Hirotsugu Kakugawa

Availability of k-coterie

The distributed k-mutual-exclusion problem (k-mutex problem) is the problem of guaranteeing that at most k processes at a time can enter a critical section at a time in a distribution system. A method proposed for the solution of the distributed mutual exclusion problem (i.e., 1-mutex problem) by D. Barbara and H. Garcia-Molina (1987) is an extension of majority consensus and uses coteries. The goodness of coterie-based 1-mutex algorithm strongly depends on the availability of coterie, and it has been shown that majority coterie is optimal in this sense, provided that: the network topology is a complete graph, the links never fail, and p, the reliability of the process, is at least 1/2. The concept of a k-coterie, an extension of a coterie, is introduced for solving the k-mutex problem, and lower and upper bounds are derived on the reliability p for k-majority coterie, a natural extension of majority coterie, to be optimal, under conditions (1)-(3). For example, when k=3, p must be greater than 0.994 for k-majority coterie to be optimal. >

A self-stabilizing minimal dominating set algorithm with safe convergence

A self-stabilizing distributed system is a fault-tolerant distributed system that tolerates any kind and any finite number of transient faults, such as message loss and memory corruption. In this paper, we formulate a concept of safe convergence in the framework of self-stabilization. An ordinary self-stabilizing algorithm has no safety guarantee while it is in converging from any initial configuration. The safe convergence property guarantees that a system quickly converges to a safe configuration, and then, it gracefully moves to an optimal configuration without breaking safety. Then, we propose a minimal independent dominating set algorithm with safe convergence property. Especially, the proposed algorithm computes the lexicographically first minimal independent dominating set according to the process identifier as a priority. The priority scheme can be arbitrarily changed such as stability, battery power and/or computation power of node

A Self-Stabilizing Distributed Approximation Algorithm for the Minimum Connected Dominating Set

Self-stabilization is a theoretical framework of non-masking fault-tolerant distributed algorithms. A self-stabilizing system tolerates any kind and any finite number of transient faults, such as message loss, memory corruption, and topology change. Because such transient faults occur so frequently in mobile ad hoc networks, distributed algorithms on them should tolerate such events. In this paper, we propose a self-stabilizing distributed approximation algorithm for the minimum connected dominating set, which can be used, for example, as a virtual backbone or routing in mobile ad hoc networks. The size of the solution by our algorithm is at most 8 |Dopt | + 1, where Dopt is a minimum connected dominating set. The time complexity is O(n2) steps.

Uniform and self-stabilizing token rings allowing unfair daemon

A distributed system consists of a set of processes and a set of communication links, each connecting a pair of processes. A distributed system is said to be self-stabilizing if it converges to a correct system state no matter which system state it starts with. A self-stabilizing system is considered to be an ideal fault tolerant system, since it tolerates any kind and any finite number of transient failures. In this paper, we investigate uniform randomized self-stabilizing mutual exclusion systems on unidirectional rings. As far as deterministic systems are concerned, it is well-known that there is no such system when the number 6 of processes (i.e., ring size) is composite, even if a fair central-daemon (c-daemon) is assumed. A fair daemon guarantees that every process will be selected for activation infinitely many times. As for randomized systems, regardless of the ring size, we can design a self-stabilizing system even for a distributed-daemon (d-daemon). However, every system proposed so far assumes a daemon to be fair, and effectively replies on this assumption. This paper tackles the problem of designing a self-stabilizing system, without assuming the fairness of a daemon. As a result, we present a randomized self-stabilizing mutual exclusion system for any size n (including composite size) of a unidirectional ring. The number of process states of the system is 2(n-1).

