the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

location on tree networks p centre and n dispersion problems we consider two problems of locating facilities on trees in the first we wish to determine the location of n points so as to maximize the minimum distance between any pair in the second we wish to locate p centers of a single type of facility so as to minimize the maximum distance between any point and the center nearest to it we provide polynomial algorithms for both problems of o n 2 log n log n for the first problem and of o n 2 log p for the second where n is the number of nodes in the tree

improved approximability and non approximability results for graph diameter decreasing problems in this paper we study two variants of the problem of adding edges to a graph so as to reduce the resulting diameter more precisely given a graph g v e and two positive integers d and b the minimum cardinality bounded diameter edge addition mcbd problem is to find a minimum cardinality set f of edges to be added to g in such a way that the diameter of g f is less than or equal to d while the bounded cardinality minimum diameter edge addition bcmd problem is to find a set f of b edges to be added to g in such a way that the diameter of g f is minimized both problems are well known to be np hard as well as approximable within o lognlogd and 4 up to an additive term of 2 respectively in this paper we improve these long standing approximation ratios to o logn and to 2 up to an additive term of 2 respectively as a consequence we close in an asymptotic sense the gap on the approximability of mcbd which was known to be not approximable within clogn for some constant c 0 unless p np remarkably as we further show in the paper our approximation ratio remains asymptotically tight even if we allow for a solution whose diameter is optimal up to a multiplicative factor approaching 53 on the other hand on the positive side we show that at most twice of the minimal number of additional edges suffices to get at most twice of the required diameter some of our results extend to the edge weighted version of the problems

noncoherent coded modulation trellis coded modulation with two or multidimensional signal constellations together with coherent maximum likelihood detection is considered an attractive solution for communications over the additive white gaussian noise awgn channel in this paper a new noncoherent communication system is introduced called noncoherent coded modulation ncm as an alternative to coherent coded modulation ncm achieves almost the same power efficiency without bandwidth expansion or an extensive increase in complexity as a noncoherent system the method does not need carrier phase estimation nonetheless differential encoding is not required high performance noncoherent detection is achieved by using multiple symbol observations unlike previous approaches a sliding window for the observations is used with each observation covering several branches of the trellis such that the observations are time overlapped we define a new type of noncoherent maximum likelihood sequence estimator mlse and analyze its performance over the awgn channel by numerical calculation of the union bound we perform a computerized search and present new codes for noncoherent detection with their performance the new codes cover many useful rates and complexities and achieve higher performance than existing codes for noncoherent detection the method can also be used for multiple symbol demodulation of mdpsk with better results than existing methods

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

on arithmetic models and functoriality of bost connes systems with an appendix by sergey neshveyev this paper has two parts in the first part we construct arithmetic models of bost connes systems for arbitrary number fields which has been an open problem since the seminal work of bost and connes sel math 1 3 411 457 1995 in particular our construction shows how the class field theory of an arbitrary number field can be realized through the dynamics of a certain operator algebra this is achieved by working in the framework of endomotives introduced by connes consani and marcolli adv math 214 2 761 831 2007 and using a classification result of borger and de smit arxiv 1105 4662 for certain rings in terms of the deligne ribet monoid moreover the uniqueness of the arithmetic model is shown by sergey neshveyev in an appendix in the second part of the paper we introduce a base change functor for a class of algebraic endomotives and construct in this way an algebraic refinement of a functor from the category of number fields to the category of bost connes systems constructed recently by laca neshveyev and trifkovic arxiv 1010 4766

on the solution value of the continuous p center location problem on a graph let g v e be an undirected graph with positive edge lengths let rp denote the solution value to the continuous p center location problem on g we prove that rp is of the form rp t 2q where t is the length of an euler tour of a subgraph of g which belongs to one of four possible types and q is an integer 1 q 2p we also discuss algorithmic implications of this result

