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141
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Improvements To Propositional Satisfiability Search Algorithms
, 1995
"... ... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable ..."
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Cited by 161 (0 self)
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... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable random 3SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NPcomplete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.
The Complexity of Multiterminal Cuts
 SIAM Journal on Computing
, 1994
"... In the Multiterminal Cut problem we are given an edgeweighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, maxflow problem, and ..."
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Cited by 139 (0 self)
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In the Multiterminal Cut problem we are given an edgeweighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, maxflow problem, and can be solved in polynomial time. We show that the problem becomes NPhard as soon as k = 3, but can be solved in polynomial time for planar graphs for any fixed k. The planar problem is NPhard, however, if k is not fixed. We also describe a simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2  2/k of the optimal cut weight.
Minimumenergy broadcast in allwireless networks: Npcompleteness and distribution
 In Proc. of ACM MobiCom
, 2002
"... In allwireless networks a crucial problem is to minimize energy consumption, as in most cases the nodes are batteryoperated. We focus on the problem of poweroptimal broadcast, for which it is well known that the broadcast nature of the radio transmission can be exploited to optimize energy consump ..."
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Cited by 129 (2 self)
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In allwireless networks a crucial problem is to minimize energy consumption, as in most cases the nodes are batteryoperated. We focus on the problem of poweroptimal broadcast, for which it is well known that the broadcast nature of the radio transmission can be exploited to optimize energy consumption. Several authors have conjectured that the problem of poweroptimal broadcast is NPcomplete. We provide here a formal proof, both for the general case and for the geometric one; in the former case, the network topology is represented by a generic graph with arbitrary weights, whereas in the latter a Euclidean distance is considered. We then describe a new heuristic, Embedded Wireless Multicast Advantage. We show that it compares well with other proposals and we explain how it can be distributed. Categories and Subject Descriptors
Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 127 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
Surface Approximation and Geometric Partitions
 IN PROC. 5TH ACMSIAM SYMPOS. DISCRETE ALGORITHMS
, 1994
"... Motivated by applications in computer graphics, visualization, and scientific computation, we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x; y) and an input parameter " ? 0, compute a piecewise linear function \Sigma(x ..."
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Cited by 97 (15 self)
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Motivated by applications in computer graphics, visualization, and scientific computation, we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x; y) and an input parameter " ? 0, compute a piecewise linear function \Sigma(x; y) of minimum complexity (that is, a xymonotone polyhedral surface, with a minimum number of vertices, edges, or faces) such that j\Sigma(x p ; y p ) \Gamma z p j "; for all (x p ; y p ; z p ) 2 S: We prove that the decision version of this problem is NPHard . The main result of our paper is a polynomialtime approximation algorithm that computes a piecewise linear surface of size O(K o log K o ), where K o is the complexity of an optimal surface satisfying the constraints of the problem. The technique
Minimizing broadcast latency and redundancy in ad hoc networks
 In Proc. of the Fourth ACM Int. Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC'03
, 2003
"... z ..."
On Rectangular Partitionings in Two Dimensions: Algorithms, Complexity, and Applications
 In Proceedings of the 7th International Conference on Database Theory
, 1999
"... . Partitioning a multidimensional data set into rectangular partitions subject to certain constraints is an important problem that arises in many database applications, including histogrambased selectivity estimation, loadbalancing, and construction of index structures. While provably optimal ..."
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Cited by 44 (7 self)
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. Partitioning a multidimensional data set into rectangular partitions subject to certain constraints is an important problem that arises in many database applications, including histogrambased selectivity estimation, loadbalancing, and construction of index structures. While provably optimal and efficient algorithms exist for partitioning onedimensional data, the multidimensional problem has received less attention, except for a few special cases. As a result, the heuristic partitioning techniques that are used in practice are not well understood, and come with no guarantees on the quality of the solution. In this paper, we present algorithmic and complexitytheoretic results for the fundamental problem of partitioning a twodimensional array into rectangular tiles of arbitrary size in a way that minimizes the number of tiles required to satisfy a given constraint. Our main results are approximation algorithms for several partitioning problems that provably approxima...
Point Labeling with Sliding Labels
 Computational Geometry: Theory and Applications
, 1999
"... This paper discusses algorithms for labeling sets of points in the plane, where labels are not restricted to some nite number of positions. We show that continuously sliding labels allows more points to be labeled both in theory and in practice. We dene six dierent models of labeling, and analyze ho ..."
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Cited by 38 (10 self)
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This paper discusses algorithms for labeling sets of points in the plane, where labels are not restricted to some nite number of positions. We show that continuously sliding labels allows more points to be labeled both in theory and in practice. We dene six dierent models of labeling, and analyze how much better  more points get a label  one model can be than another. We show that maximizing the number of labeled points is NPhard in the most general of the new models. Nevertheless, we give a polynomialtime approximation scheme and a simple and ecient factor 1 2 approximation algorithm for each of the new models. Finally, we give experimental results based on the factor 1 2 approximation algorithm to compare the models in practice. We also compare this algorithm experimentally to other algorithms suggested in the literature. 1 Introduction Annotating sets of points is a common task to be performed in Geographic Information Systems. Cities on smallscale maps are shown as...
On Approximating Rectangle Tiling and Packing
 Proc Symp. on Discrete Algorithms (SODA
"... Our study of tiling and packing with rectangles in twodimensional regions is strongly motivated by applications in database mining, histogrambased estimation of query sizes, data partitioning, and motion estimation in video compression by block matching, among others. An example of the problems tha ..."
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Cited by 37 (6 self)
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Our study of tiling and packing with rectangles in twodimensional regions is strongly motivated by applications in database mining, histogrambased estimation of query sizes, data partitioning, and motion estimation in video compression by block matching, among others. An example of the problems that we tackle is the following: given an n \Theta n array A of positive numbers, find a tiling using at most p rectangles (that is, no two rectangles must overlap, and each array element must fall within some rectangle) that minimizes the maximum weight of any rectangle; here the weight of a rectangle is the sum of the array elements that fall within it. If the array A were onedimensional, this problem could be easily solved by dynamic programming. We prove that in the twodimensional case it is NPhard to approximate this problem to within a factor of 1:25. On the other hand, we provide a nearlinear time algorithm that returns a solution at most 2:5 times the optimal. Other rectangle tiling...