flows of congestion less than c p dmax where c is the congestion of the best splittable flow and dmax is the maximum demand of any node in g the proof of this existence theorem is non constructive and relies on topological techniques introduced by lovasz

dominating problems in swapped networks swapped networks sns are a family of two level interconnection networks suitable for constructing large parallel and distributed systems in this paper the minimum dominating set mds problem and the minimum connected dominating set mcds problem in sns are investigated based on the connectivity rule of sns we prove the two problems in sns are np hard and present two efficient algorithms for building dominating sets and connected dominating sets in sns the proposed algorithms use as input a given connected dominating set of the factor network and yield a good approximation of an mds or mcds for the sn provided that the input is a good approximation of an mds or mcds for the factor network we also derive several non trivial bounds on the connected domination parameters of sns we believe this work is of theoretical interest in graph theory since sns form a family of graphs it may also motivate further research on dominating problems in sns with their potential applications

on the k tuple domination of generalized de brujin and kautz digraphs a vertex u in a digraph g v a is said to dominate itself and vertices v such that u v a for a positive integer k a k tuple dominating set of g is a subset d of vertices such that every vertex in g is dominated by at least k vertices in d the k tuple domination number of g is the minimum cardinality of a k tuple dominating set of g this paper deals with the k tuple domination problem on generalized de bruijn and kautz digraphs we establish bounds on the k tuple domination number for the generalized de bruijn and kautz digraphs and we obtain some conditions for the k tuple domination number attaining the bounds

a linear kernel for a planar connected dominating set we provide polynomial time data reduction rules for connected dominating set on planar graphs and analyze these to obtain a linear kernel for the planar connected dominating set problem to obtain the desired kernel we introduce a method that we call reduce or refine our kernelization algorithm analyzes the input graph and either finds an appropriate reduction rule that can be applied or zooms in on a region of the graph which is more amenable to reduction we find this method of independent interest and believe that it will be useful for obtaining linear kernels for other problems on planar graphs

interactive proofs and the hardness of approximating cliques the contribution of this paper is two fold first a connection is established between approximating the size of the largest clique in a graph and multi prover interactive proofs second an efficient multi prover interactive proof for np languages is constructed where the verifier uses very few random bits and communication bits last the connection between cliques and efficient multi prover interaction proofs is shown to yield hardness results on the complexity of approximating the size of the largest clique in a graph of independent interest is our proof of correctness for the multilinearity test of functions

thresholded covering algorithms for robust and max min optimization in a two stage robust covering problem one of several possible scenarios will appear tomorrow and require to be covered but costs are higher tomorrow than today what should you anticipatorily buy today so that the worst case cost summed over both days is minimized we consider the k k robust model where the possible scenarios tomorrow are given by all demand subsets of size k k in this paper we give the following simple and intuitive template for k k robust covering problems having built some anticipatory solution if there exists a single demand whose augmentation cost is larger than some threshold augment the anticipatory solution to cover this demand as well and repeat we show that this template gives good approximation algorithms for k k robust versions of many standard covering problems set cover steiner tree steiner forest minimum cut and multicut our k k robust approximation ratios nearly match the best bounds known for their deterministic counterparts the main technical contribution lies in proving certain net type properties for these covering problems which are based on dual rounding and primal dual ideas these properties might be of some independent interest as a by product of our techniques we also get algorithms for max min problems of the form given a covering problem instance which k k of the elements are costliest to cover for the problems mentioned above we show that their k k max min versions have performance guarantees similar to those for the k k robust problems

on rainbow domination numbers of graphs given a graph g and a set of t colors assume that we assign an arbitrary subset of these colors to each vertex of g if we require that each vertex to which an empty set is assigned has in its neighborhood all t colors then this assignment is called a t rainbow dominating function of the graph g the corresponding invariant c r t g which is the minimum sum of numbers of assigned colors over all vertices of g is called the t rainbow domination number of g in this paper bounds for the t rainbow domination number of an arbitrary graph for an arbitrary positive integer t are given the 3 rainbow domination numbers of several classes of graphs such as paths cycles and the generalized petersen graphs p n k are investigated the 3 rainbow domination number of p n 1 is determined and the upper bounds for p n 2 and p n 3 are provided by computer search we obtain that the upper bounds for p n 2 match their exact values for n 17

there is no binary 35 10 13 code it is shown that the generator matrix of a putative linear binary code 36 10 14 contains the generator matrix of a 32 7 14 or a 33 8 14 binary linear code in a first step all nonisomorphic 32 7 14 and 33 8 14 binary codes are enumerated then it is shown that none of these codes yields a 35 10 13 linear binary code

