Monotonicity Testing and Shortest-Path Routing on the Cube

We study the problem of monotonicity testing over the hypercube. As previously observed in several works, a positive answer to a natural question about routing properties of the hypercube network would imply the existence of efficient monotonicity testers. In particular, if any set of source-sink pairs on the directed hypercube (with all sources and all sinks distinct) can be connected with edge-disjoint paths, then monotonicity of functions f : {0, 1}n R can be tested with O(n/ ) queries, for any totally ordered range R. More generally, if at least an

• Type: Conference
• Year: 2010
• Where: APPROX
• Authors: Jop Briët, Sourav Chakraborty, David García-Soriano, Arie Matsliah
• Keywords: Algorithms, APPROX 2010, Edge-disjoint Paths, Hypercube, Monotonicity