Tight Analysis of a Multiple-Swap Heurstic for Budgeted Red-Blue Median

Authors Zachary Friggstad, Yifeng Zhang

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Zachary Friggstad
Yifeng Zhang

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Zachary Friggstad and Yifeng Zhang. Tight Analysis of a Multiple-Swap Heurstic for Budgeted Red-Blue Median. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 75:1-75:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


Budgeted Red-Blue Median is a generalization of classic k-Median in that there are two sets of facilities, say R and B, that can be used to serve clients located in some metric space. The goal is to open kr facilities in R and kb facilities in B for some given bounds kr, kb and connect each client to their nearest open facility in a way that minimizes the total connection cost. We extend work by Hajiaghayi, Khandekar, and Kortsarz [2012] and show that a multipleswap local search heuristic can be used to obtain a (5 + epsilon)-approximation for Budgeted RedBlue Median for any constant epsilon > 0. This is an improvement over their single swap analysis and beats the previous best approximation guarantee of 8 by Swamy [2014]. We also present a matching lower bound showing that for every p >= 1, there are instances of Budgeted Red-Blue Median with local optimum solutions for the p-swap heuristic whose cost is 5 + Omega(1/p) times the optimum solution cost. Thus, our analysis is tight up to the lower order terms. In particular, for any epsilon > 0 we show the single-swap heuristic admits local optima whose cost can be as bad as 7 - epsilon times the optimum solution cost.
  • Approximation Algorithms
  • Local search
  • Red-Blue Meidan


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