there is no binary 25 8 10 code the existence of a binary 25 8 10 code is considered it is shown that such a code must have a generator matrix of a specific form however all generator matrices of this form were tested and none generated a 25 8 10 code thus such a code does not exist

the implicit hitting set approach to solve combinatorial optimization problems with an application to multigenome alignment we develop a novel framework the implicit hitting set approach for solving a class of combinatorial optimization problems the explicit hitting set problem is as follows given a set u and a family s of subsets of u find a minimum cardinality set that intersects hits every set in s in the implicit hitting set problem ihsp the family of subsets s is not explicitly listed its size is generally exponential in terms of the size of u instead it is given via a polynomial time oracle that verifies if a given set h is a hitting set or returns a set in s that is not hit by h many np hard problems can be straightforwardly formulated as implicit hitting set problems we show that the implicit hitting set approach is valuable in developing exact and heuristic algorithms for solving this class of combinatorial optimization problems specifically we provide a generic algorithmic strategy which combines efficient heuristics and exact methods to solve any ihsp given an instance of an ihsp the propose

dominating sets in directed graphs we consider the problem of incrementally computing a minimal dominating set of a directed graph after the insertion or deletion of a set of arcs earlier results have either focused on the study of the properties that minimum not minimal dominating sets preserved or lacked to investigate which update affects a minimal dominating set and in what ways in this paper we first show how to incrementally compute a minimal dominating set on arc insertions we then reduce the case of computing a minimal dominating set on arc deletions to the case of insertions some properties on minimal dominating sets are provided to support the incremental strategy lastly we give a new bound on the size of minimum dominating sets based on those results

strong lp formulations for scheduling splittable jobs on unrelated machines a natural extension of the makespan minimization problem on unrelated machines is to allow jobs to be partially processed by different machines while incurring an arbitrary setup time in this paper we present increasingly stronger lp relaxations for this problem and their implications on the approximability of the problem first we show that the straightforward lp extending the approach for the original problem has an integrality gap of 3 and yields an approximation algorithm of the same factor by applying a lift and project procedure we are able to improve both the integrality gap and the implied approximation factor to 1 phi 1 where phi is the golden ratio since this bound remains tight for the seemingly stronger machine configuration lp we propose a new job configuration lp that is based on an infinite continuum of fractional assignments of each job to the machines we prove that this lp has a finite representation and can be solved in polynomial time up to any accuracy interestingly we show that our problem cannot be approximated within a factor better than frac e e 1 approx 1 582 hbox unless mathcal p mathcal np ee 1 1 582 unlessp np which is larger than the inapproximability bound of 1 5 for the original problem

non deterministic polynomial optimization problems and their approximations abstract a unified and general framework for the study of nondeterministic polynomial optimization problems npop is presented and some properties of npop s are investigated a characterization of npop s with regard to their approximability properties is given by proving necessary and sufficient conditions for two approximability schemes known approximability results are shown to fit within the general frame developed in the paper finally npop s are classified and studied with regard to the possibility or impossibility of reducing certain types of npop s to other types in a sense specified in the text

algebraic methods for interactive proof systems a new algebraic technique for the construction of interactive proof systems is presented our technique is used to prove that every language in the polynomial time hierarchy has an interactive proof system this technique played a pivotal role in the recent proofs that ip pspace 28 and that mip nexp 4

proof verification and the hardness of approximation problems we show that every language in np has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof if a string is in the language then there exists a proof such that the verifier accepts with probability 1 i e for every choice of its random string for strings not in the language the verifier rejects every provided proof with probability at least 1 2 our result builds upon and improves a recent result of arora and safra 1998 whose verifiers examine a nonconstant number of bits in the proof though this number is a very slowly growing function of the input length as a consequence we prove that no max snp hard problem has a polynomial time approximation scheme unless np p the class max snp was defined by papadimitriou and yannakakis 1991 and hard problems for this class include vertex cover maximum satisfiability maximum cut metric tsp steiner trees and shortest superstring we also improve upon the clique hardness results of feige et al 1996 and arora and safra 1998 and show that there exists a positive e such that approximating the maximum clique size in an n vertex graph to within a factor of n e is np hard

approximating the spanning star forest problem and its application to genomic sequence alignment this paper studies the algorithmic issues of the spanning star forest problem we prove the following results 1 there is a polynomial time approximation scheme for planar graphs 2 there is a polynomial time frac 3 5 approximation algorithm for graphs 3 it is np hard to approximate the problem within ratio frac 259 260 epsilon for graphs 4 there is a linear time algorithm to compute the maximum star forest of a weighted tree 5 there is a polynomial time frac 1 2 approximation algorithm for weighted graphs we also show how to apply this spanning star forest model to aligning multiple genomic sequences over a tandem duplication region

