On Parameterized Complexity of Group Activity Selection Problems on Social Networks

In Group Activity Selection Problem (GASP), players form coalitions to participate in activities and have preferences over pairs of the form (activity, group size). Recently, Igarashi et al. have initiated the study of group activity selection problems on social networks (gGASP): a group of players can engage in the same activity if the members of the group form a connected subset of the underlying communication structure. Igarashi et al. have primarily focused on Nash stable outcomes, and showed that many associated algorithmic questions are computationally hard even for very simple networks. In this paper we study the parameterized complexity of gGASP with respect to the number of activities as well as with respect to the number of players, for several solution concepts such as Nash stability, individual stability and core stability. The first parameter we consider in the number of activities. For this parameter, we propose an FPT algorithm for Nash stability for the case where the social network is acyclic and obtain a W[1]-hardness result for cliques (i.e., for classic GASP); similar results hold for individual stability. In contrast, finding a core stable outcome is hard even if the number of activities is bounded by a small constant, both for classic GASP and when the social network is a star. Another parameter we study is the number of players. While all solution concepts we consider become polynomial-time computable when this parameter is bounded by a constant, we prove W[1]-hardness results for cliques (i.e., for classic GASP).Comment: 9 pages, long version of accepted AAMAS-17 pape

Group Activity Selection with Few Agent Types

The Group Activity Selection Problem (GASP) models situations where a group of agents needs to be distributed to a set of activities while taking into account preferences of the agents w.r.t. individual activities and activity sizes. The problem, along with its well-known variants sGASP and gGASP, has previously been studied in the parameterized complexity setting with various parameterizations, such as number of agents, number of activities and solution size. However, the complexity of the problem parameterized by the number of types of agents, a natural parameter proposed already in the first paper that introduced GASP, has so far remained unexplored. In this paper we establish the complexity map for GASP, sGASP and gGASP when the number of types of agents is the parameter. Our positive results, consisting of one fixed-parameter algorithm and one XP algorithm, rely on a combination of novel Subset Sum machinery (which may be of general interest) and identifying certain compression steps which allow us to focus on solutions which are "acyclic". These algorithms are complemented by matching lower bounds, which among others close a gap to a recently obtained tractability result of Gupta, Roy, Saurabh and Zehavi (2017). In this direction, the techniques used to establish W[1]-hardness of sGASP are of particular interest: as an intermediate step, we use Sidon sequences to show the W[1]-hardness of a highly restricted variant of multi-dimensional Subset Sum, which may find applications in other settings as well

Fair Resource Sharing with Externailities

We study a fair resource sharing problem, where a set of resources are to be shared among a set of agents. Each agent demands one resource and each resource can serve a limited number of agents. An agent cares about what resource they get as well as the externalities imposed by their mates, whom they share the same resource with. Apparently, the strong notion of envy-freeness, where no agent envies another for their resource or mates, cannot always be achieved and we show that even to decide the existence of such a strongly envy-free assignment is an intractable problem. Thus, a more interesting question is whether (and in what situations) a relaxed notion of envy-freeness, the Pareto envy-freeness, can be achieved: an agent i envies another agent j only when i envies both the resource and the mates of j. In particular, we are interested in a dorm assignment problem, where students are to be assigned to dorms with the same capacity and they have dichotomous preference over their dorm-mates. We show that when the capacity of the dorms is 2, a Pareto envy-free assignment always exists and we present a polynomial-time algorithm to compute such an assignment; nevertheless, the result fails to hold immediately when the capacities increase to 3, in which case even Pareto envy-freeness cannot be guaranteed. In addition to the existential results, we also investigate the implications of envy-freeness on proportionality in our model and show that envy-freeness in general implies approximations of proportionality

Anonymous hedonic game for task allocation in a large-scale multiple agent system

This paper proposes a novel game-theoretical autonomous decision-making framework to address a task allocation problem for a swarm of multiple agents. We consider cooperation of self-interested agents, and show that our proposed decentralized algorithm guarantees convergence of agents with social inhibition to a Nash stable partition (i.e., social agreement) within polynomial time. The algorithm is simple and executable based on local interactions with neighbor agents under a strongly connected communication network and even in asynchronous environments. We analytically present a mathematical formulation for computing the lower bound of suboptimality of the outcome, and additionally show that at least 50% of suboptimality can be guaranteed if social utilities are nondecreasing functions with respect to the number of coworking agents. The results of numerical experiments confirm that the proposed framework is scalable, fast adaptable against dynamical environments, and robust even in a realistic situation

Effective task allocation frameworks for large-scale multiple agent systems.

