13,701 research outputs found
Parameterized Algorithms for Load Coloring Problem
One way to state the Load Coloring Problem (LCP) is as follows. Let
be graph and let be a 2-coloring. An
edge is called red (blue) if both end-vertices of are red (blue).
For a 2-coloring , let and be the number of red and blue edges
and let . Let be the maximum of
over all 2-colorings.
We introduce the parameterized problem -LCP of deciding whether , where is the parameter. We prove that this problem admits a kernel with
at most . Ahuja et al. (2007) proved that one can find an optimal
2-coloring on trees in polynomial time. We generalize this by showing that an
optimal 2-coloring on graphs with tree decomposition of width can be found
in time . We also show that either is a Yes-instance of -LCP
or the treewidth of is at most . Thus, -LCP can be solved in time
$O^*(4^k).
Insights into the development of strategy from a complexity perspective
This paper provides an account of an ongoing project with an independent school in the UK. The project focuses on a strategy development intervention which, from the start, was systemic in orientation. The intention was to integrate simple systems concepts and approaches into the strategy development process to: address power relations in actively engaging a wide range of stakeholders with the school’s strategy-making process; generate a range of good ideas; and make the strategy-making process transparent in order to inspire stakeholder confidence in, and commitment to, it and its outcomes. This paper describes how seeking to meet these aims entailed a series of workshops during the course of which an awareness of the relevance, in our interpretation, of Complex Adaptive Systems concepts grew
Warrnambool exchange fire: consumer and social impact analysis
How can governments, communities, businesses and individuals prepare for a total communications blackout in the 21st century?
Overview
This report presents the findings of a research project which assessed the social impact of the Warrnambool exchange fire. The fire occurred on November 22, 2012 and caused a telecommunications outage that lasted for about 20 days. The outage affected about 100,000 people in South West Victoria, a region of Australia covering approximately 67,340 square kilometers.
The social impact of the fire was researched by conducting focus groups, by gathering quantitative and qualitative data, and interviewing people affected. The research project findings call for an understanding of the need for government, communities, business and individuals to be prepared for future “extreme events” which result in telecommunications network failures.
This research was supported by a grant from the Australian Communications Consumer Action Network
Kernels for Below-Upper-Bound Parameterizations of the Hitting Set and Directed Dominating Set Problems
In the {\sc Hitting Set} problem, we are given a collection of
subsets of a ground set and an integer , and asked whether has a
-element subset that intersects each set in . We consider two
parameterizations of {\sc Hitting Set} below tight upper bounds: and
. In both cases is the parameter. We prove that the first
parameterization is fixed-parameter tractable, but has no polynomial kernel
unless coNPNP/poly. The second parameterization is W[1]-complete,
but the introduction of an additional parameter, the degeneracy of the
hypergraph , makes the problem not only fixed-parameter
tractable, but also one with a linear kernel. Here the degeneracy of
is the minimum integer such that for each the
hypergraph with vertex set and edge set containing all edges of
without vertices in , has a vertex of degree at most
In {\sc Nonblocker} ({\sc Directed Nonblocker}), we are given an undirected
graph (a directed graph) on vertices and an integer , and asked
whether has a set of vertices such that for each vertex there is an edge (arc) from a vertex in to . {\sc Nonblocker} can be
viewed as a special case of {\sc Directed Nonblocker} (replace an undirected
graph by a symmetric digraph). Dehne et al. (Proc. SOFSEM 2006) proved that
{\sc Nonblocker} has a linear-order kernel. We obtain a linear-order kernel for
{\sc Directed Nonblocker}
New lower bounds for the topological complexity of aspherical spaces
Date of Acceptance: 5/04/2015 15 pages, 4 figuresPeer reviewedPostprin
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