433 research outputs found
On Maltsev Digraphs
This is an Open Access article, first published by E-CJ on 25 February 2015.We study digraphs preserved by a Maltsev operation: Maltsev digraphs. We show that these digraphs retract either onto a directed path or to the disjoint union of directed cycles, showing in this way that the constraint satisfaction problem for Maltsev digraphs is in logspace, L. We then generalize results from Kazda (2011) to show that a Maltsev digraph is preserved not only by a majority operation, but by a class of other operations (e.g., minority, Pixley) and obtain a O(|VG|4)-time algorithm to recognize Maltsev digraphs. We also prove analogous results for digraphs preserved by conservative Maltsev operations which we use to establish that the list homomorphism problem for Maltsev digraphs is in L. We then give a polynomial time characterisation of Maltsev digraphs admitting a conservative 2-semilattice operation. Finally, we give a simple inductive construction of directed acyclic digraphs preserved by a Maltsev operation, and relate them with series parallel digraphs.Peer reviewedFinal Published versio
Finding an induced subdivision of a digraph
We consider the following problem for oriented graphs and digraphs: Given an
oriented graph (digraph) , does it contain an induced subdivision of a
prescribed digraph ? The complexity of this problem depends on and on
whether must be an oriented graph or is allowed to contain 2-cycles. We
give a number of examples of polynomial instances as well as several
NP-completeness proofs
Structural Routability of n-Pairs Information Networks
Information does not generally behave like a conservative fluid flow in
communication networks with multiple sources and sinks. However, it is often
conceptually and practically useful to be able to associate separate data
streams with each source-sink pair, with only routing and no coding performed
at the network nodes. This raises the question of whether there is a nontrivial
class of network topologies for which achievability is always equivalent to
routability, for any combination of source signals and positive channel
capacities. This chapter considers possibly cyclic, directed, errorless
networks with n source-sink pairs and mutually independent source signals. The
concept of downward dominance is introduced and it is shown that, if the
network topology is downward dominated, then the achievability of a given
combination of source signals and channel capacities implies the existence of a
feasible multicommodity flow.Comment: The final publication is available at link.springer.com
http://link.springer.com/chapter/10.1007/978-3-319-02150-8_
Routing with Congestion in Acyclic Digraphs
We study the version of the -disjoint paths problem where demand pairs
, , are specified in the input and the paths in
the solution are allowed to intersect, but such that no vertex is on more than
paths. We show that on directed acyclic graphs the problem is solvable in
time if we allow congestion for paths. Furthermore, we
show that, under a suitable complexity theoretic assumption, the problem cannot
be solved in time for any computable function
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