Near-Optimal Disjoint-Path Facility Location Through Set Cover by Pairs
David S. Johnson, Lee Breslau, Ilias Diakonikolas, Nick Duffield, Yu Gu, MohammadTaghi Hajiaghayi, Howard Karloff, Mauricio G. C. Resende, Subhabrata Sen
Operations Research · 2020 · Volume 68 · Issue 3
Abstract
In this paper, we consider two special cases of the “cover-by-pairs” optimization problem that arises when we need to place facilities so that each customer is served by two facilities that reach it by disjoint shortest paths. These problems arise in a network traffic-monitoring scheme proposed by Breslau et al. and have potential applications to content distribution. The “set-disjoint” variant applies to networks that use the open shortest path first routing protocol, and the “path-disjoint” variant applies when multiprotocol label switching routing is enabled, making better solutions possible at the cost of greater operational expense. Although we can prove that no polynomial-time algorithm can guarantee good solutions for either version, we are able to provide heuristics that do very well in practice on instances with real-world network structure. Fast implementations of the heuristics, made possible by exploiting mathematical observations about the relationship between the network instances and the corresponding instances of the cover-by-pairs problem, allow us to perform an extensive experimental evaluation of the heuristics and what the solutions they produce tell us about the effectiveness of the proposed monitoring scheme. For the set-disjoint variant, we validate our claim of near-optimality via a new lower-bounding integer programming formulation. Although computing this lower bound requires solving the NP-hard hitting set problem and can underestimate the optimal value by a linear factor in the worst case, it can be computed quickly by CPLEX, and it equals the optimal solution value for all the instances in our extensive test bed.
Keywords
communications, facilities/equipment planning: location, networks/graphs: heuristics, Optimization, facility location, network measurement, set cover by pairs, heuristics, path diversity, routing, network tomography
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