an analysis of network location problems with distance constraints this paper concerns a class of network location problems with minimum or maximum separation requirements between uncapacitated facilities or between demand points and the facilities or both its purpose is three fold first it is to recognize distance constraints as increasing real life restrictions through various motivating illustrations using a new classification scheme the paper introduces a variety of distance constrained problems defined in a unified manner these include a number of new problems second it is to survey existing solution techniques available only for a few of such constrained problems finally it is to shed some light on yet unstudied problems by exploring possible extensions of some of the known solution techniques or discussing varying degrees of difficulties involved in particular the paper presents integer programming formulations of several new problems along with the results of applying linear programming relaxation methods although the computational experience is somewhat disappointing for some of these problems the results provide greater insight into the problems with the stated purpose it is hoped that this paper will stimulate future research in this important problem area

locating an absolute center on graphs that are almost trees abstract physical models that exhibit a treelike graph structure frequently arise in telecommunication networks interstate highway systems and computer communication networks treelike graphs are characterized and properties related to the absolute center problem are analyzed that are preserved under two transformations of the graph utilizing these preserved properties a linear time algorithm is presented for the absolute center problem whenever the underlying graph is homeomorphic to a treelike 3 cactus graph

discrete convexity and polynomial solvability in minimum 0 extension problems a 0 0 extension of graph vargamma is a metric d d on a set v v containing the vertex set v vargamma v of vargamma such that d d extends the shortest path metric of vargamma and for all x in v x v there exists a vertex s s in vargamma with d x s 0 d x s 0 the minimum 0 0 extension problem 0 ext vargamma on vargamma is given a set v supseteq v vargamma v v and a nonnegative cost function c c defined on the set of all pairs of v v find a 0 0 extension d d of vargamma with sum xy c xy d x y xyc xy d x y minimum the 0 0 extension problem generalizes a number of basic combinatorial optimization problems such as minimum s t s t cut problem and multiway cut problem karzanov proved the polynomial solvability of 0 ext vargamma for a certain large class of modular graphs vargamma and raised the question what are the graphs vargamma for which 0 ext vargamma can be solved in polynomial time he also proved that 0 ext vargamma is np hard if vargamma is not modular or not orientable in a certain sense in this paper we prove the converse if vargamma is orientable and modular then 0 ext vargamma can be solved in polynomial time this completes the classification of graphs vargamma for which 0 ext vargamma is tractable to prove our main result we develop a theory of discrete convex functions on orientable modular graphs analogous to discrete convex analysis by murota and utilize a recent result of thapper and ivn on valued csp

maximum likelihood block detection of noncoherent continuous phase modulation the authors examine maximum likelihood block detection of uncoded full response continuous phase modulation cpm over an additive white gaussian noise awgn channel both the maximum likelihood metrics and the bit error probability performances of the associated detection algorithms are considered the special and popular case of minimum shift keying msk corresponding to h 0 5 and constant amplitude frequency pulse is treated separately the many new receiver structures that result from this investigation can be compared to the traditional ones that have been used in the past both from the standpoint of simplicity of implementation and optimality of performance

locating centers on a tree with discontinuous supply and demand regions consider a tree t n e with supply and demand regions and each composed of a finite number of disjoint closed and connected subregions of t some of which may possibly consist of just one point given an integer p we seek a collection of p centers x1 xp which minimize the expression maxy mini 1 pd y xi we present a polynomial algorithm for this problem its running time is bounded by o n log2n if either or is discrete and by o n min p log2n n log p if both sets contain at least one full edge

multiple bit differential detection of offset qpsk analogous to multiple symbol differential detection of quadrature phase shift keying qpsk a multiple bit differential detection scheme is described for offset qpsk that also exhibits continuous improvement in performance with increasing observation interval being derived from maximum likelihood considerations together with the representation of differentially encoded offset qpsk as a continuous phase modulation the proposed scheme is purported to be the most power efficient scheme for such a modulation and detection method

