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Inapproximability of HTransversal/Packing∗
"... Given an undirected graph G = (VG, EG) and a fixed “pattern ” graph H = (VH, EH) with k vertices, we consider the HTransversal and HPacking problems. The former asks to find the smallest S ⊆ VG such that the subgraph induced by VG \S does not have H as a subgraph, and the latter asks to find the m ..."
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the maximum number of pairwise disjoint ksubsets S1,..., Sm ⊆ VG such that the subgraph induced by each Si has H as a subgraph. We prove that if H is 2connected, HTransversal and HPacking are almost as hard to approximate as general kHypergraph Vertex Cover and kSet Packing, so it is NP
Hardness Of Approximations
, 1996
"... This chapter is a selfcontained survey of recent results about the hardness of approximating NPhard optimization problems. ..."
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Cited by 120 (5 self)
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This chapter is a selfcontained survey of recent results about the hardness of approximating NPhard optimization problems.
Algorithmic and complexity results for decompositions of biological networks into monotone subsystems
 IN LECTURE NOTES IN COMPUTER SCIENCE: EXPERIMENTAL ALGORITHMS: 5TH INTERNATIONAL WORKSHOP, WEA 2006, SPRINGERVERLAG, 253–264. (CALA GALDANA, MENORCA
, 2006
"... A useful approach to the mathematical analysis of largescale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions which are optimal in an appropriate sense. In graphtheoretic la ..."
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Cited by 22 (6 self)
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theoretic language, the problems can be recast in terms of maximal signconsistent subgraphs. The theoretical results include polynomialtime approximation algorithms as well as constantratio inapproximability results. One of the algorithms, which has a worstcase guarantee of 87.9 % from optimality, is based
The computational complexity of the restricted isometry property, the nullspace property, and related concepts in compressed sensing
 IEEE Trans. Inf. Theory
, 2014
"... ar ..."
Revenue Submodularity
 EC'09
, 2009
"... We introduce revenue submodularity, the property that market expansion has diminishing returns on an auction’s expected revenue. We prove that revenue submodularity is generally possible only in matroid markets, that Bayesianoptimal auctions are always revenuesubmodular in such markets, and that t ..."
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Cited by 22 (8 self)
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We introduce revenue submodularity, the property that market expansion has diminishing returns on an auction’s expected revenue. We prove that revenue submodularity is generally possible only in matroid markets, that Bayesianoptimal auctions are always revenuesubmodular in such markets, and that the VCG mechanism is revenuesubmodular in matroid markets with i.i.d. bidders and “sufficient competition”. We also give two applications of revenue submodularity: good approximation algorithms for novel market expansion problems, and approximate revenue guarantees for the VCG mechanism with i.i.d. bidders.
Sketching Valuation Functions
, 2011
"... Motivated by the problem of querying and communicating bidders ’ valuations in combinatorial auctions, we study how well different classes of set functions can be sketched. More formally, let f be a function mapping subsets of some ground set [n] to the nonnegative real numbers. We say that f ′ is ..."
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Cited by 22 (2 self)
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′ is an αsketch of f if for every set S, the value f ′ (S) lies between f(S)/α and f(S), and f ′ can be specified by poly(n) bits. We show that for every subadditive function f there exists an αsketch where α = n 1/2 · O(polylog(n)). Furthermore, we provide an algorithm that finds these sketches with a
Results 1  10
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127