fast approximation algorithms for the one warehouse multi retailer problem under general cost structures and capacity constraints we consider a well studied multi echelon deterministic inventory control problem known in the literature as the one warehouse multi retailer owmr problem we propose a simple and fast 2 approximation algorithm for this np hard problem by recombining the solutions of single echelon relaxations at the warehouse and at the retailers we then show that our approach remains valid under quite general assumptions on the cost structures and under capacity constraints at some retailers in particular we present the first approximation algorithms for the owmr problem with nonlinear holding costs truckload discount on procurement costs or with capacity constraints at some retailers in all cases the procedure is purely combinatorial and can be implemented to run in low polynomial time

some optimal inapproximability results we prove optimal up to an arbitrary e 0 inapproximability results for max e k sat for k 3 maximizing the number of satisfied linear equations in an over determined system of linear equations modulo a prime p and set splitting as a consequence of these results we get improved lower bounds for the efficient approximability of many optimization problems studied previously in particular for max e2 sat max cut max di cut and vertex cover

semiparametric analysis of the additive risk model in contrast to the proportional hazards model the additive risk model specifies that the hazard function associated with a set of possibly time varying covariates is the sum of rather than the product of the baseline hazard function and the regression function of covariates this formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model and is more plausible than the latter for many applications in the present paper simple procedures with high efficiencies are developed for making inference about the regression parameters under the additive risk model with an unspecified baseline hazard function

construction of strongly connected dominating sets in asymmetric multihop wireless networks consider an asymmetric wireless network represented by a digraph g v e a subset of vertices u is called a strongly connected dominating set scds if the subgraph induced by u is strongly connected and every vertex not in u has both an in neighbor in u and an out neighbor in u scds plays an important role of the virtual backbone in asymmetric wireless networks motivated by the construction of a small virtual backbone we study the problem minimum scds which seeks a smallest scds of a digraph for any constant 0 r 1 there is no polynomial time rlnn approximation for minimum scds unless np dtime n o l n n where n is the number of nodes however none of the polynomial time heuristics for minimum scds proposed in the literature are logarithmic approximations in this paper we present a polynomial time 3h n 1 1 approximation algorithm for minimum scds where h is the harmonic function the approximation ratio of this algorithm is thus within a factor of 3 from the best possible approximation ratio achievable by any polynomial time algorithm

on reliability of the folded hypercubes in this paper we explore the 2 extra connectivity and 2 extra edge connectivity of the folded hypercube fq n we show that k 2 fq n 3n 2 for n 8 and l 2 fq n 3n 1 for n 5 that is for n 8 resp n 5 at least 3n 2 vertices resp 3n 1 edges of fq n are removed to get a disconnected graph that contains no isolated vertices resp edges when the folded hypercube is used to model the topological structure of a large scale parallel processing system these results can provide more accurate measurements for reliability and fault tolerance of the system

algorithm and hardness results on neighborhood total domination in graphs abstract a set d v of a graph g v e is called a neighborhood total dominating set of g if d is a dominating set and the subgraph of g induced by the open neighborhood of d has no isolated vertex given a graph g min ntds is the problem of finding a neighborhood total dominating set of g of minimum cardinality the decision version of min ntds is known to be np complete for bipartite graphs and chordal graphs in this paper we extend this np completeness result to undirected path graphs chordal bipartite graphs and planar graphs we also present a linear time algorithm for computing a minimum neighborhood total dominating set in proper interval graphs we show that for a given graph g v e min ntds cannot be approximated within a factor of 1 e log v unless np dtime v o log log v and can be approximated within a factor of o log where is the maximum degree of the graph g finally we show that min ntds is apx complete for graphs of degree at most 3

on the complexity of minimizing interference in ad hoc and sensor networks one of the most critical factors for lifetime and operability of ad hoc and sensor networks is the limited amount of available energy to this respect minimizing the interference in the network i e the overlapping of signals at network nodes has certainly a positive effect because it induces a reduction of the number of conflicting transmissions and then results in an overall saving of energy consumption along this direction in this paper we study the computational hardness of several interference minimization problems which arise while supporting some classic network communication patterns such as broadcasting one to all gossiping all to all and symmetric gossiping symmetric all to all in particular concerning the non approximability results we prove that for any of the above communication patterns the prominent problem of minimizing the maximum interference experienced by any node in the network is hard to approximate within better than a logarithmic factor unless np admits slightly superpolynomial time algorithms on a positive side we show that any approximation algorithm for the problem of minimizing the total transmission power assigned to the nodes in order to guarantee any of the above communication patterns can be transformed by maintaining the same performance ratio into an approximation algorithm for the problem of minimizing the total interference experienced by all the nodes in the network