This research aims to develop innovative and transformative decision-making frameworks that enable a large-scale multi-robot system, called robotic swarm, to autonomously address multi-robot task allocation problem: given a set of complicated tasks, requiring cooperation, how to partition themselves into subgroups (or called coalitions) and assign the subgroups to each task while maximising the system performance. The frameworks should be executable based on local information in a decentralised manner, operable for a wide range of the system size (i.e., scalable), predictable in terms of collective behaviours, adaptable to dynamic environments, operable asynchronously, and preferably able to accommodate heterogeneous agents. Firstly, for homogeneous robots, this thesis proposes two frameworks based on biological inspiration and game theories, respectively. The former, called LICA-MC (Markov-Chan-based approach under Local Information Consistency Assumption), is inspired by fish in nature: despite insufficient awareness of the entire group, they are well-coordinated by sensing social distances from neighbours. Analogously, each agent in the framework relies only on local information and requires its local consistency over neighbouring agents to adaptively generate the stochastic policy. This feature offers various advantages such as less inter-agent communication, a shorter timescale for using new information, and the potential to accommodate asynchronous behaviours of agents. We prove that the agents can converge to a desired collective status without resorting to any global information, while maintaining scalability, flexibility, and long-term system efficiency. Numerical experiments show that the framework is robust in a realistic environment where information sharing over agents is partially and temporarily disconnected. Furthermore, we explicitly present the design requirements to have all these advantages, and implementation examples concerning travelling costs minimisation, over-congestion avoidance, and quorum models, respectively. The game-theoretical framework, called GRAPE (GRoup Agent Partitioning and placing Event), regards each robot as a self-interested player attempting to join the most preferred coalition according to its individual preferences regarding the size of each coalition. We prove that selfish agents who have social inhibition can always converge to a Nash stable partition (i.e., a social agreement) within polynomial time under the proposed framework. The framework is executable based on local interactions with neighbour agents under a strongly-connected communication network and even in asynchronous environments. This study analyses an outcome’s minimum-guaranteed suboptimality, and additionally shows that at least 50% is guaranteed if social utilities are non-decreasing functions with respect to the number of co-working agents. Numerical experiments confirm that the framework is scalable, fast adaptable against dynamical environments, and robust even in a realistic situation where some of the agents temporarily halt operation during a mission. The two proposed frameworks are compared in the domain of division of labour. Empirical results show that LICA-MC provides excellent scalability with respect to the number of agents, whereas GRAPE has polynomial complexity but is more efficient in terms of convergence time (especially when accommodating a moderate number of robots) and total travelling costs. It also turns out that GRAPE is sensitive to traffic congestion, meanwhile LICA-MC suffers from slower robot speed. We discuss other implicit advantages of the frameworks such as mission suitability and additionally-builtin decision-making functions. Importantly, it is found that GRAPE has the potential to accommodate heterogeneous agents to some extent, which is not the case for LICA-MC. Accordingly, this study attempts to extend GRAPE to incorporate the heterogeneity of agents. Particularly, we consider the case where each task has its minimum workload requirement to be fulfilled by multiple agents and the agents have different work capacities and costs depending on the tasks. The objective is to find an assignment that minimises the total cost of assigned agents while satisfying the requirements. GRAPE cannot be directly used because of the heterogeneity, so we adopt tabu-learning heuristics where an agent penalises its previously chosen coalition whenever it changes decision: this variant is called T-GRAPE. We prove that, by doing so, a Nash stable partition is always guaranteed to be determined in a decentralised manner. Experi-mental results present the properties of the proposed approach regarding suboptimality and algorithmic complexity. Finally, the thesis addresses a more complex decision-making problem involving team formation, team-to-task assignment, agent-to-working-position selection, fair resource allocation concerning tasks’ minimum requirements for completion, and trajectory optimisation with collision avoidance. We propose an integrated framework that decouples the original problem into three subproblems (i.e., coalition formation, position allocation, and path planning) and deals with them sequentially by three respective modules. The coalition formation module based on T-GRAPE deals with a max-min problem, balancing the work resources of agents in proportion to the task’s requirements. We show that, given reasonable assumptions, the position allocation subproblem can be solved efficiently in terms of computational complexity. For the path planning, we utilise an MPC-SCP (Model Predictive Control and Sequential Convex Programming) approach that enables the agents to produce collision-free trajectories. As a proof of concept, we implement the framework into a cooperative stand-in jamming mission scenario using multiple UAVs. Numerical experiments suggest that the framework could be computationally feasible, fault-tolerant, and near-optimal. Comparison of the proposed frameworks for multi-robot task allocation is discussed in the last chapter regarding the desired features described at first (i.e., decentralisation, scalability, predictability, flexibility, asynchronisation, heterogeneity), along with future work and possible applications in other domains.PhD in Aerospac

