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98
Combinatorial auctions: A survey
, 2000
"... Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes and furniture. Because of complementarities (or substitution effects) between the different assets, bidders have preferences not just for particular items but for sets or bundles of items ..."
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Cited by 212 (1 self)
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Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes and furniture. Because of complementarities (or substitution effects) between the different assets, bidders have preferences not just for particular items but for sets or bundles of items. For this reason, economic efficiency is enhanced if bidders are allowed to bid on bundles or combinations of different assets. This paper surveys the state of knowledge about the design of combinatorial auctions. Second, it uses this subject as a vehicle to convey the aspects of integer programming that are relevant for the
On spectrum sharing games
 In proc. of PODC 2004
, 2004
"... Each access point (AP) in a WiFi network must be assigned a channel for it to service users. There are only finitely many possible channels that can be assigned. Moreover, neighboring access points must use different channels so as to avoid interference. Currently these channels are assigned by admi ..."
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Cited by 78 (3 self)
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Each access point (AP) in a WiFi network must be assigned a channel for it to service users. There are only finitely many possible channels that can be assigned. Moreover, neighboring access points must use different channels so as to avoid interference. Currently these channels are assigned by administrators who carefully consider channel conflicts and network loads. Channel conflicts among APs operated by different entities are currently resolved in an ad hoc manner or not resolved at all. We view the channel assignment problem as a game, where the players are the service providers and APs are acquired sequentially. We consider the price of anarchy of this game, which is the ratio between the total coverage of the APs in the worst Nash equilibrium of the game and what the total coverage of the APs would be if the channel assignment were done by a central authority. We provide bounds on the price of anarchy depending on assumptions on the underlying network and the type of bargaining allowed between service providers. The key tool in the analysis is the identification of the Nash equilibria with the solutions to a maximal coloring problem in an appropriate graph. We relate the price of anarchy of these games to the approximation factor of local optimization algorithms for the maximum�colorable subgraph problem. We also study the speed of convergence in these games.
Scheduling Split Intervals
, 2002
"... We consider the problem of scheduling jobs that are given as groups of nonintersecting segments on the real line. Each job Jj is associated with an interval, Ij, which consists of up to t segments, for some t _) 1, a of their segments intersect. Such jobs show up in a I.I Problem Statement and Mo ..."
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Cited by 58 (5 self)
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We consider the problem of scheduling jobs that are given as groups of nonintersecting segments on the real line. Each job Jj is associated with an interval, Ij, which consists of up to t segments, for some t _) 1, a of their segments intersect. Such jobs show up in a I.I Problem Statement and Motivation. We wide range of applications, including the transmission consider the problem of scheduling jobs that are given of continuousmedia data, allocation of linear resources as groups of nonintersecting segments on the real line. (e.g. bandwidth in linear processor arrays), and in Each job Jj is associated with a tinterval, Ij, which
Submodular Maximization Over Multiple Matroids via Generalized Exchange Properties
, 2009
"... Submodularfunction maximization is a central problem in combinatorial optimization, generalizing many important NPhard problems including Max Cut in digraphs, graphs and hypergraphs, certain constraint satisfaction problems, maximumentropy sampling, and maximum facilitylocation problems. Our mai ..."
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Cited by 45 (6 self)
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Submodularfunction maximization is a central problem in combinatorial optimization, generalizing many important NPhard problems including Max Cut in digraphs, graphs and hypergraphs, certain constraint satisfaction problems, maximumentropy sampling, and maximum facilitylocation problems. Our main result is that for any k ≥ 2 and any ε> 0, there is a natural localsearch algorithm which has approximation guarantee of 1/(k + ε) for the problem of maximizing a monotone submodular function subject to k matroid constraints. This improves a 1/(k + 1)approximation of Nemhauser, Wolsey and Fisher, obtained more than 30 years ago. Also, our analysis can be applied to the problem of maximizing a linear objective function and even a general nonmonotone submodular function subject to k matroid constraints. We show that in these cases the approximation guarantees of our algorithms are 1/(k − 1 + ε) and 1/(k + 1 + 1/k + ε), respectively.
Approximation of kSet Cover by SemiLocal Optimization
 In Proc. 29th STOC
, 1997
"... We define a powerful new approximation technique called semilocal optimization. It provides very natural heuristics that are distinctly more powerful than those based on local optimization. With an appropriate metric, semilocal optimization can still be viewed as a local optimization, but it has t ..."
