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Bypassing UGC from some Optimal Geometric Inapproximability Results
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 177
, 2010
"... The Unique Games conjecture (UGC) has emerged in recent years as the starting point for several optimal inapproximability results. While for none of these results a reverse reduction to Unique Games is known, the assumption of bijective projections in the Label Cover instance seems critical in these ..."
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Cited by 8 (2 self)
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in these proofs. In this work we bypass the UGC assumption in inapproximability results for two geometric problems, obtaining a tight NPhardness result in each case. The first problem known as the Lp Subspace Approximation is a generalization of the classic least squares regression problem. Here, the input
Conditional Inapproximability and Limited Independence
, 2008
"... Understanding the theoretical limitations of efficient computation is one of the most fundamental open problems of modern mathematics. This thesis studies the approximability of intractable optimization problems. In particular, we study socalled Max CSP problems. These are problems in which we are ..."
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Understanding the theoretical limitations of efficient computation is one of the most fundamental open problems of modern mathematics. This thesis studies the approximability of intractable optimization problems. In particular, we study socalled Max CSP problems. These are problems in which we
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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hard to approximate them within a factor of Ω(k) and Ω̃(k) respectively. We also show that there is a 1connected H where HTransversal admits an O(log k)approximation algorithm, so that the connectivity requirement cannot be relaxed from 2 to 1. For a special case of HTransversal where H is a (family of) cycles
Inapproximability Reductions and Integrality Gaps
, 2013
"... In this thesis we prove intractability results for several well studied problems in combinatorial optimization. Closest ..."
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In this thesis we prove intractability results for several well studied problems in combinatorial optimization. Closest
New Results in the Theory of Approximation  Fast Graph Algorithms and Inapproximability
, 2013
"... For several basic optimization problems, it is NPhard to find an exact solution. As a result, understanding the best possible tradeoff between the running time of an algorithm and its approximation guarantee, is a fundamental question in theoretical computer science, and the central goal of the th ..."
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For several basic optimization problems, it is NPhard to find an exact solution. As a result, understanding the best possible tradeoff between the running time of an algorithm and its approximation guarantee, is a fundamental question in theoretical computer science, and the central goal
Inapproximability for planar embedding problems
, 2009
"... We consider the problem of computing a minimumdistortion bijection between two pointsets in R 2.Weprove the first nontrivial inapproximability result for this problem, for the case when the distortion is constant. More precisely, we show that there exist constants 0 <α<β, such that it is NP ..."
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We consider the problem of computing a minimumdistortion bijection between two pointsets in R 2.Weprove the first nontrivial inapproximability result for this problem, for the case when the distortion is constant. More precisely, we show that there exist constants 0 <α<β, such that it is NP
The Unique Games Conjecture and some of its Implications on Inapproximability
, 2005
"... In this report, we study the Unique Games conjecture of Khot [32] and its implications on the hardness of approximating some important optimization problems. The conjecture states that it is NPhard to determine whether the value of a unique 1round game between two provers and a verifier is close t ..."
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In this report, we study the Unique Games conjecture of Khot [32] and its implications on the hardness of approximating some important optimization problems. The conjecture states that it is NPhard to determine whether the value of a unique 1round game between two provers and a verifier is close
Inapproximability for metric embeddings into R d
, 2008
"... We consider the problem of computing the smallest possible distortion for embedding of a given npoint metric space into R d, where d is fixed (and small). For d = 1, it was known that approximating the minimum distortion with a factor better than roughly n 1/12 is NPhard. From this result we deriv ..."
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Cited by 2 (1 self)
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derive inapproximability with factor roughly n 1/(22d−10) for every fixed d ≥ 2, by a conceptually very simple reduction. However, the proof of correctness involves a nontrivial result in geometric topology (whose current proof is based on ideas due to Jussi Väisälä). For d ≥ 3, we obtain a stronger
INAPPROXIMABILITY FOR METRIC EMBEDDINGS INTO R d
"... Abstract. We consider the problem of computing the smallest possible distortion for embedding of a given npoint metric space into R d,whered is fixed (and small). For d = 1, it was known that approximating the minimum distortion with a factor better than roughly n 1/12 is NPhard. From this result ..."
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we derive inapproximability with a factor roughly n 1/(22d−10) for every fixed d ≥ 2, by a conceptually very simple reduction. However, the proof of correctness involves a nontrivial result in geometric topology (whose current proof is based on ideas due to Jussi Väisälä). For d ≥ 3, we obtain a
Results 1  10
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24,493