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Exact Weight Subgraphs and the k-Sum Conjecture

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7965)

Abstract

We consider the Exact-Weight-H problem of finding a (not necessarily induced) subgraph H of weight 0 in an edge-weighted graph G. We show that for every H, the complexity of this problem is strongly related to that of the infamous k-sum problem. In particular, we show that under the k-sum Conjecture, we can achieve tight upper and lower bounds for the Exact-Weight-H problem for various subgraphs H such as matching, star, path, and cycle.

One interesting consequence is that improving on the O(n 3) upper bound for Exact-Weight-4-path or Exact-Weight-5-path will imply improved algorithms for 3-sum, 5-sum, All-Pairs Shortest Paths and other fundamental problems. This is in sharp contrast to the minimum-weight and (unweighted) detection versions, which can be solved easily in time O(n 2). We also show that a faster algorithm for any of the following three problems would yield faster algorithms for the others: 3-sum, Exact-Weight-3-matching, and Exact-Weight-3-star.

Keywords

  • Edge Weight
  • Full Version
  • Edge Deletion
  • Subgraph Problem
  • Small Subgraph

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Abboud, A., Lewi, K. (2013). Exact Weight Subgraphs and the k-Sum Conjecture. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_1

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  • DOI: https://doi.org/10.1007/978-3-642-39206-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39205-4

  • Online ISBN: 978-3-642-39206-1

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