technical note equivalence between the direct search approach and the cut approach to the rectilinear distance location problem picard and ratliff recently proposed a cut approach to the rectilinear distance location problem and claimed it is fundamentally different from the direct search approach as developed by pritsker and ghare rao juel and love and sherali and shetty our objective is to show that the cut approach is essentially a direct search approach

dominant an algorithm for the p center problem abstract in this paper we present dominant an algorithm for the p center problem that is the problem of locating p facilities on a network so as to minimise the maximum distance from each customer to his nearest facility the algorithm dominant solves a series of set covering problems according to a predefined maximum distance it has four versions two of which can solve optimally problems with up to 900 demand points a set of 45 test problems taken from literature is solved and results are reported

half integrality of node capacitated multiflows and tree shaped facility locations on trees in this paper we establish a novel duality relationship between node capacitated multiflows and tree shaped facility locations we prove that the maximum value of a tree distance weighted maximum node capacitated multiflow problem is equal to the minimum value of the problem of locating subtrees in a tree and the maximum is attained by a half integral multiflow utilizing this duality we show that a half integral optimal multiflow and an optimal location can be found in strongly polynomial time these extend previously known results in the maximum free multiflow problems we also show that the set of tree distance weights is the only class having bounded fractionality in maximum node capacitated multiflow problems

noncoherently detected trellis coded partial response cpm on mobile radio channels a noncoherent receiver is proposed for partial response trellis coded continuous phase modulation tc cpm on interleaved flat rician fading channels by using a multiple symbol observation interval and a simple metric calculator the power efficiency is improved over a receiver that uses a single symbol observation interval performance bounds on the bit error probability are derived by defining a set of characteristic distances for cpm signals and showing that tc cpm is equivalent to a tcm scheme our results show that with the same observation length the proposed receiver is less than 0 5 db inferior to a coherent receiver for which perfect channel information is needed we also conclude that in terms of joint power bandwidth complexity 2rc is the best candidate for rate 1 2 tcm codes

solving np hard problems on graphs that are almost trees and an application to facility location problems description d une technique generale pour resoudre certains problemes de graphes np durs en un temps qui est exponentiel dans un parametre k defini comme le maximum sur tous les composants c non separables du graphe d un nombre de bords qui peut etre ajoute a l arbre pour produire c on donne un algorithme de temps de complexite o e 6r rh 27

iterative multisymbol noncoherent reception of coded cpfsk a system involving the multisymbol noncoherent reception of coded continuous phase frequency shift keying is developed optimized and analyzed unlike coherent systems the modulation index of the waveform does not need to be rational with a small denominator and the oscillator only needs to be stable for the duration of a small block of symbols the achievable performance over awgn and rayleigh block fading channels is determined by computing the average mutual information which is the capacity of a channel using the given modulation format and receiver architecture under the constraint of uniformly distributed input symbols the code rate and modulation index are jointly optimized with respect to average mutual information under a bandwidth constraint for binary and quaternary signaling the information theoretic results are corroborated by bit error rate curves generated using a standardized turbo code in conjunction with iterative demodulation and decoding it is shown that while more robust than a system with coherent reception the proposed system offers superior energy efficiency compared with conventional single symbol noncoherent reception

a new compact formulation for the discrete p dispersion problem abstract this paper addresses the discrete p dispersion problem pdp which is about selecting p facilities from a given set of candidates in such a way that the minimum distance between selected facilities is maximized we propose a new compact formulation for this problem in addition we discuss two simple enhancements of the new formulation simple bounds on the optimal distance can be exploited to reduce the size and to increase the tightness of the model at a relatively low cost of additional computation time moreover the new formulation can be further strengthened by adding valid inequalities we present a computational study carried out over a set of large scale test instances in order to compare the new formulation against a standard mixed integer programming model of the pdp a line search and a binary search our numerical results indicate that the new formulation in combination with the simple bounds is solved to optimality by an out of the box mixed integer programming solver in 34 out of 40 instances while this is neither possible with the standard model nor with the search procedures for instances in which the line and binary search fail to find a provably optimal solution we achieve this by adding cuts to our enhanced formulation with the new techniques we are able to exactly solve instances of one order of magnitude larger than previously solved in the literature

