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- Amin Coja-Oghlan, Mikael Onsjö, Osamu Watanabe
- APPROX-RANDOM
- 2009

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.

We consider the problem of computing fm(fm−1(· · ·f1(x) · · · )) where each function f i : R → R 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 (uk, ul) and so on. This generalizes “butterfly” algorithms, such as Radix-2 for computing… (More)

- Mikael Onsjö, Osamu Watanabe
- ISAAC
- 2006

Based on the Belief Propagation Method, we propose simple and deterministic 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 planted… (More)

- Robert Berke, Mikael Onsjo, Mikael Onsjö
- 2009

This report addresses the problem of identifying a threshold for propagation connectivity 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). Unfortunately there is some uncertainty regarding a detail in the lemma that was used to provide the upper… (More)

Bisection Problem is to patition a given graph G into subgraphs G1 and G2 of equal size with minimum number of cut edges, i.e., edges between G1 and G2. 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 propose yet another algorithm… (More)

- Mikael Onsjö, Osamu Watanabe
- Theory of Computing Systems
- 2007

- Mikael Onsjö, Osamu Watanabe
- Theory of Computing Systems
- 2009

As a framework for simple but basic statistical inference problems we introduce the genetic Most Likely Solution problem, the task of finding a most likely solution (MLS in short) for a given problem instance under some given probability model. Although many MLS problems are NP-hard, we propose for these problems, to study their average-case complexity… (More)

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