Gerechte Zuordnungen: Kollektive Entscheidungsprobleme aus der Perspektive von Mathematik und theoretischer Informatik

Wir untersuchen verschiedene Fragestellungen der Sozialwahltheorie aus Sicht der Computational Social Choice. Für ein Problem, das in Bezug zu einem Kollektiv von Agenten steht (z.B. Aufteilungen von Ressourcen oder Repräsentantenwahlen), stehen verschiedene Alternativen als Lösung zur Verfügung; ein wesentlicher Aspekt sind dabei die diversen Pr\"aferenzen der Agenten gegenüber den Alternativen. Die Qualität der Lösungen wird anhand von Kriterien aus den Sozialwissenschaften (Fairness), der Spieltheorie (Stabilität) und den Wirtschaftswissenschaften (Effizienz) charakterisiert. In Computational Social Choice werden solche Fragestellungen mit Werkzeugen der Mathematik (z.B. Logik und Kombinatorik) und Informatik (z.B. Komplexitätstheorie und Algorithmik) behandelt. Als roter Faden zieht sich die Frage nach sogenannten "`gerechten Zuordnungen"' durch die Dissertation. Für die Zuordnung von Gütern zu Agenten zeigen wir, wie mithilfe eines dezentralisierten Ansatzes Zuordnungen gefunden werden können, die Ungleichheit minimieren. Wir analysieren das Verhalten dieses Ansatzes für Worst-Case-Instanzen und benutzen dabei eine innovative Beweismethode, die auf impliziten rekursiven Konstruktionen unter Verwendung von Argumenten der Infinitesimalrechnung beruht. Bei der Zuordnung von Agenten zu Aktivitäten betrachten wir das vereinfachte Szenario, in dem die Agenten Präferenzen bezüglich der Aktivitäten haben und die Menge der zulässigen Zuordnungen Beschränkungen bezüglich der Teilnehmerzahlen pro Aktivität unterliegt. Wir führen verschiedene Lösungskonzepte ein und erläutern die Zusammenhänge und Unterschiede dieser Konzepte. Die zugehörigen Entscheidungsprobleme zur Existenz und Maximalität entsprechender Zuordnungen unterziehen wir einer ausführlichen Komplexitätsanalyse. Zuordnungsprobleme können auch als Auktionen aufgefasst werden. Wir betrachten ein Szenario, in dem die Agenten Gebote auf Transformationen von Gütermengen abgeben. In unserem Modell sind diese durch die Existenz von Gütern charakterisiert, die durch die Transformationen nicht verbraucht werden. Von Interesse sind die Kombinationen von Transformationen, die den Gesamtnutzen maximieren. Wir legen eine (parametrisierte) Komplexitätsanalyse dieses Modells vor. Etwas abseits der Grundfragestellung liegen unsere Untersuchungen zu kombinierten Wettkämpfen. Diese interpretieren wir als Wahlproblem, d.h. als Aggregation von Ordnungen. Wir untersuchen die Anfälligkeit für Manipulationen durch die Athleten.We investigate questions from social choice theory from the viewpoint of computational social choice. We consider the setting that a group of agents faces a collective decision problem (e.g., resource allocation or the choice of a representative): they have to choose among various alternatives. A crucial aspect are the agents' individual preferences over these alternatives. The quality of the solutions is measured by various criteria from the fields of social sciences (fairness), game theory (stability) and economics (efficiency). In computational social choice, such problems are analyzed and accessed via methods of mathematics (e.g., logic and combinatoric) and theoretical computer science (e.g. complexity theory and algorithms). The question of so called `fair assignments' runs like a common thread through most parts of this dissertation. Regarding allocations of goods to agents, we show how to achieve allocations with minimal inequality by means of a distributed approach. We analyze the behavior of this approach for worst case instances; therefor we use an innovative proof technique which relies on implicit recursive constructions and insights from basic calculus. For assignments of agents to activities, we consider a simplified scenario where the agents express preferences over activities and the set of feasible assignments is restricted by the number of agents which can participate in a (specific) activity. We introduce several solution concepts and elucidate the connections and differences between these concepts. Furthermore, we provide an elaborated complexity analysis of the associated decision problems addressing existence and maximality of the corresponding solution concepts. Assignment problems can also be seen as auctions. We consider a scenario where the agents bid on transformations of goods. In our model, each transformation requires the existence of a `tool good' which is not consumed by the transformation. We are interested in combinations of transformations which maximize the total utility. We study the computational complexity of this model in great detail, using methods from both classical and parameterized complexity theory. Slightly off topic are our investigations on combined competitions. We interpret these as a voting problem, i.e., as the aggregation of orders. We investigate the susceptibility of these competitions to manipulation by the athletes