Additive Approximation for Edge-Deletion Problems
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Szemerédi's regularity lemma and its applications to pairwise clustering and segmentation
EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
Quasi-Randomness and Algorithmic Regularity for Graphs with General Degree Distributions
SIAM Journal on Computing
Approximate Hypergraph Partitioning and Applications
SIAM Journal on Computing
On Computing the Frequencies of Induced Subhypergraphs
SIAM Journal on Discrete Mathematics
A deterministic algorithm for the Frieze-Kannan regularity lemma
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Additive approximation for edge-deletion problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Research paper: Combinatorial and computational aspects of graph packing and graph decomposition
Computer Science Review
A Deterministic Algorithm for the Frieze-Kannan Regularity Lemma
SIAM Journal on Discrete Mathematics
Quasi-randomness and algorithmic regularity for graphs with general degree distributions
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Hi-index | 0.00 |
We present a deterministic algorithm ${\cal A}$ that, in O(m2) time, verifies whether a given m by m bipartite graph G is regular, in the sense of Szemerédi [Regular partitions of graphs, in Problèmes Combinatoires et Théorie des Graphes (Orsay, 1976), Colloques Internationaux CNRS 260, CNRS, Paris, 1978, pp. 399--401]. In the case in which G is not regular enough, our algorithm outputs a witness to this irregularity. Algorithm ${\cal A}$ may be used as a subroutine in an algorithm that finds an $\varepsilon$-regular partition of a given n-vertex graph $\Gamma$ in time O(n2). This time complexity is optimal, up to a constant factor, and improves upon the bound O(M(n)), proved by Alon et al. [The algorithmic aspects of the regularity lemma, J. Algorithms, 16 (1994), pp. 80--109], where M(n)=O(n2.376) is the time required to square a 0--1 matrix over the integers. Our approach is elementary, except that it makes use of linear-sized expanders to accomplish a suitable form of deterministic sampling.