inapproximability results for equations over infinite groups an equation over a group g is an expression of form w 1 w k 1 g where each w i is either a variable an inverted variable or a group constant and 1 g denotes the identity element such an equation is satisfiable if there is a setting of the variables to values in g such that the equality is realized engebretsen et al 2002 10 in this paper we study the problem of simultaneously satisfying a family of equations over an infinite group g let eq g k denote the problem of determining the maximum number of simultaneously satisfiable equations in which each equation has occurrences of exactly k different variables when g is an infinite cyclic group we show that it is np hard to approximate eq 1 g 3 to within 48 47 e where eq 1 g 3 denotes the special case of eq g 3 in which a variable may only appear once in each equation it is np hard to approximate eq 1 g 2 to within 30 29 e it is np hard to approximate the maximum number of simultaneously satisfiable equations of degree at most d to within d e for any e for any k 4 it is np hard to approximate eq g k within any constant factor these results extend hastad s results hastad 2001 17 and results of engebretsen et al 2002 10 who established the inapproximability results for equations over finite abelian groups and any finite groups respectively

bounding the payment of approximate truthful mechanisms in a stacs 2003 paper talwar analyzes the overpayment the vcg mechanism incurs for ensuring truthfulness in auctions among other results he studies k set cover given a universe u and a collection of sets s 1 s 2 s m each having a cost c s i and at most k elements of u find a minimum cost subcollection a cover whose union equals u and shows that the payment of the vcg mechanism is at most k c opt where opt is the best cover disjoint from the optimum cover opt the vcg mechanism requires finding an optimum cover for k 3 k set cover is known to be np hard and thus truthful mechanisms based on approximation algorithms are desirable we show that the payment incurred by two mechanisms based on approximation algorithms including the greedy algorithm is bounded by k 1 c opt k c opt the same approximation algorithms have payment bounded by k c opt c opt when applied to more general set systems which include k polymatroid cover a problem related to steiner tree computations if q is such that an element in a k set cover instance appears in at most q sets we show that the total payment based on our algorithms is bounded by q k 2 times the total payment of the vcg mechanism

a constant approximation algorithm for the one warehouse multiretailer problem deterministic inventory theory provides streamlined optimization models that attempt to capture trade offs in managing the flow of goods through a supply chain we will consider two well studied deterministic inventory models called the one warehouse multiretailer owmr problem and its special case the joint replenishment problem jrp and give approximation algorithms with worst case performance guarantees that is for each instance of the problem our algorithm produces a solution with cost that is guaranteed to be at most 1 8 times the optimal cost this is called a 1 8 approximation algorithm our results are based on an lp rounding approach we provide the first constant approximation algorithm for the owmr problem and improve the previous results for the jrp

hardness of approximation for vertex connectivity network design problems in the survivable network design problem sndp the goal is to find a minimum cost spanning subgraph satisfying certain connectivity requirements we study the vertex connectivity variant of sndp in which the input specifies for each pair of vertices a required number of vertex disjoint paths connecting them we give the first strong lower bound on the approximability of sndp showing that the problem admits no efficient 2 log 1 epsilon n ratio approximation for any fixed epsilon 0 unless np subseteq dtime n polylog n we show hardness of approximation results for some important special cases of sndp and we exhibit the first lower bound on the approximability of the related classical np hard problem of augmenting the connectivity of a graph using edges from a given set

the local lemma is asymptotically tight for sat the local lemma is a fundamental tool of probabilistic combinatorics and theoretical computer science yet there are hardly any natural problems known where it provides an asymptotically tight answer the main theme of our article is to identify several of these problems among them a couple of widely studied extremal functions related to certain restricted versions of the k sat problem where the local lemma does give essentially optimal answers as our main contribution we construct unsatisfiable k cnf formulas where every clause has k distinct literals and every variable appears in at most 2 e o 1 2k k clauses the lopsided local lemma applied with an assignment of random values according to counterintuitive probabilities shows that this is asymptotically best possible the determination of this extremal function is particularly important as it represents the value where the corresponding k sat problem exhibits a complexity hardness jump from having every instance being a yes instance it becomes np hard just by allowing each variable to occur in one more clause the construction of our unsatisfiable cnf formulas is based on the binary tree approach of gebauer 2012 and thus the constructed formulas are in the class mu 1 of minimal unsatisfiable formulas having one more clause than variables the main novelty of our approach here comes in setting up an appropriate continuous approximation of the problem this leads us to a differential equation the solution of which we are able to estimate the asymptotically optimal binary trees are then obtained through a discretization of this solution the importance of the binary trees constructed is also underlined by their appearance in many other scenarios in particular they give asymptotically precise answers for seemingly unrelated problems like the european tenure game introduced by doerr 2004 and a search problem allowing a limited number of consecutive lies as yet another consequence we slightly improve the best known bounds on the maximum degree and maximum edge degree of a k uniform maker s win hypergraph in the neighborhood conjecture of beck