group centre and group median of a tree abstract we consider the problem of identifying group centre and group median of a tree algorithms are presented that are better than the available algorithms which solve these problems on general networks for the group median problem an alternate approach is suggested which runs in linear time on specially structured problems properties of the set of all optimal solutions of these problems are also investigated

semigroup crossed products and the toeplitz algebras of nonabelian groups abstract we consider the quasi lattice ordered groups g p recently introduced by nica we realise their universal toeplitz algebra as a crossed product b p p by a semigroup of endomorphisms and show that the toeplitz representation is faithful precisely when an amenability condition is satisfied we then show directly that many interesting free products are amenable the final result contains theorems of cuntz and dinh on the uniqueness of toeplitz cuntz algebras as special cases

rotating maxrs queries given a set of weighted objects in a data space the maxrs problem in spatial databases studied in a vldb 2012 paper is to find a location for a rectangular region of a given size such that the weighted sum of all the objects covered by the rectangular region centered at the optimal location is maximized this problem is useful in lots of location based service applications such as finding the location for a new fast food restaurant with a limited delivery range attracting the greatest number of customers the existing maxrs problem assumes that the rectangular region is always placed horizontally and is non rotatable however under this assumption the weighted sum of all the covered objects may not be the greatest when the rectangular region is rotatable in this paper we propose a generalized maxrs problem called rotating maxrs without this assumption in rotating maxrs the rectangular region is rotatable and can be associated with an inclination angle the goal of our problem is to find a location and an inclination angle such that the weighted sum of all the objects covered by the rectangular region of a given size centered at this location with this inclination angle is the greatest we also present an efficient algorithm for the problem extensive experiments were conducted to verify the efficiency of our algorithms based on the real and synthetic datasets the experimental results show that the weighted sum of all the objects in the rotating maxrs queries can be increased with up to 300 on the synthetic datasets compared with existing non rotating maxrs queries which shows the significance of the new rotating maxrs queries

a finite algorithm for the continuousp center location problem on a graph letg v e be an undirected graph with positive integer edge lengths letm be the number of edges ine and letd be the sum of the edge lengths we prove that the solution value to the continuousp center location problem is a rationalp1 p2 where logp1 o m5 logd m6 logp i 1 2 this result is then used to construct a finite algorithm for the continuousp center problem

an overview of representative problems in location research we present a survey of over 50 representative problems in location research our goal is not to review all variants of different location models or to describe solution results but rather to provide a broad overview of major location problems that have been studied indicating briefly how they are formulated and how they relate to one another we review standard problems such as median center and warehouse location problems as well as less traditional location problems which have emerged in recent years our primary focus is on problems for which operations research type models have been developed most of the problems we review have been formulated as optimization problems

effective metaheuristic algorithms for the minimum differential dispersion problem abstract this paper presents tabu search and memetic search algorithms for solving the minimum differential dispersion problem the tabu search algorithm employs a neighborhood decomposition candidate list strategy and a rarely used solution based tabu memory unlike the typical attribute based tabu list the solution based tabu strategy leads to a more highly focused intensification process and avoids tuning the tabu tenure while employing coordinated hash functions that accelerate the determination of tabu status the memetic search algorithm incorporates the tabu search procedure within it and makes use of a crossover operator that generates solution assignments by an evaluation mechanism that includes both quality and distance criteria experimental results on a benchmark testbed of 250 problems reveal that our tabu search algorithm is capable of discovering better solutions for 179 71 6 of the problem instances while our memetic search algorithm finds better solutions for 157 62 8 of the instances collectively yielding better solutions for 181 72 4 of the test problems than recently reported state of the art algorithms

