arXiv subjects

Yuichi Sudo

Publications and source records attributed to Yuichi Sudo.

28 records · Page 2Linked to original sources

arXiv2021

Gathering of seven autonomous mobile robots on triangular grids

In this paper, we consider the gathering problem of seven autonomous mobile robots on triangular grids. The gathering problem requires that, starting from any connected initial configuration where a subgraph induced by all robot nodes (nodes where a robot exists) constitutes one connected graph, robots reach a configuration such that the maximum distance between two robots is minimized. For the case of seven robots, gathering is achieved when one robot has six adjacent robot nodes (they form a shape like a hexagon). In this paper, we aim to clarify the relationship between the capability of robots and the solvability of gathering on a triangular grid. In particular, we focus on visibility range of robots. To discuss the solvability of the problem in terms of the visibility range, we consider strong assumptions except for visibility range. Concretely, we assume that robots are fully synchronous and they agree on the direction and orientation of the x-axis, and chirality in the triangular grid. In this setting, we first consider the weakest assumption about visibility range, i.e., robots with visibility range 1. In this case, we show that there exists no collision-free algorithm to solve the gathering problem. Next, we extend the visibility range to 2. In this case, we show that our algorithm can solve the problem from any connected initial configuration. Thus, the proposed algorithm is optimal in terms of visibility range.

cs.RO↗

arXiv2020

Self-Stabilizing Construction of a Minimal Weakly $\mathcal{ST}$-Reachable Directed Acyclic Graph

We propose a self-stabilizing algorithm to construct a minimal weakly $\mathcal{ST}$-reachable directed acyclic graph (DAG), which is suited for routing messages on wireless networks. Given an arbitrary, simple, connected, and undirected graph $G=(V, E)$ and two sets of nodes, senders $\mathcal{S} (\subset V)$ and targets $\mathcal{T} (\subset V)$, a directed subgraph $\vec{G}$ of $G$ is a weakly $\mathcal{ST}$-reachable DAG on $G$, if $\vec{G}$ is a DAG and every sender can reach at least one target, and every target is reachable from at least one sender in $\vec{G}$. We say that a weakly $\mathcal{ST}$-reachable DAG $\vec{G}$ on $G$ is minimal if any proper subgraph of $\vec{G}$ is no longer a weakly $\mathcal{ST}$-reachable DAG. This DAG is a relaxed version of the original (or strongly) $\mathcal{ST}$-reachable DAG, where every target is reachable from every sender. This is because a strongly $\mathcal{ST}$-reachable DAG $G$ does not always exist; some graph has no strongly $\mathcal{ST}$-reachable DAG even in the case $|\mathcal{S}|=|\mathcal{T}|=2$. On the other hand, the proposed algorithm always constructs a weakly $\mathcal{ST}$-reachable DAG for any $|\mathcal{S}|$ and $|\mathcal{T}|$. Furthermore, the proposed algorithm is self-stabilizing; even if the constructed DAG deviates from the reachability requirement by a breakdown or exhausting the battery of a node having an arc in the DAG, this algorithm automatically reconstructs the DAG to satisfy the requirement again. The convergence time of the algorithm is $O(D)$ asynchronous rounds, where $D$ is the diameter of a given graph. We conduct small simulations to evaluate the performance of the proposed algorithm. The simulation result indicates that its execution time decreases when the number of sender nodes or target nodes is large.

cs.DC↗

arXiv2020

Time-Optimal Self-Stabilizing Leader Election on Rings in Population Protocols

We propose a self-stabilizing leader election protocol on directed rings in the model of population protocols. Given an upper bound $N$ on the population size $n$, the proposed protocol elects a unique leader within $O(nN)$ expected steps starting from any configuration and uses $O(N)$ states. This convergence time is optimal if a given upper bound $N$ is asymptotically tight, i.e., $N=O(n)$.

cs.DC↗

arXiv2020

Efficient Dispersion of Mobile Agents without Global Knowledge

We consider the dispersion problem for mobile agents. Initially, k agents are located at arbitrary nodes in an undirected graph. Agents can migrate from node to node via an edge in the graph synchronously. Our goal is to let the k agents be located at different k nodes with minimizing the number of steps before dispersion is completed and the working memory space used by the agents. Kshemkalyani and Ali [ICDCN, 2019] present a fast and space-efficient dispersion algorithm with the assumption that each agent has global knowledge such as the number of edges and the maximum degree of a graph. In this paper, we present a dispersion algorithm that does not require such global knowledge but keeps the asymptotically same running time and slightly smaller memory space.

cs.DC↗

arXiv2020

The Power of Global Knowledge on Self-stabilizing Population Protocols

In the population protocol model, many problems cannot be solved in a self-stabilizing way. However, global knowledge, such as the number of nodes in a network, sometimes allows us to design a self-stabilizing protocol for such problems. In this paper, we investigate the effect of global knowledge on the possibility of self-stabilizing population protocols in arbitrary graphs. Specifically, we clarify the solvability of the leader election problem, the ranking problem, the degree recognition problem, and the neighbor recognition problem by self-stabilizing population protocols with knowledge of the number of nodes and/or the number of edges in a network.