estimation of exposure attributable fractions from time series a simulation study burden analysis in public health often involves the estimation of exposure attributable fractions from observed time series when the entire population is exposed the association between the exposure and outcome must be carefully modelled before the attributable fractions can be estimated this article derives asymptotic convergences for the estimation of attributable fractions for commonly used time series models armax poisson negative binomial and serfling using for the most part the delta method for the poisson regression the estimation of the attributable fraction is achieved by a monte carlo algorithm taking into account both an estimation and a prediction error a simulation study compares these estimations in the case of an epidemic exposure and highlights the importance of thorough analysis of the data when the outcome is generated under an additive model the additive models are satisfactory and the multiplicative models are poor and vice versa however the serfling model performs poorly in all cases of note a misspecification in the form or delay of the association between the exposure and the outcome leads to mediocre estimation of the attributable fraction an application to the fraction of french outpatient antibiotic use attributable to influenza between 2003 and 2010 illustrates the asymptotic convergences this study suggests that the serfling model should be avoided when estimating attributable fractions while the model of choice should be selected after careful investigation of the association between the exposure and outcome

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

polynomial time approximation schemes for maximizing gross substitutes utility under budget constraints we consider the maximization of a gross substitutes utility function under budget constraints this problem naturally arises in applications such as exchange economies in mathematical economics and combinatorial auctions in algorithmic game theory we show that this problem admits a polynomial time approximation scheme ptas more generally we present a ptas for maximizing a discrete concave function called an m concave function under budget constraints our ptas is based on rounding an optimal solution of a continuous relaxation problem which is shown to be solvable in polynomial time by the ellipsoid method we also consider the maximization of the sum of two m concave functions under a single budget constraint this problem is a generalization of the budgeted max weight matroid intersection problem to the one with certain nonlinear objective functions we show that this problem also admits a ptas

connectivity of regular directed graphs with small diameters this paper clarifies the relation between the diameter k and the edge or node connectivity ce or c of digraphs the following two inequalities are derived where n is the number of nodes d is the maximum degree and d is the minimum degree

free bits pcps and nonapproximability towards tight results this paper continues the investigation of the connection between probabilistically checkable proofs pcps and the approximability of np optimization problems the emphasis is on proving tight nonapproximability results via consideration of measures such as the free bit complexity and the amortized free bit complexity of proof systems the first part of the paper presents a collection of new proof systems based on a new error correcting code called the long code we provide a proof system that has amortized free bit complexity of 2 epsilon implying that approximating maxclique within n frac13 e and approximating the chromatic number within n frac15 e are hard assuming np neq corp for any e 0 we also derive the first explicit and reasonable constant hardness factors for min vertex cover msat 2 and max cut and we improve the hardness factor for msat 3 we note that our nonapproximability factors for maxsnp problems are appreciably close to the values known to be achievable by polynomial time algorithms finally we note a general approach to the derivation of strong nonapproximability results under which the problem reduces to the construction of certain gadgets the increasing strength of nonapproximability results obtained via the pcp connection motivates us to ask how far this can go and whether pcps are inherent in any way the second part of the paper addresses this the main result is a reversal of the connection due to feige et al fglss connection j acm 43 1996 pp 268 292 where the latter had shown how to translate proof systems for np into np hardness of approximation results for maxclique we show how any np hardness of approximation result for maxclique yields a proof system for np roughly our result says that for any constant f if maxclique is np hard to approximate within n 1 1 f then np subseteq overline fpcp log f the latter being the class of languages possessing proofs of logarithmic randomness and amortized free bit complexity f this suggests that pcps are inherent to obtaining nonapproximability results furthermore the tight relation suggests that reducing the amortized free bit complexity is necessary for improving the nonapproximability results for maxclique the third part of our paper initiates a systematic investigation of the properties of pcp and fpcp free pcp as a function of the following various parameters randomness query complexity free bit complexity amortized free bit complexity proof size etc we are particularly interested in triviality results which indicate which classes are not powerful enough to capture np we also distill the role of randomized reductions in this area and provide a variety of useful transformations between proof checking complexity classes

