max planck institut
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Title: Algorithmic Results for Clustering and Refined Physarum Analysis Pavel Kolev Max-Planck-Institut für Informatik - D1 Promotionskolloquium D1, D3, D4, RG1, MMCI, D2, D5, SWSWe use this to send out email in the morning. Public Audience English
Date: Tuesday, 27 November 2018 16:15 60 Minutes Saarbrücken E1 5 029
 In the first part of this thesis, we study the Binary $\ell_0$-Rank-$k$ problem which given a binary matrix $A$ and a positive integer $k$, seeks to find a rank-$k$ binary matrix $B$ minimizing the number of non-zero entries of $A-B$. A central open question is whether this problem admits a polynomial time approximation scheme. We give an affirmative answer to this question by designing the first randomized almost-linear time approximation scheme for constant $k$ over the reals, $\mathbb{F}_2$, and the Boolean semiring. In addition, we give novel algorithms for important variants of $\ell_0$-low rank approximation. The second part of this dissertation, studies a popular and successful heuristic, known as Approximate Spectral Clustering (ASC), for partitioning the nodes of a graph $G$ into clusters with small conductance. We give a comprehensive analysis, showing that ASC runs efficiently and yields a good approximation of an optimal $k$-way node partition of $G$. In the final part of this thesis, we present two results on slime mold computations: i) the continuous undirected Physarum dynamics converges for undirected linear programs with a non-negative cost vector; and ii) for the discrete directed Physarum dynamics, we give a refined analysis that yields strengthened and close to optimal convergence rate bounds, and shows that the model can be initialized with any strongly dominating point.
Name(s): Pavel Kolev