21,464 research outputs found
Triple-loop networks with arbitrarily many minimum distance diagrams
Minimum distance diagrams are a way to encode the diameter and routing
information of multi-loop networks. For the widely studied case of double-loop
networks, it is known that each network has at most two such diagrams and that
they have a very definite form "L-shape''.
In contrast, in this paper we show that there are triple-loop networks with
an arbitrarily big number of associated minimum distance diagrams. For doing
this, we build-up on the relations between minimum distance diagrams and
monomial ideals.Comment: 17 pages, 8 figure
Constrained Submodular Maximization: Beyond 1/e
In this work, we present a new algorithm for maximizing a non-monotone
submodular function subject to a general constraint. Our algorithm finds an
approximate fractional solution for maximizing the multilinear extension of the
function over a down-closed polytope. The approximation guarantee is 0.372 and
it is the first improvement over the 1/e approximation achieved by the unified
Continuous Greedy algorithm [Feldman et al., FOCS 2011]
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