Correlation Clustering Based Coalition Formation For Multi-Robot Task Allocation

In this paper, we study the multi-robot task allocation problem where a group of robots needs to be allocated to a set of tasks so that the tasks can be finished optimally. One task may need more than one robot to finish it. Therefore the robots need to form coalitions to complete these tasks. Multi-robot coalition formation for task allocation is a well-known NP-hard problem. To solve this problem, we use a linear-programming based graph partitioning approach along with a region growing strategy which allocates (near) optimal robot coalitions to tasks in a negligible amount of time. Our proposed algorithm is fast (only taking 230 secs. for 100 robots and 10 tasks) and it also finds a near-optimal solution (up to 97.66% of the optimal). We have empirically demonstrated that the proposed approach in this paper always finds a solution which is closer (up to 9.1 times) to the optimal solution than a theoretical worst-case bound proved in an earlier work

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

Network Members Can Hide from Group Centrality Measures

Group centrality measures are a generalization of standard centrality, designed to quantify the importance of not just a single node (as is the case with standard measures) but rather that of a group of nodes. Some nodes may have an incentive to evade such measures, i.e., to hide their actual importance, in order to conceal their true role in the network. A number of studies have been proposed in the literature to understand how nodes can rewire the network in order to evade standard centrality, but no study has focused on group centrality to date. We close this gap by analyzing four group centrality measures: degree, closeness, betweenness, and GED-walk. We show that an optimal way to rewire the network can be computed efficiently given the former measure, but the problem is NP-complete given closeness and betweenness. Moreover, we empirically evaluate a number of hiding strategies, and show that an optimal way to hide from degree group centrality is also effective in practice against the other measures. Altogether, our results suggest that it is possible to hide from group centrality measures based solely on the local information available to the group members about the network topology

Matchings with externalities and attitudes

Two-sided matchings are an important theoretical tool used to model markets and social interactions. In many real-life problems the utility of an agent is influenced not only by their own choices, but also by the choices that other agents make. Such an influence is called an externality. Whereas fully expressive representations of externalities in matchings require exponential space, in this paper we propose a compact model of externalities, in which the influence of a match on each agent is computed additively. Under this framework, we analyze many-to-many matchings and one-to-one matchings where agents take different attitudes when reasoning about the actions of others. In particular, we study optimistic, neutral and pessimistic attitudes and provide both computational hardness results and polynomial-time algorithms for computing stable outcomes

Computational Aspects of Extending the Shapley Value to Coalitional Games with Externalities

Until recently, computational aspects of the Shapley value were only studied under the assumption that there are no externalities from coalition formation, i.e., that the value of any coalition is independent of other coalitions in the system. However, externalities play a key role in many real-life situations and have been extensively studied in the game-theoretic and economic literature. In this paper, we consider the issue of computing extensions of the Shapley value to coalitional games with externalities proposed by Myerson [21], Pham Do and Norde [23], and McQuillin [17]. To facilitate efficient computation of these extensions, we propose a new representation for coalitional games with externalities, which is based on weighted logical expressions. We demonstrate that this representation is fully expressive and, sometimes, exponentially more concise than the conventional partition function game model. Furthermore, it allows us to compute the aforementioned extensions of the Shapley value in time linear in the size of the input