Between O(nm) and O(nα)

Authors:
Dieter Kratsch;Jeremy Spinrad
Affiliations:
LITA, Université de Metz, France;Vanderbilt University, Nashville TN
Venue:
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2003

Citing 9
Cited 15

Matrix multiplication via arithmetic progressions

Journal of Symbolic Computation - Special issue on computational algebraic complexity
An efficient algorithm for finding a two-pair, and its applications

Discrete Applied Mathematics
Triangulating graphs without asteroidal triples

Discrete Applied Mathematics
Asteroidal Triple-Free Graphs

SIAM Journal on Discrete Mathematics
Fast rectangular matrix multiplication and applications

Journal of Complexity
Graph classes: a survey

Graph classes: a survey
Linear Time Algorithms for Dominating Pairs in Asteroidal Triple-free Graphs

SIAM Journal on Computing
Decremental dynamic connectivity

Journal of Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Detecting short directed cycles using rectangular matrix multiplication and dynamic programming

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Computing minimal triangulations in time O(nα log n) = o(n2.376)

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Fast sparse matrix multiplication

ACM Transactions on Algorithms (TALG)
Colored intersection searching via sparse rectangular matrix multiplication

Proceedings of the twenty-second annual symposium on Computational geometry
A wide-range algorithm for minimal triangulation from an arbitrary ordering

Journal of Algorithms
The sandwich problem for cutsets: clique cutset, k-star cutset

Discrete Applied Mathematics - Special issue: Traces of the Latin American conference on combinatorics, graphs and applications: a selection of papers from LACGA 2004, Santiago, Chile
Improved algorithms for weakly chordal graphs

ACM Transactions on Algorithms (TALG)
Dynamic programming and fast matrix multiplication

ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Minimal comparability completions of arbitrary graphs

Discrete Applied Mathematics
Minimal split completions

Discrete Applied Mathematics
A wide-range algorithm for minimal triangulation from an arbitrary ordering

Journal of Algorithms
Algorithms on graphs with small dominating targets

ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Making arbitrary graphs transitively orientable: minimal comparability completions

ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Minimal split completions of graphs

LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Graph expansion analysis for communication costs of fast rectangular matrix multiplication

MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper uses periodic matrix multiplication to improve the time complexities for a number of graph problems. The time for finding a clique cutset in a graph is reduced from O(nm) to O(n2.69), the time for finding an asteroidal triple is reduced to O(n2.82), and the time for finding a star cutset, a two-pair, and a dominating pair is reduced from O(nm) to O(n2.79).It is also shown that each of these problems is at least as hard as one of three basic graph problems for which the best known algorithms run in time O(nm) and O(nα).