Hirotsugu Kakugawa’s research while affiliated with Ryukoku University and other places

Fault‐tolerance and self‐organization are critical properties in modern distributed systems. Self‐stabilization is a class of fault‐tolerant distributed algorithms which has the ability to recover from any kind and any finite number of transient faults and topology changes. In this article, we propose a self‐stabilizing distributed algorithm for the 1‐MIS problem under the unfair central daemon assuming the distance‐3 model. Here, in the distance‐3 model, each process can refer to the values of local variables of processes within three hops. Intuitively speaking, the 1‐MIS problem is a variant of the maximal independent set (MIS) problem with improved local optimizations. The time complexity (convergence time) of our algorithm is O(n) O(n) steps and the space complexity is O(logn)$O\left(\log n\right)$ bits, where n n is the number of processes. Finally, we extend the notion of 1‐MIS to p p ‐MIS for each nonnegative integer p p , and compare the set sizes of p p ‐MIS (p=0,1,2,…$p=0,1,2,\dots$) and the maximum independent set.

The domination problem is one of the fundamental graph problems, and there are many variations. In this article, we propose a new problem called the minus (L,K,Z)$\left(L,K,Z\right)$‐domination problem where L,K L,K , and Z Z are integers such that L≤−1$L\le -1$, K≥1$K\ge 1$, and Z≥1$Z\ge 1$. The problem is to assign a value from L,L+1,…,0,…,K−1,K$L,L+1,\dots, 0,\dots, K-1,K$ for each vertex in a graph such that the local summation of values is greater than or equal to Z Z . We also propose a framework named the bounded lattice domination for a class of domination problems, including the minus (L,K,Z)$\left(L,K,Z\right)$‐domination problem. Then, we present a self‐stabilizing distributed algorithm under the distance‐2 model for the bounded lattice domination. Here, self‐stabilization is a class of fault‐tolerant distributed algorithms that tolerate transient faults. The time complexity for convergence is O(n) O(n) , where n n is the number of processes in a network if the cardinality of the domain of process values is finite and constant. Otherwise, the time complexity for convergence is O(n2)$O\left({n}^2\right)$.

This paper considers perpetual exploration of anonymous cactus graphs with distinguishable cycles by a single mobile agent under the restriction that nodes have no storage (e.g., whiteboards or token places). A cactus with distinguishable cycles allows the agent to distinguish at each node the two incident edges contained in each cycle from other incident edges. This paper introduces the concept of snap-stabilization into the perpetual exploration and shows that snap-stabilizing perpetual exploration is possible when the agent has one-bit persistent memory. The exploration time of the presented algorithm exactly matches a trivial lower bound. This paper also shows the necessity of one-bit agent memory by showing that any oblivious (or memory-less) agent cannot explore a cactus graph even when it has only a single distinguishable cycle. Finally, this paper shows that snap-stabilizing perpetual exploration by an oblivious agent is possible when a cactus graph with distinguishable cycles has a sense of direction.KeywordsMobile agentGraph explorationCactus graphSnap-stabilization

A self-stabilizing distributed algorithm is guaranteed eventually to reach and stay at a legitimate configuration regardless of the initial configuration of a distributed system. In this paper, we propose the generalized dominating set problem, which is a generalization of the dominating set and k-redundant dominating set problems. In the generalized dominating set we propose in this paper, each node $P_{i}$ is given its set of domination wish sets, and a generalized dominating set is a set of nodes such that each node is contained in the set or has a wish set in which all its members are in the set. We propose a self-stabilizing distributed algorithm for finding a minimal generalized dominating set in an arbitrary network under the unfair distributed daemon. The proposed algorithm converges in $O(n^{3}m)$ steps and O(n) rounds, where n (resp., m) is the number of nodes (resp., edges). Furthermore, it has the safe convergence property with safe convergence time in O(1) rounds. The space complexity of the proposed algorithm is $O(\Delta \log n)$ bits per node, where $\Delta$ is the maximum degree of nodes.