924 research outputs found
Complexity of coalition structure generation
We revisit the coalition structure generation problem in which the goal is to
partition the players into exhaustive and disjoint coalitions so as to maximize
the social welfare. One of our key results is a general polynomial-time
algorithm to solve the problem for all coalitional games provided that player
types are known and the number of player types is bounded by a constant. As a
corollary, we obtain a polynomial-time algorithm to compute an optimal
partition for weighted voting games with a constant number of weight values and
for coalitional skill games with a constant number of skills. We also consider
well-studied and well-motivated coalitional games defined compactly on
combinatorial domains. For these games, we characterize the complexity of
computing an optimal coalition structure by presenting polynomial-time
algorithms, approximation algorithms, or NP-hardness and inapproximability
lower bounds.Comment: 17 page
Shapley Meets Shapley
This paper concerns the analysis of the Shapley value in matching games.
Matching games constitute a fundamental class of cooperative games which help
understand and model auctions and assignments. In a matching game, the value of
a coalition of vertices is the weight of the maximum size matching in the
subgraph induced by the coalition. The Shapley value is one of the most
important solution concepts in cooperative game theory.
After establishing some general insights, we show that the Shapley value of
matching games can be computed in polynomial time for some special cases:
graphs with maximum degree two, and graphs that have a small modular
decomposition into cliques or cocliques (complete k-partite graphs are a
notable special case of this). The latter result extends to various other
well-known classes of graph-based cooperative games.
We continue by showing that computing the Shapley value of unweighted
matching games is #P-complete in general. Finally, a fully polynomial-time
randomized approximation scheme (FPRAS) is presented. This FPRAS can be
considered the best positive result conceivable, in view of the #P-completeness
result.Comment: 17 page
Pareto Optimal Allocation under Uncertain Preferences
The assignment problem is one of the most well-studied settings in social
choice, matching, and discrete allocation. We consider the problem with the
additional feature that agents' preferences involve uncertainty. The setting
with uncertainty leads to a number of interesting questions including the
following ones. How to compute an assignment with the highest probability of
being Pareto optimal? What is the complexity of computing the probability that
a given assignment is Pareto optimal? Does there exist an assignment that is
Pareto optimal with probability one? We consider these problems under two
natural uncertainty models: (1) the lottery model in which each agent has an
independent probability distribution over linear orders and (2) the joint
probability model that involves a joint probability distribution over
preference profiles. For both of the models, we present a number of algorithmic
and complexity results.Comment: Preliminary Draft; new results & new author
Pareto Optimal Allocation under Compact Uncertain Preferences
The assignment problem is one of the most well-studied settings in multi-agent resource allocation. Aziz, de Haan, and Rastegari (2017) considered this problem with the additional feature that agents’ preferences involve uncertainty. In particular, they considered two uncertainty models neither of which is necessarily compact. In this paper, we focus on three uncertain preferences models whose size is polynomial in the number of agents and items. We consider several interesting computational questions with regard to Pareto optimal assignments. We also present some general characterization and algorithmic results that apply to large classes of uncertainty models
Unmanned Ground Robots for Rescue Tasks
This chapter describes two unmanned ground vehicles that can help search and rescue teams in their difficult, but life-saving tasks. These robotic assets have been developed within the framework of the European project ICARUS. The large unmanned ground vehicle is intended to be a mobile base station. It is equipped with a powerful manipulator arm and can be used for debris removal, shoring operations, and remote structural operations (cutting, welding, hammering, etc.) on very rough terrain. The smaller unmanned ground vehicle is also equipped with an array of sensors, enabling it to search for victims inside semi-destroyed buildings. Working together with each other and the human search and rescue workers, these robotic assets form a powerful team, increasing the effectiveness of search and rescue operations, as proven by operational validation tests in collaboration with end users
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