Shortest Reconfiguration of Perfect Matchings via Alternating Cycles

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

Pontryagin's Minimum Principle and Forward-Backward Sweep Method for the System of HJB-FP Equations in Memory-Limited Partially Observable Stochastic Control

Memory-limited partially observable stochastic control (ML-POSC) is the stochastic optimal control problem under incomplete information and memory limitation. In order to obtain the optimal control function of ML-POSC, a system of the forward Fokker-Planck (FP) equation and the backward Hamilton-Jacobi-Bellman (HJB) equation needs to be solved. In this work, we firstly show that the system of HJB-FP equations can be interpreted via the Pontryagin's minimum principle on the probability density function space. Based on this interpretation, we then propose the forward-backward sweep method (FBSM) to ML-POSC, which has been used in the Pontryagin's minimum principle. FBSM is an algorithm to compute the forward FP equation and the backward HJB equation alternately. Although the convergence of FBSM is generally not guaranteed, it is guaranteed in ML-POSC because the coupling of HJB-FP equations is limited to the optimal control function in ML-POSC

Mean-Field Control Approach to Decentralized Stochastic Control with Finite-Dimensional Memories

Decentralized stochastic control (DSC) considers the optimal control problem of a multi-agent system. However, DSC cannot be solved except in the special cases because the estimation among the agents is generally intractable. In this work, we propose memory-limited DSC (ML-DSC), in which each agent compresses the observation history into the finite-dimensional memory. Because this compression simplifies the estimation among the agents, ML-DSC can be solved in more general cases based on the mean-field control theory. We demonstrate ML-DSC in the general LQG problem. Because estimation and control are not clearly separated in the general LQG problem, the Riccati equation is modified to the decentralized Riccati equation, which improves estimation as well as control. Our numerical experiment shows that the decentralized Riccati equation is superior to the conventional Riccati equation.Comment: arXiv admin note: text overlap with arXiv:2203.1068

Multi-Robot Patrol Algorithm with Distributed Coordination and Consciousness of the Base Station's Situation Awareness

Multi-robot patrolling is the potential application for robotic systems to survey wide areas efficiently without human burdens and mistakes. However, such systems have few examples of real-world applications due to their lack of human predictability. This paper proposes an algorithm: Local Reactive (LR) for multi-robot patrolling to satisfy both needs: (i)patrol efficiently and (ii)provide humans with better situation awareness to enhance system predictability. Each robot operating according to the proposed algorithm selects its patrol target from the local areas around the robot's current location by two requirements: (i)patrol location with greater need, (ii)report its achievements to the base station. The algorithm is distributed and coordinates the robots without centralized control by sharing their patrol achievements and degree of need to report to the base station. The proposed algorithm performed better than existing algorithms in both patrolling and the base station's situation awareness.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Complexity of the Multi-Service Center Problem

The multi-service center problem is a variant of facility location problems. In the problem, we consider locating p facilities on a graph, each of which provides distinct service required by all vertices. Each vertex incurs the cost determined by the sum of the weighted distances to the p facilities. The aim of the problem is to minimize the maximum cost among all vertices. This problem is known to be NP-hard for general graphs, while it is solvable in polynomial time when p is a fixed constant. In this paper, we give sharp analyses for the complexity of the problem from the viewpoint of graph classes and weights on vertices. We first propose a polynomial-time algorithm for trees when p is a part of input. In contrast, we prove that the problem becomes strongly NP-hard even for cycles. We also show that when vertices are allowed to have negative weights, the problem becomes NP-hard for paths of only three vertices and strongly NP-hard for stars

Shortest Reconfiguration of Colorings Under Kempe Changes

International audienc

<Poster Presentation 3>Covariant Lyapunov Analysis of Chaotic Kolmogorov Flows and Time-correlation Function

[Date] November 28 (Mon) - December 2 (Fri), 2011: [Place] Kyoto University Clock Tower Centennial Hall, Kyoto, JAPA

近代南都仏教史の課題

publisher奈良小文は、平成24年度奈良大学研究助成（研究課題「南都仏教と真言宗の近代に関する予備的研究」）による研究成果の一部である。研究助成では、主として奈良の地方新聞『奈良新聞』の検索作業を通じて、近代における南都仏教の動向に関する基礎的な事実の収集に努めた。小文では、今後も引き続き作業を行うため、近代南都仏教史の現状を踏まえ、今後の検討課題を整理した。南都仏教については、古代・中世史においては関心が高く、研究蓄積も多いが、近代史に関しては史料の所在状況も明らかではなく、研究も緒に就いたばかりである。それでも、近年は法隆寺や清水寺（京都にあるが興福寺一乗院の末寺）、西大寺などを対象に研究が進展している。そこで、それらを手がかりに主要な論点を挙げると次のようなものが挙げられる。すなわち、（1）社寺領上知とその影響、（2）宗派の公認問題、（3）社寺総代制度の創設、（4）寺院組織近代化をめぐる葛藤、（5）近代化を担ったり抵抗したりした人々の人物像などである。小文は、奈良を中心に展開した南都仏教の、明治維新後の変容について、研究の現状を振り返り、今後の課題を検討しようとするものである