779 research outputs found
Fast algorithms for min independent dominating set
We first devise a branching algorithm that computes a minimum independent
dominating set on any graph with running time O*(2^0.424n) and polynomial
space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A
branch-and-reduce algorithm for finding a minimum independent dominating set in
graphs, Proc. WG'06). We then show that, for every r>3, it is possible to
compute an r-((r-1)/r)log_2(r)-approximate solution for min independent
dominating set within time O*(2^(nlog_2(r)/r))
On Finding Optimal Polytrees
Inferring probabilistic networks from data is a notoriously difficult task.
Under various goodness-of-fit measures, finding an optimal network is NP-hard,
even if restricted to polytrees of bounded in-degree. Polynomial-time
algorithms are known only for rare special cases, perhaps most notably for
branchings, that is, polytrees in which the in-degree of every node is at most
one. Here, we study the complexity of finding an optimal polytree that can be
turned into a branching by deleting some number of arcs or nodes, treated as a
parameter.
We show that the problem can be solved via a matroid intersection formulation
in polynomial time if the number of deleted arcs is bounded by a constant. The
order of the polynomial time bound depends on this constant, hence the
algorithm does not establish fixed-parameter tractability when parameterized by
the number of deleted arcs. We show that a restricted version of the problem
allows fixed-parameter tractability and hence scales well with the parameter.
We contrast this positive result by showing that if we parameterize by the
number of deleted nodes, a somewhat more powerful parameter, the problem is not
fixed-parameter tractable, subject to a complexity-theoretic assumption.Comment: (author's self-archived copy
On Finding Optimal Polytrees
Peer reviewe
Evolutionary branching in a stochastic population model with discrete mutational steps
Evolutionary branching is analysed in a stochastic, individual-based
population model under mutation and selection. In such models, the common
assumption is that individual reproduction and life career are characterised by
values of a trait, and also by population sizes, and that mutations lead to
small changes in trait value. Then, traditionally, the evolutionary dynamics is
studied in the limit of vanishing mutational step sizes. In the present
approach, small but non-negligible mutational steps are considered. By means of
theoretical analysis in the limit of infinitely large populations, as well as
computer simulations, we demonstrate how discrete mutational steps affect the
patterns of evolutionary branching. We also argue that the average time to the
first branching depends in a sensitive way on both mutational step size and
population size.Comment: 12 pages, 8 figures. Revised versio
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