Mikael Onsjö

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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)
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)
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)
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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