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139
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
Greedy Randomized Adaptive Search Procedures For The Steiner Problem In Graphs
 QUADRATIC ASSIGNMENT AND RELATED PROBLEMS, VOLUME 16 OF DIMACS SERIES ON DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1999
"... We describe four versions of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions of general instances of the Steiner Problem in Graphs. Di#erent construction and local search algorithms are presented. Preliminary computational results with one of the versions ..."
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Cited by 105 (29 self)
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We describe four versions of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions of general instances of the Steiner Problem in Graphs. Di#erent construction and local search algorithms are presented. Preliminary computational results with one of the versions on a variety of test problems are reported. On the majority of instances from the ORLibrary, a set of standard test problems, the GRASP produced optimal solutions. On those that optimal solutions were not found, the GRASP found good quality approximate solutions.
Tighter Bounds for Graph Steiner Tree Approximation
 SIAM Journal on Discrete Mathematics
, 2005
"... Abstract. The classical Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialln 3 time heuristic that achieves a bestknown approximation ratio of 1 + ≈ 1.55 for general graphs 2 and best ..."
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Cited by 66 (7 self)
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Abstract. The classical Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialln 3 time heuristic that achieves a bestknown approximation ratio of 1 + ≈ 1.55 for general graphs 2 and bestknown approximation ratios of ≈ 1.28 for both quasibipartite graphs (i.e., where no two nonterminals are adjacent) and complete graphs with edge weights 1 and 2. Our method is considerably simpler and easier to implement than previous approaches. We also prove the first known nontrivial performance bound (1.5 · OPT) for the iterated 1Steiner heuristic of Kahng and Robins in quasibipartite graphs.
Solving Steiner tree problems in graphs to optimality
 Networks
, 1998
"... Abstract: In this paper, we present the implementation of a branchandcut algorithm for solving Steiner tree problems in graphs. Our algorithm is based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms, and primal heuristics. We are able to ..."
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Cited by 44 (1 self)
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Abstract: In this paper, we present the implementation of a branchandcut algorithm for solving Steiner tree problems in graphs. Our algorithm is based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms, and primal heuristics. We are able to solve nearly all problem instances discussed in the literature to optimality, including one problem that—to our knowledge—has not yet been solved. We also report on our computational experiences with some very large Steiner tree problems arising from the design of electronic circuits. All test problems are gathered in a newly introduced library called SteinLib that is accessible via the World Wide Web. � 1998 John
When Hamming Meets Euclid: The Approximability of Geometric TSP and MST (Extended Abstract)
, 1997
"... We prove that the Traveling Salesperson Problem (MIN TSP) and the Minimum Steiner Tree Problem (MIN ST) are Max SNPhard (and thus NPhard to approximate within some constant r ? 1) even if all cities (respectively, points) lie in the geometric space R n (n is the number of cities/points) and ..."
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Cited by 41 (2 self)
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We prove that the Traveling Salesperson Problem (MIN TSP) and the Minimum Steiner Tree Problem (MIN ST) are Max SNPhard (and thus NPhard to approximate within some constant r ? 1) even if all cities (respectively, points) lie in the geometric space R n (n is the number of cities/points) and distances are computed with respect to the l 1 (rectilinear) metric. The TSP hardness results also hold for any l p metric, including the Euclidean metric, and in R logn . The running time of Arora's approximation scheme for geometric MIN TSP in R d is doubly exponential in d. Our results imply that this dependance is necessary unless NP has subexponential algorithms. We also prove, as an intermediate step, the hardness of approximating MIN TSP and MIN ST in Hamming spaces. The reduction for MIN TSP uses errorcorrecting codes and random sampling; the reduction for MIN ST uses the integrality property of MINCUT. The only previous nonapproximability results for ...
Multicast Communication in Multicomputer Networks
 IEEE Transactions on Parallel and Distributed Systems
, 1990
"... Efficient routing of messages is the key to the performance of multicomputers. Multicast communication refers to the delivery of the same message from a source node to an arbitrary number of destination nodes. While multicast communication is highly demanded in many applications, it is not directly ..."
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Cited by 39 (5 self)
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Efficient routing of messages is the key to the performance of multicomputers. Multicast communication refers to the delivery of the same message from a source node to an arbitrary number of destination nodes. While multicast communication is highly demanded in many applications, it is not directly supported by all existing multicomputers; rather it is indirectly supported by multiple onetoone or broadcast communications, which result in more network traffic and a waste of system resources. In this paper, we study routing evaluation criteria for multicast communication under different communication paradigms. Multicast communication in multicomputers is formulated as a graph theoretical problem. Depending on the evaluation criteria and communication mechanisms, we study three optimal multicast communication problems, which are equivalent to the finding of the following three subgraphs: optimal multicast path, optimal multicast cycle, and minimal Steiner tree, where the interconnectio...
Packing Steiner Trees: A Cutting Plane Algorithm and Computational Results
 Mathematical Programming
, 1992
"... In this paper we describe a cutting plane algorithm for the Steiner tree packing problem. We use our algorithm to solve some switchbox routing problems of VLSIdesign and report on our computational experience. This includes a brief discussion of separation algorithms, a new LPbased primal heuristi ..."
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Cited by 31 (12 self)
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In this paper we describe a cutting plane algorithm for the Steiner tree packing problem. We use our algorithm to solve some switchbox routing problems of VLSIdesign and report on our computational experience. This includes a brief discussion of separation algorithms, a new LPbased primal heuristic and implementation details. The paper is based on the polyhedral theory for the Steiner tree packing polyhedron developed in our companion paper [GMW92] and meant to turn this theory into an algoritmic tool for the solution of practical problems.
The Cougar project: A workinprogress report
 ACM SIGMOD Record
, 2003
"... Abstract — We present an update on the status of the Cougar Sensor Database Project in which we are investigating a database approach to sensor networks: Clients “program ” the sensors through queries in a highlevel declarative language (such as a variant of SQL). In this paper, we give an overview ..."
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Cited by 31 (0 self)
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Abstract — We present an update on the status of the Cougar Sensor Database Project in which we are investigating a database approach to sensor networks: Clients “program ” the sensors through queries in a highlevel declarative language (such as a variant of SQL). In this paper, we give an overview of our activities on energyefficient data dissemination and query processing. Due to space constraints, we cannot present a full menu of results; instead, we decided to only whet the reader’s appetite with some interesting problems in energyefficient routing and innetwork aggregation and some thoughts on how to approach them. I.
Embedding vertices at points: Few bends suffice for planar graphs
 in Graph Drawing (Proc. GD '99), LNCS 1731
, 2002
"... The existing literature gives ecient algorithms for mapping trees or less restrictively outerplanar graphs on a given set of points in a plane, so that the edges are drawn planar and as straight lines. We relax the latter requirement and allow very few bends on each edge while considering general ..."
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Cited by 28 (1 self)
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The existing literature gives ecient algorithms for mapping trees or less restrictively outerplanar graphs on a given set of points in a plane, so that the edges are drawn planar and as straight lines. We relax the latter requirement and allow very few bends on each edge while considering general plane graphs. Our results show two algorithms for mapping fourconnected plane graphs with at most one bend per edge and for mapping general plane graphs with at most two bends per edge. Furthermore we give a point set, where for arbitrary plane graphs it is NPcomplete to decide whether there is an mapping such that each edge has at most one bend.