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39
Computationally Manageable Combinatorial Auctions
, 1998
"... There is interest in designing simultaneous auctions for situations in which the value of assets to a bidder depends upon which other assets he or she wins. In such cases, bidders may well wish to submit bids for combinations of assets. When this is allowed, the problem of determining the revenue ma ..."
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Cited by 314 (1 self)
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There is interest in designing simultaneous auctions for situations in which the value of assets to a bidder depends upon which other assets he or she wins. In such cases, bidders may well wish to submit bids for combinations of assets. When this is allowed, the problem of determining the revenue maximizing set of nonconflicting bids can be a difficult one. We analyze this problem, identifying several different structures of combinatorial bids for which computational tractability is constructively demonstrated and some structures for which computational tractability 1 Introduction Some auctions sell many assets simultaneously. Often these assets, like U.S. treasury bills, are interchangeable. However, sometimes the assets and the bids for them are distinct. This happens frequently, as in the U.S. Department of the Interior's simultaneous sales of offshore oil leases, in some private farm land auctions, and in the Federal Communications Commission's recent multibillion dollar sales...
On the Solution of Traveling Salesman Problems
 DOC. MATH. J. DMV
, 1998
"... Following the theoretical studies of J.B. Robinson and H.W. Kuhn in the late 1940s and the early 1950s, G.B. Dantzig, R. Fulkerson, and S.M. Johnson demonstrated in 1954 that large instances of the TSP could be solved by linear programming. Their approach remains the only known tool for solving TS ..."
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Cited by 164 (7 self)
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Following the theoretical studies of J.B. Robinson and H.W. Kuhn in the late 1940s and the early 1950s, G.B. Dantzig, R. Fulkerson, and S.M. Johnson demonstrated in 1954 that large instances of the TSP could be solved by linear programming. Their approach remains the only known tool for solving TSP instances with more than several hundred cities; over the years, it has evolved further through the work of M. Grötschel , S. Hong , M. Jünger , P. Miliotis , D. Naddef , M. Padberg
Approximation Algorithms for Disjoint Paths Problems
, 1996
"... The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for w ..."
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Cited by 140 (0 self)
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The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for which very little is known from the point of view of approximation algorithms. It has recently been brought into focus in work on problems such as VLSI layout and routing in highspeed networks; in these settings, the current lack of understanding of the disjoint paths problem is often an obstacle to the design of practical heuristics.
Oracle quantum computing
 Brassard & U.Vazirani, Strengths and weaknesses of quantum computing
, 1994
"... \Because nature isn't classical, dammit..." ..."
Approximating Minimum Feedback Sets and Multicuts in Directed Graphs
 ALGORITHMICA
, 1998
"... This paper deals with approximating feedback sets in directed graphs. We consider two related problems: the weighted feedback vertex set (fvs) problem, and the weighted feedback edge set problem (fes). In the fvs (resp. fes) problem, one is given a directed graph with weights (each of which is at le ..."
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Cited by 98 (3 self)
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This paper deals with approximating feedback sets in directed graphs. We consider two related problems: the weighted feedback vertex set (fvs) problem, and the weighted feedback edge set problem (fes). In the fvs (resp. fes) problem, one is given a directed graph with weights (each of which is at least 1) on the vertices (resp. edges), and is asked to find a subset of vertices (resp. edges) with minimum total weight that intersects every directed cycle in the graph. These problems are among the classical NPHard problems and have many applications. We also consider a generalization of these problems: subsetfvs and subsetfes, in which the feedback set has to intersect only a subset of the directed cycles in the graph. This subset consists of all the cycles that go through a distinguished input subset of vertices and edges, denoted by X . This generalization is also NPHard even when X = 2. We present approximation algorithms for the subsetfvs and subsetfes problems. The first algorithm we present achieves an approximation factor of O(log2 X). The second algorithm achieves an approximation factor of O(min(log tau log log tau; log n log log n)), where tau is the value of the optimum fractional solution of the problem at hand, and n is the number of vertices in the graph. We also define a multicut problem in a special type of directed networks which we call circular networks, and show that the subsetfes and subsetfvs problems are equivalent to this multicut problem. Another contribution of our paper is a combinatorial algorithm that computes a (1 + epsilon) approximation to the fractional optimal feedback vertex set. Computing the approximate solution is much simpler and more efficient than general linear programming methods. All of our algorithms use this approximate solution.
Some NPcomplete Geometric Problems
"... We show that the STEINER TREE problem and TRAVELING SALESMAN problem for points in the plane are NPcomplete when distances are measured either by the rectilinear (Manhattan) metric or by a natural discretized version of the Euclidean metric. Our proofs also indicate that the problems are NPhard i ..."
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Cited by 83 (2 self)
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We show that the STEINER TREE problem and TRAVELING SALESMAN problem for points in the plane are NPcomplete when distances are measured either by the rectilinear (Manhattan) metric or by a natural discretized version of the Euclidean metric. Our proofs also indicate that the problems are NPhard if the distance I~asure is the (unmodified) Euclidean metric. However, for reasons we discuss, there is some question as to whether these problems, or even the wellsolved MINIMUM SPANNING TREE problem, are in NP when the distance measure is the Euclidean metric.
