Exact Weight Subgraphs and the k-Sum Conjecture

  title={Exact Weight Subgraphs and the k-Sum Conjecture},
  author={Amir Abboud and Kevin Lewi},
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… 
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Popular Conjectures as a Barrier for Dynamic Planar Graph Algorithms
  • Amir Abboud, Søren Dahlgaard
  • Computer Science, Mathematics
    2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2016
A new framework which is inspired by techniques from the literatures on distance labelling schemes and on parameterized complexity is introduced, showing that no algorithm for dynamic shortest paths or maximum weight bipartite matching in planar graphs can support both updates and queries in amortized O(n1/2-ε) time, unless the classical all-pairs-shortest-paths problem can be solved in truly subcubic time.


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