
On the Parameterized Complexity of the Connected Flow and Many Visits TSP Problem
We study a variant of Min Cost Flow in which the flow needs to be connec...
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Polylogarithmic Approximation Algorithm for kConnected Directed Steiner Tree on QuasiBipartite Graphs
In the kConnected Directed Steiner Tree problem (kDST), we are given a...
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Separating Colored Points with Minimum Number of Rectangles
In this paper we study the following problem: Given k disjoint sets of p...
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A Constant Factor Approximation for Navigating Through Connected Obstacles in the Plane
Given two points s and t in the plane and a set of obstacles defined by ...
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An Õ(n^5/4) Time εApproximation Algorithm for RMS Matching in a Plane
The 2Wasserstein distance (or RMS distance) is a useful measure of simi...
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Improved approximation ratios for two Euclidean maximum spanning tree problems
We study the following two maximization problems related to spanning tre...
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Network Optimization on Partitioned Pairs of Points
Given n pairs of points, S = {{p_1, q_1}, {p_2, q_2}, ..., {p_n, q_n}}, ...
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On Minimum Generalized Manhattan Connections
We consider minimumcardinality Manhattan connected sets with arbitrary demands: Given a collection of points P in the plane, together with a subset of pairs of points in P (which we call demands), find a minimumcardinality superset of P such that every demand pair is connected by a path whose length is the ℓ_1distance of the pair. This problem is a variant of three wellstudied problems that have arisen in computational geometry, data structures, and network design: (i) It is a nodecost variant of the classical Manhattan network problem, (ii) it is an extension of the binary search tree problem to arbitrary demands, and (iii) it is a special case of the directed Steiner forest problem. Since the problem inherits basic structural properties from the context of binary search trees, an O(log n)approximation is trivial. We show that the problem is NPhard and present an O(√(log n))approximation algorithm. Moreover, we provide an O(loglog n)approximation algorithm for complete bipartite demands as well as improved results for unitdisk demands and several generalizations. Our results crucially rely on a new lower bound on the optimal cost that could potentially be useful in the context of BSTs.
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