Coalition structure generation over graphs

We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) → R over the subsets of nodes, the problem is to find a partition of N into connected subsets, that maximises the sum of the components values. This problem is generally NP-complete; in particular, it is hard for a defined class of valuation functions which are independent of disconnected members — that is, two nodes have no effect on each others marginal contribution to their vertex separator. Nonetheless, for all such functions we provide bounds on the complexity of coalition structure generation over general and minor free graphs. Our proof is constructive and yields algorithms for solving corresponding instances of the problem. Furthermore, we derive linear time bounds for graphs of bounded treewidth. However, as we show, the problem remains NP-complete for planar graphs, and hence, for any Kk minor free graphs where k ≥ 5. Moreover, a 3-SAT problem with m clauses can be represented by a coalition structure generation problem over a planar graph with O(m2) nodes. Importantly, our hardness result holds for a particular subclass of valuation functions, termed edge sum, where the value of each subset of nodes is simply determined by the sum of given weights of the edges in the induced subgraph

Algorithms for Graph-Constrained Coalition Formation in the Real World

Coalition formation typically involves the coming together of multiple, heterogeneous, agents to achieve both their individual and collective goals. In this paper, we focus on a special case of coalition formation known as Graph-Constrained Coalition Formation (GCCF) whereby a network connecting the agents constrains the formation of coalitions. We focus on this type of problem given that in many real-world applications, agents may be connected by a communication network or only trust certain peers in their social network. We propose a novel representation of this problem based on the concept of edge contraction, which allows us to model the search space induced by the GCCF problem as a rooted tree. Then, we propose an anytime solution algorithm (CFSS), which is particularly efficient when applied to a general class of characteristic functions called $m+a$ functions. Moreover, we show how CFSS can be efficiently parallelised to solve GCCF using a non-redundant partition of the search space. We benchmark CFSS on both synthetic and realistic scenarios, using a real-world dataset consisting of the energy consumption of a large number of households in the UK. Our results show that, in the best case, the serial version of CFSS is 4 orders of magnitude faster than the state of the art, while the parallel version is 9.44 times faster than the serial version on a 12-core machine. Moreover, CFSS is the first approach to provide anytime approximate solutions with quality guarantees for very large systems of agents (i.e., with more than 2700 agents).Comment: Accepted for publication, cite as "in press

A hybrid algorithm for coalition structure generation

The current state-of-the-art algorithm for optimal coalition structure generation is IDP-IP—an algorithm that combines IDP (a dynamic programming algorithm due to Rahwan and Jennings, 2008b) with IP (a tree-search algorithm due to Rahwan et al., 2009). In this paper we analyse IDP-IP, highlight its limitations, and then develop a new approach for combining IDP with IP that overcomes these limitations

Knowing who likes who: The early developmental basis of coalition understanding

Group biases based on broad category membership appear early in human development. However, like many other primates humans inhabit social worlds also characterised by small groups of social coalitions which are not demarcated by visible signs or social markers. A critical cognitive challenge for a young child is thus how to extract information concerning coalition structure when coalitions are dynamic and may lack stable and outwardly visible cues to membership. Therefore, the ability to decode behavioural cues of affiliations present in everyday social interactions between individuals would have conferred powerful selective advantages during our evolution. This would suggest that such an ability may emerge early in life, however, little research has investigated the developmental origins of such processing. The present paper will review recent empirical research which indicates that in the first 2 years of life infants achieve a host of social-cognitive abilities that make them well adapted to processing coalition-affiliations of others. We suggest that such an approach can be applied to better understand the origins of intergroup attitudes and biases. Copyright © 2010 John Wiley & Sons, Ltd

The Socio-Economic Value of Natural Riverbanks in the Netherlands

Ecologists and economists both use a different approach to determine the value of nature. Its ecological value can be measured using criteria like rarity and diversity of species in an ecosystem. The economic value can be determined using non-market valuation techniques. This paper focuses on an empirical application of the Contingent Valuation Method (CVM) to find out whether this valuation method is a suitable method to estimate the economic value of natural riverbanks in the Netherlands. Natural riverbanks will provide habitat for species that particularly depend on the land water transit area. Since common riverbanks do not provide this habitat, natural river banks increase biodiversity in the Netherlands. On the basis of technical and ecological characteristics nine different types of natural riverbanks were distinguished. For each type a laymen description was made. This description served as a basis for economic valuation by means of CVM. The results of the CVM study shows that the average willingness to pay for non-use of a natural riverbank varied between 16 and 25 Dutch guilders per household year. The willingness to pay for recreational use ranged from 1,07 to 2,50 guilders per visit. The generated outcomes proved to be consistent with results from other studies. At first sight, the economic value of natural riverbanks seemed to be higher than their construction and maintenance cost.Nature friendly river banks, Land water interactions, Economic value, Nature, CVM, Non-use value

Uncertainty and risk: politics and analysis

In environmental and sustainable development policy issues, and in infrastructural megaprojects and issues of innovative medical technologies as well, public authorities face emergent complexity, high value diversity, difficult-to-structure problems, high decision stakes, high uncertainty, and thus risk. In practice, it is believed, this often leads to crises, controversies, deadlocks, and policy fiascoes. Decision-makers are said to face a crisis in coping with uncertainty. Both the cognitive structure of uncertainty and the political structure of risk decisions have been studied. So far, these scientific literatures exist side by side, with few apparent efforts at theoretically conceptualizing and empirically testing the links between the two. Therefore, this exploratory and conceptual paper takes up the challenge: How should we conceptualize the cognitive structure of uncertainty? How should we conceptualize the political structure of risk? How can we conceptualize the link(s) between the two? Is there any empirical support for a conceptualization that bridges the analytical and political aspects of risk? What are the implications for guidelines for risk analysis and assessment