Masaki Yamamoto

An improved constant-time approximation algorithm for maximum~matchings

This paper studies approximation algorithms for problems on degree-bounded graphs. Let n and d be the number of vertices and the degree bound, respectively. This paper presents an algorithm to approximate the size of some maximal independent set with additive error ε n whose running time is O(d2). Using this algorithm, it also shows that there are approximation algorithms for many other problems, e.g., the maximum matching problem, the minimum vertex cover problem, and the minimum set cover problem, that run exponentially faster than existing algorithms with respect to d and 1/ε. Its approximation algorithm for the maximum matching problem can be transformed to a testing algorithm for the property of having a perfect matching with two-sided error. On the contrary, it also shows that every one-sided error tester for the property requires at least Ω(n) queries.

Improved Constant-Time Approximation Algorithms for Maximum Matchings and Other Optimization Problems

We study constant-time approximation algorithms for bounded-degree graphs, which run in time independent of the number of vertices

An exact algorithm for the Boolean connectivity problem for k-CNF

n

Determining a Singleton Attractor of a Boolean Network with Nested Canalyzing Functions

. We present an algorithm that decides whether a vertex is contained in a some fixed maximal independent set with expected query complexity

An Improved Exact Algorithm for the Domatic Number Problem

O(d^2)

Derandomizing HSSW algorithm for 3-SAT

, where

On the Boolean connectivity problem for Horn relations

d

Average-case analysis for the MAX-2SAT problem

is the degree bound. Using this algorithm, we show constant-time approximation algorithms with certain multiplicative error and additive error

Derandomizing the HSSW Algorithm for 3-SAT

epsilon n

Approximately counting paths and cycles in a graph

for many other problems, e.g., the maximum matching problem, the minimum vertex cover problem, and the minimum set cover problem, that run exponentially faster than existing algorithms with respect to