A Self-stabilizing Approximation for the Minimum Connected Dominating Set with Safe Convergence

In wireless ad hoc or sensor networks, a connected dominating set is useful as the virtual backbone because there is no fixed infrastructure or centralized management. Additionally, in such networks, transient faults and topology changes occur frequently. A self-stabilizing system tolerates any kind and any finite number of transient faults, and does not need any initialization. An ordinary self-stabilizing algorithm has no safety guarantee and requires that the network remains static during converging to the legitimate configuration. Safe converging self-stabilization is one of the extension of self-stabilization which is suitable for dynamic networks such that topology changes and transient faults occur frequently. The safe convergence property guarantees that the system quickly converges to a safe configuration, and then, it moves to an optimal configuration without breaking safety. In this paper, we propose a self-stabilizing 7.6-approximation algorithm with safe convergence for the minimum connected dominating set in the networks modeled by unit disk graphs.

A Timestamp Based Transformation of Self-Stabilizing Programs for Distributed Computing Environments

There are several models for which self-stabilizing (SS) programs have been developed. The distributed model accurately reflects a real distributed computing environment; therefore, programs developed for the model should run directly on a distributed system. However, many SS programs have been developed for the serial model which has the strongest assumptions, because it is much easier to develop and verify a program for the model than one for other models. This paper presents a transformation method that converts a program designed for the serial model to a program for the distributed model. An SS concurrency control protocol is incorporated in a transformed program to guarantee that if the original program is SS, the transformed program is also SS and performs exactly like the original program. We have implemented transformed versions of several serial model SS algorithms and tested them with various initial configurations.

Lock-based self-stabilizing distributed mutual exclusion algorithms

In 1974, Dijkstra introduced the notion of self-stabilization and presented a token circulation distributed mutual exclusion (DMX) protocol as the first self-stabilizing (SS) algorithm. Since then, many variations of SS DMX algorithms have been presented. Most, if not all, of these algorithms impose stronger assumptions on their execution environments than those provided by common distributed systems. Independently, non SS DMX algorithms have been studied extensively in the last 15 years. This paper presents two SS DMX algorithms that are based on existing non SS DMX algorithms: one is based on a link-locking algorithm and the other is on a node-locking algorithm. Our algorithms assume execution environments that are close to those provided by common distributed systems. Furthermore, they provide better synchronization delays than token circulation SS DMX algorithms. We have implemented our algorithms and tested them with various initial configurations.

A self-stabilizing algorithm for the distributed minimal k-redundant dominating set problem in tree networks

Self-stabilization is a theoretical framework of nonmasking fault-tolerant distributed algorithms. We investigate self-stabilizing distributed solutions to the minimal k-redundant dominating set (MRDS) problem in tree networks. The MRDS problem is a generalization of the well-known dominating set problem in graph theory. For a graph G=(V,E), a set M/spl sube/V is a k-redundant dominating set of G if and only if each vertex not in M is adjacent to at least k vertices in M. We propose a self-stabilizing distributed algorithm that solves the MRDS problem for anonymous tree networks.

Self-stabilizing local mutual exclusion on networks in which process identifiers are not distinct

A self-stabilizing system is a system such that it autonomously converges to a legitimate system state, regardless of the initial system state. The local mutual exclusion problem is the problem of guaranteeing that no two processes neighboring each other execute their critical sections at a time. The process identifiers are said to be chromatic if no two processes neighboring each other have the same identifiers. Under the assumption that the process identifiers are chromatic, this paper proposes two self-stabilizing local mutual exclusion algorithms; one assumes a tree as the topology of communication network and requires 3 states per process, while the other which works on any communication network, requires n + 1 states per process, where n is the number of processes in the system. We also show that the process identifiers being chromatic is close to necessary for a system to have a self-stabilizing local mutual exclusion algorithm. We adopt the shared memory model for communication and the unfair distributed daemon for process scheduling.

Uniform and Self-Stabilizing Fair Mutual Exclusion on Unidirectional Rings under Unfair Distributed Daemon

This paper presents a uniform randomized self-stabilizing mutual exclusion algorithm for an anonymous unidirectional ring of any size n, running under an unfair distributed scheduler (d-daemon). The system is stabilized with probability 1 in O(n3) expected number of steps, and each process is privileged at least once in every 2n steps, once it is stabilized.