Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Journal of the ACM (JACM)
Rectangular matrix multiplication revisited
Journal of Complexity
Fast rectangular matrix multiplication and applications
Journal of Complexity
Introduction to Algorithms
Group-theoretic Algorithms for Matrix Multiplication
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Finding a maximum weight triangle in n3-Δ time, with applications
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Faster algorithms for finding lowest common ancestors in directed acyclic graphs
Theoretical Computer Science
LCA queries in directed acyclic graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Finding the smallest H-Subgraph in real weighted graphs and related problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Fast algorithms for (max, min)-matrix multiplication and bottleneck shortest paths
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Efficient approximation algorithms for shortest cycles in undirected graphs
Information Processing Letters
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
An exact algorithm for subgraph homeomorphism
Journal of Discrete Algorithms
On exact complexity of subgraph homeomorphism
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Efficient approximation algorithms for shortest cycles in undirected graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
More Algorithms for All-Pairs Shortest Paths in Weighted Graphs
SIAM Journal on Computing
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We show that for any ε 0, a maximum-weight triangle in an undirected graph with n vertices and real weights assigned to vertices can be found in time O(nω + n2+ε), where ω is the exponent of fastest matrix multiplication algorithm. By the currently best bound on ω, the running time of our algorithm is O(n2.376). Our algorithm substantially improves the previous time-bounds for this problem recently established by Vassilevska et al. (STOC 2006, O(n2.688)) and (ICALP 2006, O(n2.575)). Its asymptotic time complexity matches that of the fastest known algorithm for finding a triangle (not necessarily a maximum-weight one) in a graph. By applying or extending our algorithm, we can also improve the upper bounds on finding a maximum-weight triangle in a sparse graph and on finding a maximum-weight subgraph isomorphic to a fixed graph established in the papers by Vassilevska et al. For example, we can find a maximum-weight triangle in a vertex-weighted graph with m edges in asymptotic time required by the fastest algorithm for finding any triangle in a graph with m edges, i.e., in time O(m1.41).