1,793 research outputs found
Linear Network Coding for Two-Unicast- Networks: A Commutative Algebraic Perspective and Fundamental Limits
We consider a two-unicast- network over a directed acyclic graph of unit
capacitated edges; the two-unicast- network is a special case of two-unicast
networks where one of the destinations has apriori side information of the
unwanted (interfering) message. In this paper, we settle open questions on the
limits of network coding for two-unicast- networks by showing that the
generalized network sharing bound is not tight, vector linear codes outperform
scalar linear codes, and non-linear codes outperform linear codes in general.
We also develop a commutative algebraic approach to deriving linear network
coding achievability results, and demonstrate our approach by providing an
alternate proof to the previous results of C. Wang et. al., I. Wang et. al. and
Shenvi et. al. regarding feasibility of rate in the network.Comment: A short version of this paper is published in the Proceedings of The
IEEE International Symposium on Information Theory (ISIT), June 201
(Total) Vector Domination for Graphs with Bounded Branchwidth
Given a graph of order and an -dimensional non-negative
vector , called demand vector, the vector domination
(resp., total vector domination) is the problem of finding a minimum
such that every vertex in (resp., in ) has
at least neighbors in . The (total) vector domination is a
generalization of many dominating set type problems, e.g., the dominating set
problem, the -tuple dominating set problem (this is different from the
solution size), and so on, and its approximability and inapproximability have
been studied under this general framework. In this paper, we show that a
(total) vector domination of graphs with bounded branchwidth can be solved in
polynomial time. This implies that the problem is polynomially solvable also
for graphs with bounded treewidth. Consequently, the (total) vector domination
problem for a planar graph is subexponential fixed-parameter tractable with
respectto , where is the size of solution.Comment: 16 page
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