finding the conditional location of a median path on a tree in this paper we study the problem of locating a median path of limited length on a tree under the condition that some existing facilities are already located the existing facilities may be located at any subset of vertices upper and lower bounds are proposed for both the discrete and continuous models in the discrete model a median path is not allowed to contain partial edges in the continuous model a median path may contain partial edges the proposed upper bounds for these two models are o nlogn and o nlogn a n respectively they improve the previous known bounds from o nlog 2n and o n 2 respectively the proposed lower bounds are both w nlogn

lagrangean heuristics for location problems abstract in this paper we present a framework for developing lagrangean heuristics heuristics based upon lagrangean relaxation and subgradient optimisation with respect to location problems computational results are given for four different location problems p median uncapacitated warehouse location capacitated warehouse location and capacitated warehouse location with single source constraints these results indicate that the framework presented in this paper is robust i e it gives good quality solutions for each of these different location problems

state of the art location on networks a survey part ii exploiting tree network structure the discussion of the fundamental p center and p median problems in part i of this paper provides the basis for the work surveyed in part ii part ii deals with the minimax and minisum location problems with mutual communication location problems involving multiple objectives the distance constraints problem and problems involving the location of paths in addition convexity issues in network location problems are discussed virtually all of this work exploits network structure specifically it is based on the assumption that the network is a tree the conclusion section gives a brief discussion of the state of the art and of current trends in network location research

multiple bit differential detection of shaped offset qpsk we consider multiple bit differential detection mbdd of differentially encoded shaped offset quadrature phase shift keying soqpsk a highly bandwidth efficient and popular constant envelope modulation we propose two mbdd schemes that are based on a recent continuous phase modulation interpretation of soqpsk we show that the performance of these mbdd schemes approaches that of coherent detection cd as the multiple bit observation n window increases the first scheme uses a detection window that spans the full bit observation window f mbdd and is shown to require very large values of n to approach the performance of cd this presents a practical problem since the complexity of mbdd grows exponentially with n the second scheme is an improved version i mbdd with a detection window that is shortened to n 2 bit intervals although the complexity of i mbdd also increases exponentially with n it represents a significant improvement since only modest values of n are needed for high performance these performance characteristics are identified via a detailed performance analysis which provides asymptotic formulas for the bit error probability that are confirmed with computer simulations the analysis is also used to find the symmetric frequency pulse shapes with the best and worst error performance finally we develop a simplified and practical decision feedback differential detection algorithm that achieves near optimal performance with complexity that grows only linearly with n

hopf algebras cyclic cohomology and the transverse index theorem in this paper we solve a longstanding internal problem of noncommutative geometry namely the computation of the index of transversally elliptic operators on foliations we show that the computation of the local index formula for transversally hypoelliptic operators can be settled thanks to a very specific hopf algebra associated to each integer codimension this hopf algebra reduces transverse geometry to a universal geometry of affine nature the structure of this hopf algebra its relation with the lie algebra of formal vector fields as well as the computation of its cyclic cohomology are done in the present paper in which we also show that under a suitable unimodularity condition the cosimplicial space underlying the hochschild cohomology of a hopf algebra carries a highly nontrivial cyclic structure

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

duality and distance constraints for the nonlinear p center problem and covering problem on a tree network the problem of locating a fixed number p of facilities centers on a network where there are constraints on the center locations and where the centers provide a service to customers demand points located at vertices of the network is addressed the cost or loss of servicing a given demand point is a nonlinear function of the distance between the demand point and the closest center we consider the case where the network has special structure a tree network i e there is a unique shortest path between any two points on the network we also provide and interpret a dual to this problem and give polynomially bounded procedures for solving both problems the primal location problem is solved with the aid of a related problem for which we also give a dual