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Cited by 40 (0 self)
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We define a powerful new approximation technique called semilocal optimization. It provides very natural heuristics that are distinctly more powerful than those based on local optimization. With an appropriate metric, semilocal optimization can still be viewed as a local optimization, but it has the advantage of making global changes to an approximate solution. Semilocal optimization generalizes recent heuristics of Halldorsson for 3Set Cover, Color Saving, and kSet Cover. Greatly improved performance ratios of 4/3 for 3Set Cover and 6/5 for Color Saving in graphs without independent sets of size 4 are obtained and shown to be the best possible with semilocal optimization. Also, based on the result for 3Set Cover and a restricted greedy phase for big sets, we can improve the performance ratio for kSet Cover to H k \Gamma 1=2. In Color Saving, when larger independent sets exist, we can improve the performance ratio to .
Performance guarantees of local search for multiprocessor scheduling
 INFORMS Journal on Computing
"... Increasing interest has recently been shown in analyzing the worstcase behavior of local search algorithms. In particular, the quality of local optima and the time needed to find the local optima by the simplest form of local search has been studied. This paper deals with worstcase performance of ..."
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Cited by 37 (4 self)
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Increasing interest has recently been shown in analyzing the worstcase behavior of local search algorithms. In particular, the quality of local optima and the time needed to find the local optima by the simplest form of local search has been studied. This paper deals with worstcase performance of local search algorithms for makespan minimization on parallel machines. We analyze the quality of the local optima obtained by iterative improvement over the jump, swap, multiexchange, and the newly defined push neighborhoods. Finally, for the jump neighborhood we provide bounds on the number of local search steps required to find a local optimum. Key words: productionscheduling: multiple machine; approximation heuristics; local search; analysis of algorithms
ON THE COMPLEXITY OF APPROXIMATING kSET PACKING
 COMPUTATIONAL COMPLEXITY
, 2006
"... Given a kuniform hypergraph, the Maximum kSet Packing problem is to find the maximum disjoint set of edges. We prove that this problem cannot be efficiently approximated to within a factor of Ω(k / ln k) unless P = NP. This improves the previous hardness of approximation factor of k/2 O( √ ln k) ..."
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Cited by 36 (0 self)
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Given a kuniform hypergraph, the Maximum kSet Packing problem is to find the maximum disjoint set of edges. We prove that this problem cannot be efficiently approximated to within a factor of Ω(k / ln k) unless P = NP. This improves the previous hardness of approximation factor of k/2 O( √ ln k) by Trevisan. This result extends to the problem of kDimensionalMatching.
On Local Search for Weighted kSet Packing
, 1997
"... Given a collection of sets of cardinality at most k, with weights for each set, the maximum weighted packing problem is that of finding a collection of disjoint sets of maximum total weight. We study the worst case behavior of the tlocal search heuristic for this problem proving a tight bound of k ..."
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Cited by 35 (3 self)
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Given a collection of sets of cardinality at most k, with weights for each set, the maximum weighted packing problem is that of finding a collection of disjoint sets of maximum total weight. We study the worst case behavior of the tlocal search heuristic for this problem proving a tight bound of k \Gamma 1 + 1 t . As a consequence, for any given r ! 1 k\Gamma1 we can compute in polynomial time a solution whose weight is at least r times the optimal. 1 Introduction Maximum packing problems are among the most often studied in combinatorial optimization: Given a collection X 1 ; : : : ; X q of ksets, find a largest collection of pairwise disjoint sets among them. One of the most fundamental packing problems is that of finding a maximum matching in a graph; this problem is polynomially solvable. However, many other packing problems are NPhard, including maximum 3dimensional matching, maximum triangle packing, maximum H matching, and maximum independent sets of axis parallel recta...
Approximating kSet Cover and Complementary Graph Coloring
"... We consider instances of the Set Cover problem where each set is of small size. For collections of sets of size at most three, we obtain improved performance ratios of 1.4 + ffl, for any constant ffl? 0. Similar improvements hold also for collections of larger sets. A corollary of this result is an ..."
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Cited by 29 (0 self)
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We consider instances of the Set Cover problem where each set is of small size. For collections of sets of size at most three, we obtain improved performance ratios of 1.4 + ffl, for any constant ffl? 0. Similar improvements hold also for collections of larger sets. A corollary of this result is an improved performance ratio of 4/3 for the problem of minimizing the unused colors in a graph coloring.
Local search for the minimum label spanning tree problem with bounded color classes
, 2003
"... In the Minimum Label Spanning Tree problem ..."