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What and Who
Speaker:Cornelius Brand
coming from:Max-Planck-Institut für Informatik - D1
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
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Level:AG Audience
Date, Time and Location
Date:Thursday, 12 July 2018
Duration:30 Minutes
Building:E1 4
We devise an algorithm that approximately computes the number of paths of length k in a given directed graph with n vertices up to a multiplicative error of 1±ε. Our algorithm runs in time ε^{−2}4^k(n+m)poly(k). The algorithm is based on associating with each vertex an element in the exterior (or, Grassmann) algebra, called an extensor, and then performing computations in this algebra. This connection to exterior algebra generalizes a number of previous approaches for the longest path problem and is of independent conceptual interest. Using this approach, we also obtain a deterministic 2^k⋅poly(n) time algorithm to find a k-path in a given directed graph that is promised to have few of them. Our results and techniques generalize to the subgraph isomorphism problem when the subgraphs we are looking for have bounded pathwidth. Finally, we also obtain a randomized algorithm to detect k-multilinear terms in a multivariate polynomial given as a general algebraic circuit. To the best of our knowledge, this was previously only known for algebraic circuits not involving negative constants.

Joint work with Holger Dell, Thore Husfeldt.
Presented at STOC 2018.

Name(s):Christian Ikenmeyer
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Created:Christian Ikenmeyer, 07/09/2018 12:42 PM Last modified:Uwe Brahm/MPII/DE, 07/12/2018 04:01 AM
  • Christian Ikenmeyer, 07/09/2018 12:42 PM
  • Christian Ikenmeyer, 07/09/2018 12:42 PM -- Created document.