Parameterized Complexity: A Framework for Systematically Confronting Computational Intractability
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1997
"... In this paper we give a programmatic overview of parameterized computational complexity in the broad context of the problem of coping with computational intractability. We give some examples of how fixedparameter tractability techniques can deliver practical algorithms in two different ways: (1) by ..."
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Cited by 72 (15 self)
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In this paper we give a programmatic overview of parameterized computational complexity in the broad context of the problem of coping with computational intractability. We give some examples of how fixedparameter tractability techniques can deliver practical algorithms in two different ways: (1) by providing useful exact algorithms for small parameter ranges, and (2) by providing guidance in the design of heuristic algorithms. In particular, we describe an improved FPT kernelization algorithm for Vertex Cover, a practical FPT algorithm for the Maximum Agreement Subtree (MAST) problem parameterized by the number of species to be deleted, and new general heuristics for these problems based on FPT techniques. In the course of making this overview, we also investigate some structural and hardness issues. We prove that an important naturally parameterized problem in artificial intelligence, STRIPS Planning (where the parameter is the size of the plan) is complete for W [1]. As a corollary, this implies that kStep Reachability for Petri Nets is complete for W [1]. We describe how the concept of treewidth can be applied to STRIPS Planning and other problems of logic to obtain FPT results. We describe a surprising structural result concerning the top end of the parameterized complexity hierarchy: the naturally parameterized Graph kColoring problem cannot be resolved with respect to XP either by showing membership in XP, or by showing hardness for XP without settling the P = NP question one way or the other.
Approximations for the Disjoint Paths Problem in HighDiameter Planar Networks
, 1995
"... We consider the problem of connecting distinguished terminal pairs in a graph via edgedisjoint paths. This is a classical NPcomplete problem for which no general approximation techniques are known; it has recently been brought into focus in papers discussing applications to admission control in hig ..."
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Cited by 43 (4 self)
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We consider the problem of connecting distinguished terminal pairs in a graph via edgedisjoint paths. This is a classical NPcomplete problem for which no general approximation techniques are known; it has recently been brought into focus in papers discussing applications to admission control in highspeed networks and to routing in alloptical networks. In this paper we provide O(log n)approximation algorithms for two natural optimization versions of this problem for the class of nearlyEulerian, uniformly highdiameter planar graphs, which includes twodimensional meshes and other common planar interconnection networks. We give an O(logn)approximation to the maximumnumber of terminal pairs that can be simultaneously connected via edgedisjoint paths, and an O(log n)approximation to the minimum number of wavelengths needed to route a collection of terminal pairs in the "optical routing" model considered by Raghavan and Upfal, and others. The latter result improves on an O(log 2 n...
On The Approximability Of The Traveling Salesman Problem
 Proceedings of the 32nd Annual ACM Symposium on Theory of Computing
, 2000
"... We show that the traveling salesman problem with triangle inequality cannot be approximated with a ratio better than 116 when the edge lengths are allowed to be asymmetric and 219 when the edge lengths are symmetric. The best previous lower bounds were 2804 and 3812 respectively. The reduction is fr ..."
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Cited by 37 (0 self)
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We show that the traveling salesman problem with triangle inequality cannot be approximated with a ratio better than 116 when the edge lengths are allowed to be asymmetric and 219 when the edge lengths are symmetric. The best previous lower bounds were 2804 and 3812 respectively. The reduction is from Håstad's maximum satisfiability of linear equations modulo 2, and is nonconstructive.
Pattern Routing: Use and Theory for Increasing Predictability and Avoiding Coupling
 IEEE TRANS. ON COMPUTERAIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
, 2002
"... Deep submicron effects, along with increasing interconnect densities, have increased the complexity of the routing problem. Whereas previously we could focus on minimizing wirelength, we must now consider a variety of objectives during routing. For example, an increased amount of timing restrictions ..."
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Cited by 35 (3 self)
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Deep submicron effects, along with increasing interconnect densities, have increased the complexity of the routing problem. Whereas previously we could focus on minimizing wirelength, we must now consider a variety of objectives during routing. For example, an increased amount of timing restrictions means that we must minimize interconnect delay. But, interconnect delay is no longer simply related to wirelength. Coupling capacitance has become a dominant component of delay due to the shrinking of device sizes. Regardless, the most important objective is producing a routable circuit. Unfortunately, this often conflicts with minimizing interconnect delay as minimum delay routes create congested areas, for which an exact routing cannot be realized without violating design rules. In this work, we use the concept of pattern routing to develop algorithms that guide the router to a solution that minimizes interconnect delayby considering both coupling and wirelengthwithout damaging the routability of the circuit. The paper is divided into two parts. The first part demonstrates that pattern routing can be used without affecting the routability of the circuit. We propose two schemes to choose a set of nets to pattern route. Using these schemes, we show that the routability is not hindered. The second part builds on the previous part by presenting a framework for coupling reduction using pattern routing. We develop theory and algorithms relating pattern routing and coupling. Additionally, we give suggestions on how to extend our theory and use our algorithms for both global and detailed routing.