
Solving Vertex Cover in Polynomial Time on Hyperbolic Random Graphs
The VertexCover problem is proven to be computationally hard in differen...
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Optimal Distributed Weighted Set Cover Approximation
We present a timeoptimal deterministic distributed algorithm for approx...
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A modified greedy algorithm to improve bounds for the vertex cover number
In any attempt at designing an efficient algorithm for the minimum verte...
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Empirical Evaluation of Real World Tournaments
Computational Social Choice (ComSoc) is a rapidly developing field at th...
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A Note on Degree vs Gap of MinRep Label Cover and Improved Inapproximability for Connectivity Problems
This note concerns the tradeoff between the degree of the constraint gr...
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Optimal Virtual Network Embeddings for Tree Topologies
The performance of distributed and datacentric applications often criti...
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Routing in Strongly Hyperbolic Unit Disk Graphs
Greedy routing has been studied successfully on Euclidean unit disk grap...
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Efficiently Approximating Vertex Cover on ScaleFree Networks with Underlying Hyperbolic Geometry
Finding a minimum vertex cover in a network is a fundamental NPcomplete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing nonoptimal outputs) for an improved running time. For the vertex cover problem, there is a gap between theory and practice when it comes to understanding this tradeoff. On the one hand, it is known that it is NPhard to approximate a minimum vertex cover within a factor of √(2). On the other hand, a simple greedy algorithm yields close to optimal approximations in practice. A promising approach towards understanding this discrepancy is to recognize the differences between theoretical worstcase instances and realworld networks. Following this direction, we close the gap between theory and practice by providing an algorithm that efficiently computes close to optimal vertex cover approximations on hyperbolic random graphs; a network model that closely resembles realworld networks in terms of degree distribution, clustering, and the smallworld property. More precisely, our algorithm computes a (1 + o(1))approximation, asymptotically almost surely, and has a running time of 𝒪(m log(n)). The proposed algorithm is an adaption of the successful greedy approach, enhanced with a procedure that improves on parts of the graph where greedy is not optimal. This makes it possible to introduce a parameter that can be used to tune the tradeoff between approximation performance and running time. Our empirical evaluation on realworld networks shows that this allows for improving over the nearoptimal results of the greedy approach.
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