論文

Copyright © 2016, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved. Cooperative matching games have drawn much interest partly because of the connection with bargaining solutions in the networking environment. However, it is not always guaranteed that a network under investigation gives rise to a stable bargaining outcome. To address this issue, we consider a modification process, called stabilization, that yields a network with stable outcomes, where the modification should be as small as possible. Therefore, the problem is cast to a combinatorial-optimization problem in a graph. Recently, the stabilization by edge removal was shown to be NP-hard. On the contrary, in this paper, we show that other possible ways of stabilization, namely, edge addition, vertex removal and vertex addition, are all polynomial-time solvable. Thus, we obtain a complete complexity-theoretic classification of the natural four variants of the network stabilization problem. We further study weighted variants and prove that the variants for edge addition and vertex removal are NP-hard.

© 2019 Neural information processing systems foundation. All rights reserved. We propose computationally efficient algorithms for online linear optimization with bandit feedback, in which a player chooses an action vector from a given (possibly infinite) set A ? Rd, and then suffers a loss that can be expressed as a linear function in action vectors. Although existing algorithms achieve an optimal regret bound of Õ(vT) for T rounds (ignoring factors of poly(d, log T)), computationally efficient ways of implementing them have not yet been specified, in particular when |A| is not bounded by a polynomial size in d. A standard way to pursue computational efficiency is to assume that we have an efficient algorithm referred to as oracle that solves (offline) linear optimization problems over A. Under this assumption, the computational efficiency of a bandit algorithm can then be measured in terms of oracle complexity, i.e., the number of oracle calls. Our contribution is to propose algorithms that offer optimal regret bounds of Õ(vT) as well as low oracle complexity for both non-stochastic settings and stochastic settings. Our algorithm for non-stochastic settings has an oracle complexity of Õ(T) and is the first algorithm that achieves both a regret bound of Õ(vT) and an oracle complexity of Õ(poly(T)), given only linear optimization oracles. Our algorithm for stochastic settings calls the oracle only O(poly(d, log T)) times, which is smaller than the current best oracle complexity of O(T) if T is sufficiently large.

© Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto. Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given perfect matching to another given perfect matching such that the symmetric difference of each pair of consecutive perfect matchings is a single cycle. The problem is equivalent to the combinatorial shortest path problem in perfect matching polytopes. We prove that the problem is NP-hard even when a given graph is planar or bipartite, but it can be solved in polynomial time when the graph is outerplanar.

We consider the problem of determining whether a target item assignment can be reached from an initial item assignment by a sequence of pairwise exchanges of items between agents. In particular, we consider the situation where each agent has a dichotomous preference over the items, that is, each agent evaluates each item as acceptable or unacceptable. Furthermore, we assume that communication between agents is limited, and the relationship is represented by an undirected graph. Then, a pair of agents can exchange their items only if they are connected by an edge and the involved items are acceptable. We prove that this problem is PSPACE-complete even when the communication graph is complete (that is, every pair of agents can exchange their items), and this problem can be solved in polynomial time if an input graph is a tree.