maximizing a monotone submodular function subject to a matroid constraint let f 2 x rightarrow cal r be a monotone submodular set function and let x cal i be a matroid we consider the problem rm max s in cal i f s it is known that the greedy algorithm yields a 1 2 approximation m l fisher g l nemhauser and l a wolsey math programming stud no 8 1978 pp 73 87 for this problem for certain special cases e g rm max s leq k f s the greedy algorithm yields a 1 1 e approximation it is known that this is optimal both in the value oracle model where the only access to f is through a black box returning f s for a given set s g l nemhauser and l a wolsey math oper res 3 1978 pp 177 188 and for explicitly posed instances assuming p neq np u feige j acm 45 1998 pp 634 652 in this paper we provide a randomized 1 1 e approximation for any monotone submodular function and an arbitrary matroid the algorithm works in the value oracle model our main tools are a variant of the pipage rounding technique of ageev and sviridenko j combin optim 8 2004 pp 307 328 and a continuous greedy process that may be of independent interest as a special case our algorithm implies an optimal approximation for the submodular welfare problem in the value oracle model j vondrak proceedings of the 38 th acm symposium on theory of computing 2008 pp 67 74 as a second application we show that the generalized assignment problem gap is also a special case although the reduction requires x to be exponential in the original problem size we are able to achieve a 1 1 e o 1 approximation for gap simplifying previously known algorithms additionally the reduction enables us to obtain approximation algorithms for variants of gap with more general constraints

bipolar fuzzy graphs in this paper we introduce the notion of bipolar fuzzy graphs describe various methods of their construction discuss the concept of isomorphisms of these graphs and investigate some of their important properties we then introduce the notion of strong bipolar fuzzy graphs and study some of their properties we also discuss some propositions of self complementary and self weak complementary strong bipolar fuzzy graphs

np completeness and apx completeness of restrained domination in graphs let g v e be a simple graph a vertex set email protected v is a restrained dominating set if every vertex not in s is adjacent to a vertex in s and to a vertex in v s in this paper we investigate the np completeness of the restrained domination problem in planar graphs and split graphs meanwhile it is proved that the restrained domination problem is apx complete for bounded degree graphs

mixed integer programming with convex concave constraints fixed parameter tractability and applications to multicovering and voting abstract a classic result of lenstra math oper res 1983 says that an integer linear program can be solved in fixed parameter tractable fpt time for the parameterization by the number of variables we extend this result by incorporating piecewise linear convex or concave functions to our mixed integer programs this general technique allows us to analyze the parameterized complexity of a number of classic np hard computational problems in particular we prove that weighted set multicover is in fpt when parameterized by the number of elements to cover and that there exists an fpt time approximation scheme for multiset multicover for the same parameter this is our most technical result further we use our general technique to prove that a number of problems from computational social choice e g problems related to bribery and control in elections are in fpt when parameterized by the number of candidates for bribery this resolves a nearly 10 year old family of open problems and for weighted electoral control of approval voting this improves some previously known xp memberships to fpt memberships

approximation algorithms for the partition vertex cover problem we consider a natural generalization of the partial vertex cover problem here an instance consists of a graph g v e a cost function c v z a partition p 1 p r of the edge set e and a parameter k i for each partition p i the objective is to find a minimum cost set of vertices which cover at least k i edges from the partition p i we call this the partition vc problem in this paper we give matching upper and lower bound on the approximability of this problem our algorithm is based on a novel lp relaxation for this problem this lp relaxation is obtained by adding knapsack cover inequalities to a natural lp relaxation of the problem we show that this lp has integrality gap of o log r where r is the number of sets in the partition of the edge set we also extend our result to more general settings for example we consider a problem where additionally edges have profits and we would like to pick a minimum cost set of vertices which cover edges of total profit at least i for each partition p i we call this the knapsack partition vertex cover problem we give an o log r approximation algorithm for this problem as well

probabilistic checking of proofs a new characterization of np we give a new characterization of np the class np contains exactly those languages l for which membership proofs a proof that an input x is in l can be verified probabilistically in polynomial time using logarithmic number of random bits and by reading sublogarithmic number of bits from the proof we discuss implications of this characterization specifically we show that approximating clique and independent set even in a very weak sense is np hard

quantifying degrees of necessity and of sufficiency in cause effect relationships with dichotomous and survival outcomes we suggest measures to quantify the degrees of necessity and of sufficiency of prognostic factors for dichotomous and for survival outcomes a cause represented by certain values of prognostic factors is considered necessary for an event if without the cause the event cannot develop it is considered sufficient for an event if the event is unavoidable in the presence of the cause necessity and sufficiency can be seen as the two faces of causation and this symmetry and equal relevance are reflected by the suggested measures the measures provide an approximate in some cases an exact multiplicative decomposition of explained variation as defined by schemper and henderson for censored survival and for dichotomous outcomes the measures ranging from zero to one are simple intuitive functions of unconditional and conditional probabilities of an event such as disease or death these probabilities often will be derived from logistic or cox regression models the measures however do not require any particular model the measures of the degree of necessity implicitly generalize the established attributable fraction or risk for dichotomous prognostic factors and dichotomous outcomes to continuous prognostic factors and to survival outcomes in a setting with multiple prognostic factors they provide marginal and partial results akin to marginal and partial odds and hazard ratios from multiple logistic and cox regression properties of the measures are explored by an extensive simulation study their application is demonstrated by three typical real data examples