noncoherent sequence detection of continuous phase modulations in this paper noncoherent sequence detection proposed in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1376 85 1999 is extended to the case of continuous phase modulations cpms the results in the companion paper on linear modulations with intersymbol interference isi are used here because a cpm signal is mathematically equivalent to a sum of isi affected linearly modulated components according to the laurent decomposition the proposed suboptimal detection schemes have a performance which approaches that of coherent detection with acceptable complexity allow for time varying phase models and compare favorably with previously proposed solutions

the discrete p dispersion problem considered is the problem of selecting p out of n given points in some space such that the minimum distance between pairs of selected points is maximized this objective may be appropriate if the selected points correspond to facility sites and the objective is to have as dispersed a set as possible this problem is np complete related graph theoretical problems are discussed integer programming models are proposed and an outline is given on a line search procedure to solve this problem optimally using a branch and bound procedure problems with n 40 and p 16 can be solved on a microcomputer the heuristic developed to get an initial lower bound finds an optimal solution for most of our random test problems also described is an extension to the basic problem that allows for preselected points which may correspond to existing facility locations this more general version can be solved by slight modifications of the algorithms

a horizontal categorification of gel fand duality abstract in the setting of c categories we provide a definition of spectrum of a commutative full c category as a one dimensional unital fell bundle over a suitable groupoid equivalence relation and prove a categorical gel fand duality theorem generalizing the usual gel fand duality between the categories of commutative unital c algebras and compact hausdorff spaces although many of the individual ingredients that appear along the way are well known the somehow unconventional way we glue them together seems to shed some new light on the subject

efficient algorithms for the one dimensional k center problem we consider the problem of finding k centers for n weighted points on a real line this weighted k center problem was solved in o n log n time previously by using cole s parametric search and other complicated approaches in this paper we present an easier o n log n time algorithm that avoids the parametric search and in certain special cases our algorithm solves the problem in o n time in addition our techniques involve developing interesting data structures for processing queries that find a lowest point in the common intersection of a certain subset of half planes this subproblem is interesting in its own right and our solution for it may find other applications as well

polynomially bounded algorithms for locatingp centers on a tree we discuss several forms of thep center location problems on an undirected tree network our approach is based on utilizing results for rigid circuit graphs to obtain polynomial algorithms for solving the model duality theory on perfect graphs is used to define and solve the dual location model

efficient estimation of continuous phase modulation with unknown carrier phase an efficient algorithm is presented for the estimation of continuous phase modulation cpm sequences over the gaussian channel with unknown carrier phase it operates on the excess phase trellis like the viterbi algorithm except that it is not a maximum likelihood ml estimator its decision metric for survivor selection at each node is chosen so that it achieves the node error event probability of coherent ml estimation in the limit as the carrier phase remains constant over a long interval so that the observation interval for forming the metric can be made large it is shown for the case of minimum shift keying msk that the bit error probability bep of perfectly coherent ml estimation is attained

inverse eigenvalue problem of jacobi matrix with mixed data in this paper the inverse eigenvalue problem of reconstructing a jacobi matrix from its eigenvalues its leading principal submatrix and part of the eigenvalues of its submatrix is considered the necessary and sufficient conditions for the existence and uniqueness of the solution are derived furthermore a numerical algorithm and some numerical examples are given

multiple symbol trellis coded modulation applied to noncoherent continuous phase frequency shift keying this paper considers a maximum likelihood ml noncoherent detection scheme for multiple full response continuous phase frequency shift keying cpfsk waveforms and introduces a trellis coded modulation tcm scheme for this noncoherent modulation by utilizing a gaussian approximation for rician random variables we express the pairwise error probability as a function of the equivalent normalized squared distance ensd ensd plays the same role as normalized squared euclidean distance when evaluating error probability performance for coherent detection we derive an analytical approximation on the bit error probability by employing ensd for both the coded system and the uncoded system for the uncoded system we show that the bit error probability of noncoherent detection approaches that of coherent symbol by symbol detection in the limit as the multiplicity of the symbol goes to infinity for large signal to noise ratio snr we determine specific optimal trellis encoders for binary and 4 ary cpfsk with modulation index 1 2 and 1 4 respectively by application of ungerboeck s 1982 set partitioning approach

