The Longest Common Subsequence (LCS) is one of the most basic similarity measures and it captures important applications in bioinformatics and text analysis. Following the SETH-based nearly-quadratic time lower bounds...
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We consider a generalization of k-median and k-center, called the ordered k-median problem. In this problem, we are given a metric space (D, (cij)) with n = |D| points, and a non-increasing weight vector w ∈ Rn+, and...
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In High Performance Computing, heterogeneity is now the norm with specialized accelerators like GPUs providing efficient computational power. Resulting complexity led to the development of task-based runtime systems, ...
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We give faster and simpler approximation algorithms for the (1, 2)-TSP problem, a well-studied variant of the traveling salesperson problem where all distances between cities are either 1 or 2. Our main results are tw...
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The notions of bounded expansion and nowhere denseness not only o er robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic quest...
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We study the k-median and k-center problems in uncertain graphs. We analyze the hardness of these problems, and propose several algorithms with improved approximation ratios compared with the existing proposals. Copyr...
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The 1-center clustering with outliers problem asks about identifying a prototypical robust statistic that approximates the location of a cluster of points. Given some constant 0 1 2 , and for any normed vector space, ...
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In this work, we study the trade-off between the running time of approximation algorithms and their approximation guarantees. By leveraging a structure of the "hard" instances of the Arora-Rao-Vazirani lemma...
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This paper considers the problem of finding the shortest tour to cover a given set of inverted cone views with apex angle α and height H when their apex points lie on a planar surface. This is a novel variant of the ...
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This paper considers the problem of finding the shortest tour to cover a given set of inverted cone views with apex angle α and height H when their apex points lie on a planar surface. This is a novel variant of the 3D Traveling Salesman Problem with intersecting Neighborhoods (TSPN) called Cone-TSPN. When the cones are allowed to tilt by an angle ε we have the tilted Cone-TSPN problem, to which we present an algorithm that returns a solution with an approximation ratio of O(1+tanα/1-tan ε tan α (1+log max(H)/min(H))). We demonstrate through simulations that our algorithm can be implemented in a practical way and by exploiting the structure of the cones we can achieve shorter tours. Finally, we present results from covering a reflective surface (lake area) that shows the importance of selecting different view angles under strong sunlight specularities.
In many optimization problems, a feasible solution induces a multi-dimensional cost vector. For example, in load-balancing a schedule induces a load vector across the machines. In k-clustering, opening k facilities in...
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In many optimization problems, a feasible solution induces a multi-dimensional cost vector. For example, in load-balancing a schedule induces a load vector across the machines. In k-clustering, opening k facilities induces an assignment cost vector across the clients. Typically, one seeks a solution which either minimizes the sum-or the max-of this vector, and these problems (makespan minimization, kmedian, and k-center) are classic NP-hard problems which have been extensively studied. In this paper we consider the minimum norm optimization problem. Given an arbitrary monotone, symmetric norm, the problem asks to find a solution which minimizes the norm of the induced costvector. These functions are versatile and model a wide range of problems under one umbrella. We give a general framework to tackle the minimum norm problem, and illustrate its efficacy in the unrelated machine load balancing and k-clustering setting. Our concrete results are the following. • We give constant factor approximation algorithms for the minimum norm load balancing problem in unrelated machines, and the minimum norm k-clustering problem. To our knowledge, our results constitute the first constant-factor approximations for such a general suite of objectives. • In load balancing with unrelated machines, we give a 2-approximation for the problem of finding an assignmentminimizing the sumof the largest loads, for any . We give a (2+ϵ)-approximation for the so-called ordered load-balancing problem. • For k-clustering, we give a (5 + ϵ)-approximation for the ordered k-median problem significantly improving the constant factor approximations from Byrka, Sornat, and Spoerhase (STOC 2018) and Chakrabarty and Swamy (ICALP 2018). • Our techniques also imply O(1) approximations to the best simultaneous optimization factor for any instance of the unrelated machine load-balancing and the k-clustering setting. To our knowledge, these are the first positive simultaneous optimization results in these sett
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