Journal of the ACM (JACM)
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Lower bounds for linear satisfiability problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Finding and counting small induced subgraphs efficiently
Information Processing Letters
Universal Hashing and k-Wise Independent Random Variables via Integer Arithmetic without Primes
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Finding a minimum circuit in a graph
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
On the complexity of fixed parameter clique and dominating set
Theoretical Computer Science
Lower bounds for linear degeneracy testing
Journal of the ACM (JACM)
Subquadratic Algorithms for 3SUM
Algorithmica
Finding paths of length k in O∗(2k) time
Information Processing Letters
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Towards polynomial lower bounds for dynamic problems
Proceedings of the forty-second ACM symposium on Theory of computing
On the possibility of faster SAT algorithms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Subcubic Equivalences between Path, Matrix and Triangle Problems
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Counting and detecting small subgraphs via equations and matrix multiplication
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Faster algorithms for finding and counting subgraphs
Journal of Computer and System Sciences
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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(n3) 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(n2). 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.