
New Approximation Algorithms for Maximum Asymmetric Traveling Salesman and Shortest Superstring
In the maximum asymmetric traveling salesman problem (Max ATSP) we are g...
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Approximating Nash Social Welfare under Rado Valuations
We consider the problem of approximating maximum Nash social welfare (NS...
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A ConstantFactor Approximation for Directed Latency in QuasiPolynomial Time
We give the first constantfactor approximation for the Directed Latency...
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Maximum Coverage with Cluster Constraints: An LPBased Approximation Technique
Packing problems constitute an important class of optimization problems,...
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Approximating Nash Social Welfare under Submodular Valuations through (Un)Matchings
We study the problem of approximating maximum Nash social welfare (NSW) ...
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Maximizing Determinants under Matroid Constraints
Given vectors v_1,…,v_n∈ℝ^d and a matroid M=([n],I), we study the proble...
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Lopsided Approximation of Amoebas
The amoeba of a Laurent polynomial is the image of the corresponding hyp...
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Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem
We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximumlength edge) cost. We achieve an O(log n / log log n) approximation performance guarantee by giving a novel algorithmic technique to shortcut Eulerian circuits while bounding the lengths of the shortcuts needed. This allows us to build on a related result of Asadpour, Goemans, Mądry, Oveis Gharan, and Saberi to obtain this guarantee. Furthermore, we show how our technique yields stronger approximation bounds in some cases, such as the bounded orientable genus case studied by Oveis Gharan and Saberi. We also explore the possibility of further improvement upon our main result through a comparison to the symmetric counterpart of the problem.
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