heuristic and special case algorithms for dispersion problems the dispersion problem arises in selecting facilities to maximize some function of the distances between the facilities the problem also arises in selecting nondominated solutions for multiobjective decision making it is known to be np hard under two objectives maximizing the minimum distance max min between any pair of facilities and maximizing the average distance max avg we consider the question of obtaining near optimal solutions for max min we show that if the distances do not satisfy the triangle inequality there is no polynomial time relative approximation algorithm unless p np when the distances satisfy the triangle inequality we analyze an efficient heuristic and show that it provides a performance guarantee of two we also prove that obtaining a performance guarantee of less than two is np hard for max avg we analyze an efficient heuristic and show that it provides a performance guarantee of four when the distances satisfy the triangle inequality we also present a polynomial ti

accelerating benders decomposition algorithmic enhancement and model selection criteria this paper proposes methodology for improving the performance of benders decomposition when applied to mixed integer programs it introduces a new technique for accelerating the convergence of the algorithm and theory for distinguishing good model formulations of a problem that has distinct but equivalent mixed integer programming representations the acceleration technique is based upon selecting judiciously from the alternate optima of the benders subproblem to generate strong or pareto optimal cuts this methodology also applies to a much broader class of optimization algorithms that includes dantzig wolfe decomposition for linear and nonlinear programs and related cutting plane type algorithms that arise in resource directive and price decomposition when specialized to network location problems this cut generation technique leads to very efficient algorithms that exploit the underlying structure of these models in discussing the proper formulation of mixed integer programs we suggest criteri

an o n log 2 n algorithm for the kth longest path in a tree with applications to location problems many known algorithms are based on selection in a set whose cardinality is superlinear in terms of the input length it is desirable in these cases to have selection algorithms that run in sublinear time in terms of the cardinality of the set this paper presents a successful development in this direction the methods developed here are applied to improve the previously known upper bounds for the time complexity of various location problems

one dimensional k center on uncertain data problems on uncertain data have attracted significant attention due to the imprecise nature of many measurement data in this paper we consider the k center problem on one dimensional uncertain data the input is a set p of weighted uncertain points on a real line and each uncertain point is specified by its probability density function pdf which is a piecewise uniform function i e a histogram the goal is to find a set q of k points on the line to minimize the maximum expected distance from the uncertain points of p to their expected closest points in q we present efficient algorithms for this uncertain k center problem and their running times almost match those for the deterministic k center problem

noncommutative geometry and motives the thermodynamics of endomotives we combine aspects of the theory of motives in algebraic geometry with noncommutative geometry and the classification of factors to obtain a cohomological interpretation of the spectral realization of zeros of l functions the analogue in characteristic zero of the action of the frobenius on l adic cohomology is the action of the scaling group on the cyclic homology of the cokernel in a suitable category of motives of a restriction map of noncommutative spaces the latter is obtained through the thermodynamics of the quantum statistical system associated to an endomotive a noncommutative generalization of artin motives semigroups of endomorphisms of algebraic varieties give rise canonically to such endomotives with an action of the absolute galois group the semigroup of endomorphisms of the multiplicative group yields the bost connes system from which one obtains through the above procedure the desired cohomological interpretation of the zeros of the riemann zeta function in the last section we also give a lefschetz formula for the archimedean local l factors of arithmetic varieties

spectral functionals nonholonomic dirac operators and noncommutative ricci flows we formulate a noncommutative generalization of the ricci flow theory in the framework of spectral action approach to noncommutative geometry grisha perelman s functionals are generated as commutative versions of certain spectral functionals defined by nonholonomic dirac operators and corresponding spectral triples we derive the formulas for spectral averaged energy and entropy functionals and state the conditions when such values describe non holonomic riemannian configurations