We study the concept of propagation connectivity on random 3-uniform hypergraphs. This concept is inspired by a simple linear time algorithm for solving instances of certain constraint satisfaction problems. We derive upper and lower bounds for the propagation connectivity threshold, and point out some algorithmic implications.
Based on the Belief Propagation Method, we propose simple and determin-istic algorithms for some NP-hard graph partitioning problems, such as the Most Likely Partition problem and the Graph Bisection problem. These algorithms run in O(n + m) or O((n + m) log n) time on graphs with n vertices and m edges. For their average case analysis, we consider the… (More)
This report addresses the problem of identifying a threshold for propagation connectiv-ity in random hypergraphs as specified in [BO09]. In that paper we gave upper and lower bounds for the threshold that left a gap of a factor (log n)(log log n) 2. Unfortunately there is some uncertainty regarding a detail in the lemma that was used to provide the upper… (More)
We consider the problem of computing f m (f m−1 (· · · f 1 (x) · · ·)) where each function f i : R n → R n can be broken up in pairs so that the computation at, e.g., indices k and l involve only the vales of the argument at positions k and l. That is, f j (u)) k def = f + j (u k , u l) and so on. This generalizes " butterfly " algorithms, such as Radix-2… (More)
1 Problem Description Bisection Problem is to patition a given graph G into subgraphs G 1 and G 2 of equal size with minimum number of cut edges, i.e., edges between G 1 and G 2. This problem has been studied extensively by many researchers [1, 2, 4], and several algorithms have been proposed and analyzed both mathematically and experimentally. Here we… (More)