Upper and lower time bounds for parallel random access machines without simultaneous writes
SIAM Journal on Computing
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
The critical complexity of all (monotone) Boolean functions and monotone graph properties
FCT '85 Fundamentals of Computation Theory
Bounds on the time for parallel RAM's to compute simple functions
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
An improved lower bound on the sensitivity complexity of graph properties
Theoretical Computer Science
| Hi-index | 5.23 |
Sensitivity complexity, introduced by Cook, Dwork, and Reischuk (1982, 1986) in [2,3], is an important complexity measure of Boolean functions. Turan (1984) [7] initiated the study of sensitivity complexity for graph properties. He conjectured that for any non-trivial graph property on n vertices, the sensitivity complexity is at least n-1. He proved that it is greater than n/4 in his paper. Wegener (1985) [8] verified this conjecture for all monotone graph properties. Recently Sun (2011) [6] improved the lower bound to 617n for general graph properties. We follow their steps and investigate the sensitivity complexity of bipartite graph properties. In this paper we propose the following conjecture about the sensitivity of bipartite graph properties, which can be considered as the bipartite analogue of Turan's conjecture: for any non-trivial nxm bipartite graph property f, s(f)=max{@?n+1m+1m@?,@?m+1n+1n@?}. We prove this conjecture for all nx2 bipartite graph properties. For general nxm bipartite graph properties, we show a max{@?n/2@?,@?m/2@?} lower bound. We also prove this conjecture when the bipartite graph property can be written as a composite function.