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58
Truth revelation in approximately efficient combinatorial auctions
 Journal of the ACM
, 2002
"... Abstract. Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard ..."
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Cited by 182 (1 self)
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Abstract. Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these mechanisms—in particular, their truth revelation properties—assumes that the optimization problems are solved precisely. In reality, these optimization problems can usually be solved only in an approximate fashion. We investigate the impact on such mechanisms of replacing exact solutions by approximate ones. Specifically, we look at a particular greedy optimization method. We show that the GVA payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does guarantee truthfulness for a restricted class of players. We demonstrate the latter property by identifying natural properties for combinatorial auctions and showing that, for our restricted class of players, they imply that truthful strategies are dominant. Those properties have applicability beyond the specific auction studied.
THE PRIMALDUAL METHOD FOR APPROXIMATION ALGORITHMS AND ITS APPLICATION TO NETWORK DESIGN PROBLEMS
"... The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent researc ..."
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Cited by 123 (7 self)
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The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent research applying the primaldual method to problems in network design.
Vertex Cover Might be Hard to Approximate to within 2ɛ
 IN PROCEEDINGS OF THE 18TH ANNUAL IEEE CONFERENCE ON COMPUTATIONAL COMPLEXITY
, 2003
"... We show that vertex cover is hard to approximate within any constant factor better than 2 where the hardness is based on a conjecture regarding the power of unique 2prover1round games presented in [15]. We actually show a stronger result, namely, based on the same conjecture, vertex cover on k ..."
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Cited by 119 (11 self)
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We show that vertex cover is hard to approximate within any constant factor better than 2 where the hardness is based on a conjecture regarding the power of unique 2prover1round games presented in [15]. We actually show a stronger result, namely, based on the same conjecture, vertex cover on kuniform hypergraphs is hard to approximate within any constant factor better than k.
Truthful approximation mechanisms for restricted combinatorial auctions
, 2002
"... When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCGlike payment rules will not ensure truthfulness). We dev ..."
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Cited by 94 (3 self)
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When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCGlike payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann O’Callaghan, and Shoham, who presented greedy heuristics. We show how to use IFTHENELSE constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios. 1
Incentive compatible multi unit combinatorial auctions
 In TARK 03
, 2003
"... This paper deals with multiunit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each g ..."
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Cited by 90 (10 self)
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This paper deals with multiunit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each good has exactly k units, and each bidder desires no more than a single unit of each good. We provide incentive compatible mechanisms for combinatorial auctions for the general case where bidders are not limited to single minded valuations. The mechanisms we give have approximation ratios close to the best possible for both online and offline scenarios. This is the first result where nonVCG mechanisms are derived for nonsingle minded bidders for a natural model of combinatorial auctions.
The Importance of Being Biased
, 2002
"... The Minimum Vertex Cover problem is the problem of, given a graph, finding a smallest set of vertices that touches all edges. We show that it is NPhard to approximate this problem 1.36067, improving on the previously known hardness result for a 6 factor. 1 ..."
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Cited by 86 (8 self)
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The Minimum Vertex Cover problem is the problem of, given a graph, finding a smallest set of vertices that touches all edges. We show that it is NPhard to approximate this problem 1.36067, improving on the previously known hardness result for a 6 factor. 1
Finding a large hidden clique in a random graph
, 1998
"... ABSTRACT: We consider the following probabilistic model of a graph on n labeled vertices. First choose a random graph Gn,1�2 Ž., and then choose randomly a subset Q of vertices of size k and force it to be a clique by joining every pair of vertices of Q by an edge. The problem is to give a polynomia ..."
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Cited by 83 (5 self)
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ABSTRACT: We consider the following probabilistic model of a graph on n labeled vertices. First choose a random graph Gn,1�2 Ž., and then choose randomly a subset Q of vertices of size k and force it to be a clique by joining every pair of vertices of Q by an edge. The problem is to give a polynomial time algorithm for finding this hidden clique almost surely for various values of k. This question was posed independently, in various variants, by Jerrum and by Kucera. In this paper we present an efficient algorithm for all k�cn0.5 ˇ, for
Truth Revelation in Rapid, Approximately Efficient Combinatorial Auctions
 In ACM Conference on Electronic Commerce (EC99
, 1999
"... Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for co ..."
Abstract

Cited by 77 (5 self)
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Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these mechanisms  in particular, their truth revelation properties  assumes that the optimization problems are solved precisely. In reality, these optimization problems can usually be solved only in an approximate fashion. We investigate the impact on such mechanisms of replacing exact solutions by approximate ones. Specifically, we look at a particular greedy optimization method, which has empirically been shown to perform well. We show that the GVA payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does guarantee truthfulness for a restricted class...
Reactive Local Search for the Maximum Clique Problem
 Algorithmica
"... A new Reactive Local Search (RLS ) algorithm is proposed for the solution of the MaximumClique problem. RLS is based on local search complemented by a feedback (historysensitive) scheme to determine the amount of diversification. The reaction acts on the single parameter that decides the temporary ..."
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Cited by 77 (14 self)
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A new Reactive Local Search (RLS ) algorithm is proposed for the solution of the MaximumClique problem. RLS is based on local search complemented by a feedback (historysensitive) scheme to determine the amount of diversification. The reaction acts on the single parameter that decides the temporary prohibition of selected moves in the neighborhood, in a manner inspired by Tabu Search. The performance obtained in computational tests appears to be significantly better with respect to all algorithms tested at the the second DIMACS implementation challenge. The worstcase complexity per iteration of the algorithm is O(max{n, m}) where n and m are the number of nodes and edges of the graph. In practice, when a vertex is moved, the number of operations tends to be proportional to its number of missing edges and therefore the iterations are particularly fast in dense graphs.
On the Hardness of Approximating the Chromatic Number
, 1993
"... We study the hardness of approximating the chromatic number when the input graph is kcolorable for some fixed k 3. Our main result is that it is NPhard to find a 4coloring of a 3chromatic graph. As an immediate corollary we obtain that it is NPhard to color a kchromatic graph with at most ..."
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Cited by 72 (6 self)
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We study the hardness of approximating the chromatic number when the input graph is kcolorable for some fixed k 3. Our main result is that it is NPhard to find a 4coloring of a 3chromatic graph. As an immediate corollary we obtain that it is NPhard to color a kchromatic graph with at most k + 2bk=3c 1 colors. We also give simple proofs of two results of Lund and Yannakakis [20]. The first result shows that it is NPhard to approximate the chromatic number to within n for some fixed > 0. We point