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

Parameterized Algorithms for Load Coloring Problem

One way to state the Load Coloring Problem (LCP) is as follows. Let $G=(V,E)$ be graph and let $f:V\rightarrow \{{\rm red}, {\rm blue}\}$ be a 2-coloring. An edge $e\in E$ is called red (blue) if both end-vertices of $e$ are red (blue). For a 2-coloring $f$, let $r'_f$ and $b'_f$ be the number of red and blue edges and let $\mu_f(G)=\min\{r'_f,b'_f\}$. Let $\mu(G)$ be the maximum of $\mu_f(G)$ over all 2-colorings. We introduce the parameterized problem $k$-LCP of deciding whether $\mu(G)\ge k$, where $k$ is the parameter. We prove that this problem admits a kernel with at most $7k$. 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 $t$ can be found in time $O^*(2^t)$. We also show that either $G$ is a Yes-instance of $k$-LCP or the treewidth of $G$ is at most $2k$. Thus, $k$-LCP can be solved in time $O^*(4^k).

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 $\cal F$ of subsets of a ground set $V$ and an integer $p$, and asked whether $V$ has a $p$-element subset that intersects each set in $\cal F$. We consider two parameterizations of {\sc Hitting Set} below tight upper bounds: $p=m-k$ and $p=n-k$. In both cases $k$ is the parameter. We prove that the first parameterization is fixed-parameter tractable, but has no polynomial kernel unless coNP$\subseteq$NP/poly. The second parameterization is W[1]-complete, but the introduction of an additional parameter, the degeneracy of the hypergraph $H=(V,{\cal F})$, makes the problem not only fixed-parameter tractable, but also one with a linear kernel. Here the degeneracy of $H=(V,{\cal F})$ is the minimum integer $d$ such that for each $X\subset V$ the hypergraph with vertex set $V\setminus X$ and edge set containing all edges of $\cal F$ without vertices in $X$, has a vertex of degree at most $d.$ In {\sc Nonblocker} ({\sc Directed Nonblocker}), we are given an undirected graph (a directed graph) $G$ on $n$ vertices and an integer $k$, and asked whether $G$ has a set $X$ of $n-k$ vertices such that for each vertex $y\not\in X$ there is an edge (arc) from a vertex in $X$ to $y$. {\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