Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Arboricity and subgraph listing algorithms
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Small-bias probability spaces: efficient constructions and applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
The spatial complexity of oblivious k-probe Hash functions
SIAM Journal on Computing
Computing dominances inEn (short communication)
Information Processing Letters
Witnesses for Boolean matrix multiplication and for transitive closure
Journal of Complexity
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Journal of the ACM (JACM)
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
All pairs shortest paths for graphs with small integer length edges
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Rectangular matrix multiplication revisited
Journal of Complexity
Fast rectangular matrix multiplication and applications
Journal of Complexity
Finding and counting small induced subgraphs efficiently
Information Processing Letters
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Finding Minimally Weighted Subgraphs
WG '90 Proceedings of the 16rd International Workshop on Graph-Theoretic Concepts in Computer Science
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The effect of algebraic structure on the computational complexity of matrix multiplication
The effect of algebraic structure on the computational complexity of matrix multiplication
Detecting short directed cycles using rectangular matrix multiplication and dynamic programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Tight Lower Bounds for Certain Parameterized NP-Hard Problems
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
On the complexity of fixed parameter clique and dominating set
Theoretical 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
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
An O(n3 (loglogn/logn)5/4) time algorithm for all pairs shortest paths
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
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
All-pairs shortest paths with real weights in O(n3/ log n) time
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Greedy localization and color-coding: improved matching and packing algorithms
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Computing the rooted triplet distance between galled trees by counting triangles
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Fast monotone summation over disjoint sets
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Fast monotone summation over disjoint sets
Information Processing Letters
Computing the rooted triplet distance between galled trees by counting triangles
Journal of Discrete Algorithms
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For a graph G with real weights assigned to the vertices (edges), the MAX H-SUBGRAPH problem is to find an H-subgraph of G with maximum total weight, if one exists. Our main results are new strongly polynomial algorithms for the MAX H-SUBGRAPH problem. Some of our algorithms are based, in part, on fast matrix multiplication. For vertex-weighted graphs with n vertices we solve a more general problem: the all pairs MAX H-SUBGRAPH problem, where the task is to find for every pair of vertices u,v, a maximum H-subgraph containing both u and v, if one exists. We obtain an O(nt(ω,h))-time algorithm for the all pairs MAX H-SUBGRAPH problem in the case where H is a fixed graph with h vertices and ω t(ω,h) is determined by solving a small integer program. In particular, heaviest triangles for all pairs can be found in O(n2+1/(4-ω)) ≤ o(n2.616)-time. For h=4,5,8 the running time of our algorithm essentially matches that of the (unweighted) H-subgraph detection problem. Using rectangular matrix multiplication, the value of t(ω,h) can be improved; for example, the runtime for triangles becomes O(n2.575). We also present improved algorithms for the MAX H-SUBGRAPH problem in the edge-weighted case. In particular, we obtain an O(m2−1/k log n)-time algorithm for the heaviest cycle of length 2k or 2k−1 in a graph with m edges and an O(n3/log n)-time randomized algorithm for finding the heaviest cycle of any fixed length. Our methods also yield efficient algorithms for several related problems that are faster than any previously existing algorithms. For example, we show how to find chromatic H-subgraphs in edge-colored graphs, and how to compute the most significant bits of the distance product of two real matrices, in truly subcubic time.