ip pspace in this paper it is proven that when both randomization and interaction are allowed the proofs that can be verified in polynomial time are exactly those proofs that can be generated with polynomial space

the bottleneck independent domination on the classes of bipartite graphs and block graphs let g v e w denote a graph with vertex set v and edge set e and each vertex v is associated with a cost w v for any set v v the bottleneck cost of v is defined as max w x x v this paper considers the bottleneck independent dominating set problem the bids problem which determines an independent dominating set of g such that its bottleneck cost is minimized this paper studies the problem on the classes of bipartite graphs and block graphs this paper first proves that the problem is np hard on chordal bipartite graphs second a linear time algorithm on convex bipartite graphs is proposed next a linear time algorithm on trees is designed then we generalize the algorithmic result to block graphs all algorithms are designed by the dynamic programming strategy

edge fault tolerant bipanconnectivity of hypercubes this paper shows that for any two distinct vertices u and v with distance d in the hypercube q n n 3 with at most 2n 5 faulty edges and each vertex incident with least two fault free edges there exist fault free uv paths of length in q n for every with d 4 2 n 1 and d 0 mod2 this result improves some known results on edge fault bipanconnectivity of hypercubes the proof is based on the recursive structure of q n

graph distance measures based on topological indices revisited graph distance measures based on topological indices have been already explored by dehmer et al also inequalities for those graph distance measures have been proved in this paper we continue studying such comparative graph measures based on the well known wiener index graph energy and randic index respectively we prove extremal properties of the graph distance measures for some special classes of graphs to demonstrate useful properties of the measures we also discuss numerical results to conclude the paper we state some open problems

efficient algorithms for the minimum connected domination on trapezoid graphs given the trapezoid diagram the problem of finding the minimum cardinality connected dominating set in trapezoid graphs was solved in o m n time y d liang steiner set and connected domination in trapezoid graphs inform process lett 56 2 1995 101 108 kohler e kohler connected domination and dominating clique in trapezoid graphs discr appl math 99 2000 91 110 recently improved this result to o n time for the vertex weighted case the problem of finding the minimum weighted connected dominating set in trapezoid graphs can be solved in o m nlogn time anand srinivasan m s chang k madhukar c pandu rangan efficient algorithms for the weighted domination problems on trapezoid graphs manuscript 1996 herein n m denotes the number of vertices edges of the trapezoid graph in this paper we show a different approach for the problem of finding the minimum cardinality connected dominating set in trapezoid graphs using o n time for finding the minimum weighted connected dominating set we show the problem can be solved in o nloglogn time

the bipancycle connectivity of the hypercube paths and cycles are popular interconnection networks due to their simplicity and low degrees and therefore an efficient way of embedding them into an interconnection network is of particular importance many path embedding aspects and cycle embedding aspects such as hamiltonicity hamiltonian connectivity panconnectivity bipanconnectivity pancyclicity vertex pancyclicity and edge pancyclicity have been proposed and extensively studied in fact these discussions are meaningful for interconnection networks of resource allocated systems or heterogeneous computing systems in this paper we propose a new cycle embedding aspect called bipancycle connectivity that combines the concepts of vertex pancyclicity and bipanconnectivity a bipartite graph is bipancycle connected if an arbitrary pair of vertices x y is contained by common cycles called bipanconnected cycles that include a cycle of every even length ranging from minc x y to n where minc x y denotes the length of the minimum cycle that contains x and y and n is the number of vertices in this paper we introduce a new graph called the cycle of ladders we show that the hypercube is bipancycle connected by presenting algorithms to embed the cycle of ladders into the hypercube

approximation algorithms for combinatorial auctions with complement free bidders in a combinatorial auction m heterogenous indivisible items are sold to n bidders this paper considers settings in which the valuation functions of the bidders are known to be complement free a k a subadditive we provide several approximation algorithms for the social welfare maximization problem in such settings first we present a logarithmic upper bound for the case that the access to the valuation functions is via demand queries for the weaker value queries model we provide a tight o m approximation unlike the other algorithms we present this algorithm is also incentive compatible finally we present two approximation algorithms for the more restricted class of xos valuations a simple deterministic algorithm that provides an approximation ratio of two and an optimal e e 1 approximation achieved via randomized rounding we also present optimal lower bounds for both the demand oracles model and the value oracles model

