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What and Who
Title:Enumeration of ({0}, {2})-Dominations
Speaker:Oussam Mustapha Larkem
coming from:University of Lorraine – France
Speakers Bio:Master of Science
Event Type:PhD Application Talk
Visibility:D1, D2, D3, D4, D5, SWS, RG1, MMCI
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Level:Public Audience
Date, Time and Location
Date:Monday, 10 February 2014
Duration:90 Minutes
Building:E1 4
Let 𝜎 and 𝜌 be two subsets of non-negative integers, a vertex subset S βŠ† V of an undirected graph G(V, E) is called a (𝜎, 𝜌)-dominating set of G if |N(v) ∩ S| ∈ 𝜎 for v ∈ S and |N(v) ∩ S| ∈𝜌 for all v ∈ V \S.

The talk will begin with a quick introduction to branching algorithms and then will cover a selected result from the master thesis, namely the enumeration of all ({0}, {2})-dominations in time O*(1.2546n) and a lower bound of Ξ©(1.2009n), by giving a sequence of graphs that contains (asymptotically) that many ({0}, {2})-dominations. In our case some graph invariants that, if small, allow a good running time, can not be both high but expressing them exactly one in function of the others turns out to be too complicated, so here we use computer aided analysis of subgraphs of bounded size to obtain the low running time stated above. If the time permits it, a second enumeration result being an algorithm enumerating a generalization of Independent Set i.e. ({0,1},β„•)-dominations will be presented.

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  • Aaron Alsancak, 02/06/2014 10:50 AM
  • Aaron Alsancak, 02/06/2014 10:48 AM -- Created document.