cs.DC↗

arXiv2020

Time-optimal Loosely-stabilizing Leader Election in Population Protocols

We consider the leader election problem in population protocol models. In pragmatic settings of population protocols, self-stabilization is a highly desired feature owing to its fault resilience and the benefit of initialization freedom. However, the design of self-stabilizing leader election is possible only under a strong assumption (i.e. the knowledge of the \emph{exact} size of a network) and rich computational resources (i.e. the number of states). Loose-stabilization, introduced by Sudo et al [Theoretical Computer Science, 2012], is a promising relaxed concept of self-stabilization to address the aforementioned issue. Loose-stabilization guarantees that starting from any configuration, the network will reach a safe configuration where a single leader exists within a short time, and thereafter it will maintain the single leader for a long time, but not forever. The main contribution of the paper is a time-optimal loosely-stabilizing leader election protocol. While the shortest convergence time achieved so far in loosely-stabilizing leader election is $O(\log^3 n)$ parallel time, the proposed protocol with design parameter $τ\ge 1$ attains $O(τ\log n)$ parallel convergence time and $Ω(n^τ)$ parallel holding time (i.e. the length of the period keeping the unique leader), both in expectation. This protocol is time-optimal in the sense of both the convergence and holding times in expectation because any loosely-stabilizing leader election protocol with the same length of the holding time is known to require $Ω(τ\log n)$ parallel time.

cs.DC↗

arXiv2019

Atomic Cross-Chain Swaps with Improved Space and Local Time Complexity

An effective atomic cross-chain swap protocol is introduced by Herlihy [Herlihy, 2018] as a distributed coordination protocol in order to exchange assets across multiple blockchains among multiple parties. An atomic cross-chain swap protocol guarantees; (1) if all parties conform to the protocol, then all assets are exchanged among parties, (2) even if some parties or coalitions of parties deviate from the protocol, no party conforming to the protocol suffers a loss, and (3) no coalition has an incentive to deviate from the protocol. Herlihy [Herlihy, 2018] invented this protocol by using hashed timelock contracts. A cross-chain swap is modeled as a directed graph D = (V,A). Vertex set V denotes a set of parties and arc set A denotes a set of proposed asset transfers. Herlihy's protocol uses the graph topology and signature information to set appropriate hashed timelock contracts. The space complexity of the protocol (i.e., the total number of bits written in the blockchains in a swap) is O(|A|^2). The local time complexity of the protocol (i.e., the maximum execution time of a contract in a swap to transfer the corresponding asset) is O(|V||L|), where L is a feedback vertex set computed by the protocol. We propose a new atomic cross-chain swap protocol which uses only signature information and improves the space complexity to O(|A||V|) and the local time complexity to O(|V|).

cs.DC↗

arXiv2019

Leader Election Requires Logarithmic Time in Population Protocols

This paper shows that every leader election protocol requires logarithmic stabilization time both in expectation and with high probability in the population protocol model. This lower bound holds even if each agent has knowledge of the exact size of a population and is allowed to use an arbitrarily large number of agent states. This lower bound concludes that the protocol given in [Sudo et al., SSS 2019] is time-optimal in expectation.

cs.DC↗

arXiv2019

A Self-Stabilizing Minimal k-Grouping Algorithm

We consider the minimal k-grouping problem: given a graph G=(V,E) and a constant k, partition G into subgraphs of diameter no greater than k, such that the union of any two subgraphs has diameter greater than k. We give a silent self-stabilizing asynchronous distributed algorithm for this problem in the composite atomicity model of computation, assuming the network has unique process identifiers. Our algorithm works under the weakly-fair daemon. The time complexity (i.e., the number of rounds to reach a legitimate configuration) of our algorithm is O(nD/k) where n is the number of processes in the network and \diam is the diameter of the network. The space complexity of each process is O((n +n_{false})log n) where n_{false} is the number of false identifiers, i.e., identifiers that do not match the identifier of any process, but which are stored in the local memory of at least one process at the initial configuration. Our algorithm guarantees that the number of groups is at most $2n/k+1$ after convergence. We also give a novel composition technique to concatenate a silent algorithm repeatedly, which we call loop composition.

cs.DC↗

arXiv2019

Logarithmic Expected-Time Leader Election in Population Protocol Model

In this paper, the leader election problem in the population protocol model is considered. A leader election protocol with logarithmic stabilization time is given. Given a rough knowledge m of the population size n such that m >= \log_2 n and m=O(log n), the proposed protocol guarantees that exactly one leader is elected from n agents within O(log n) parallel time in expectation and the unique leader is kept forever thereafter. The number of states per agent of the protocol is O(log n).

cs.DC↗