a simple method of determining confidence intervals for population attributable risk from complex surveys methods to assess uncertainty in the estimated population attributable risk par by calculating 95 per cent confidence intervals cis are not readily available in software for complex sample surveys using the bonferroni inequality a simple method to obtain cis for the par is developed the method is demonstrated using a simulation in a 2 x 2 table as well as a cohort study to calculate cis for par of coronary heart disease death using proportional hazards regression this article demonstrates a straightforward theoretically valid method of determining cis for the par using this method researchers analysing complex surveys can routinely provide a population perspective and a valid measure of the uncertainty for these estimates

efficient approximation algorithms for maximum coverage with group budget constraints abstract given a ground set u with a non negative weight w i for each i u a positive integer k and a collection of sets s which is partitioned into a family of disjoint groups g the goal of the maximum coverage problem with group budget constraints mcg is to select k sets from s such that the total weight of the union of the k sets is maximized and at most one set is selected from each group g g we first present an approximation algorithm with a factor 1 1 e and an exponential time via randomized linear programming rounding technique then we improve the time complexity of the algorithm to o m n 3 5 l k 3 5 q 7 l for s m u n and l being the length of the input by the key idea of modeling the selection of groups as computing a constrained flow in a corresponding auxiliary graph the algorithm is later shown can be extended to solve two generalizations of mcg last but not the least we present another algorithm with a time complexity o m n 3 5 l k 10 5 l and a slightly increased approximation ratio 1 e 1 1 mainly based on the idea of partition where 2 is a parameter tuning which can balance the time complexity and the ratio

attributable fractions with survival data attributable fraction af is an important concept in clinical and epidemiological studies the concept has mainly been discussed in relation to case control studies cross sectional studies and follow up studies of fixed length here we propose and discuss several ways of defining and estimating afs with right censored survival data and thus with varying lengths of follow up in particular we define the attributable hazard fraction the af before time t and the af within study these measures have different interpretations and may give different numerical values as illustrated in an application to real data on time to the first receiving of cash benefits for hearing impairment in children the results underline the need for careful selection of the type of measure and interpretation when reporting afs for survival data

there is no ternary 28 6 16 code the existence of a ternary 28 6 16 code is considered we show that without loss of generality a generator matrix of such a code must satisfy certain conditions a computer search over all matrices that satisfy these conditions reveals that a ternary 28 6 16 code does not exist

on the power of multi prover interactive protocols abstract we look at complexity issues of interactive proof systems with multiple provers separated from each other this model developed by ben or et al 1988 allows the verifier to play the provers off each other we show this model equivalent to an alternative interactive proof system model using oracles as provers we also show that every language accepted by these models lies in nondeterministic exponential time we exhibit a relativized world where a co np language does not have multiple prover interactive proofs finally we show a simple example that one cannot parallelize multiple prover protocols as easily as the single prover model

link prediction based on temporal similarity metrics using continuous action set learning automata abstract link prediction is a social network research area that tries to predict future links using network structure the main approaches in this area are based on predicting future links using network structure at a specific period without considering the links behavior through different periods for example a common traditional approach in link prediction calculates a chosen similarity metric for each non connected link and outputs the links with higher similarity scores as the prediction result in this paper we propose a new link prediction method based on temporal similarity metrics and continuous action set learning automata cala the proposed method takes advantage of using different similarity metrics as well as different time periods in the proposed algorithm we try to model the link prediction problem as a noisy optimization problem and use a team of calas to solve the noisy optimization problem cala is a reinforcement based optimization tool which tries to learn the optimal behavior from the environment feedbacks to determine the importance of different periods and similarity metrics on the prediction result we define a coefficient for each of different periods and similarity metrics and use a cala for each coefficient each cala tries to learn the true value of the corresponding coefficient final link prediction is obtained from a combination of different similarity metrics in different times based on the obtained coefficients the link prediction results reported here show satisfactory of the proposed method for some social network data sets

note on two generalizations of the randic index for a given graph g the well known randic index of g introduced by milan randic in 1975 is defined as r g u v e g d u d v 1 2 where the sum is taken over all edges uv and du denotes the degrees of u bollobas and erdos generalized this index by replacing 1 2 with any real number which is called the general randic index dvo ak et al introduced a modified version of randic index r g u v e g max d u d v 1 based on this recently knor et al introduced two generalizations r g u v e g min d u d v and r g u v e g max d u d v for any real number clearly the former is a lower bound for the general randic index and the latter is its upper bound knor et al studied extremal values of r g and r g and concluded some open problems in this paper we consider the open problems and give some comments and results some results for chemical trees are obtained