
Travelling on Graphs with Small Highway Dimension
We study the Travelling Salesperson (TSP) and the Steiner Tree problem (...
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Efficient Approximation Schemes for Stochastic Probing and Prophet Problems
Our main contribution is a general framework to design efficient polynom...
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ETHHardness of Approximating 2CSPs and Directed Steiner Network
We study the 2ary constraint satisfaction problems (2CSPs), which can ...
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Approximating the Orthogonality Dimension of Graphs and Hypergraphs
A tdimensional orthogonal representation of a hypergraph is an assignme...
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A constant parameterized approximation for hardcapacitated kmeans
Hardcapacitated kmeans (HCKM) is one of the remaining fundamental prob...
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Principal Fairness: Removing Bias via Projections
Reducing hidden bias in the data and ensuring fairness in algorithmic da...
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How to Sell Information Optimally: an Algorithmic Study
We investigate the algorithmic problem of selling information to agents ...
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Polynomial Time Approximation Schemes for Clustering in Low Highway Dimension Graphs
We study clustering problems such as kMedian, kMeans, and Facility Location in graphs of low highway dimension, which is a graph parameter modeling transportation networks. It was previously shown that approximation schemes for these problems exist, which either run in quasipolynomial time (assuming constant highway dimension) [Feldmann et al. SICOMP 2018] or run in FPT time (parameterized by the number of clusters k, the highway dimension, and the approximation factor) [Becker et al. ESA 2018, Braverman et al. 2020]. In this paper we show that a polynomialtime approximation scheme (PTAS) exists (assuming constant highway dimension). We also show that the considered problems are NPhard on graphs of highway dimension 1.
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