arXiv subjects

Koichi Wada

Publications and source records attributed to Koichi Wada.

24 records · Page 2Linked to original sources

arXiv2018

Optimal Rendezvous ${\mathcal L}$-Algorithms for Asynchronous Mobile Robots with External-Lights

We study the Rendezvous problem for 2 autonomous mobile robots in asynchronous settings with persistent memory called light. It is well known that Rendezvous is impossible in a basic model when robots have no lights, even if the system is semi-synchronous. On the other hand, Rendezvous is possible if robots have lights of various types with a constant number of colors. If robots can observe not only their own lights but also other robots' lights, their lights are called full-light. If robots can only observe the state of other robots' lights, the lights are called external-light. In this paper, we focus on robots with external-lights in asynchronous settings and a particular class of algorithms (called L-algorithms), where an L-algorithm computes a destination based only on the current colors of observable lights. When considering L-algorithms, Rendezvous can be solved by robots with full-lights and 3 colors in general asynchronous settings (called ASYNC) and the number of colors is optimal under these assumptions. In contrast, there exists no L-algorithms in ASYNC with external-lights regardless of the number of colors. In this paper, we consider a fairly large subclass of ASYNC in which Rendezvous can be solved by L-algorithms using external-lights with a finite number of colors, and we show that the algorithms are optimal in the number of colors they use.

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arXiv2017

Optimal Asynchronous Rendezvous for Mobile Robots with Lights

We study a Rendezvous problem for 2 autonomous mobile robots in asynchronous settings with persistent memory called light. It is well known that Rendezvous is impossible when robots have no lights in basic common models, even if the system is semi-synchronous. On the other hand, Rendezvous is possible if robots have lights with a constant number of colors in several types lights. In asynchronous settings, Rendezvous can be solved by robots with 4 colors of lights in non-rigid movement, if robots can use not only own light but also other robot's light (full-light), where non-rigid movement means robots may be stopped before reaching the computed destination but can move a minimum distance δ> 0 and rigid movement means robots can reach the computed destination. In semi-synchronous settings, Rendezvous can be solved with 2 colors of full-lights in non-rigid movement. In this paper, we show that in asynchronous settings, Rendezvous can be solved with 2 colors of full-lights in rigid movement and in non-rigid movement if robots know the value of the minimum distance δ. We also show that Rendezvous can be solved with 2 colors of full-lights in general non-rigid movement if we consider some reasonable restricted class of asynchronous settings.

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arXiv2011

The Gathering Problem for Two Oblivious Robots with Unreliable Compasses

Anonymous mobile robots are often classified into synchronous, semi-synchronous and asynchronous robots when discussing the pattern formation problem. For semi-synchronous robots, all patterns formable with memory are also formable without memory, with the single exception of forming a point (i.e., the gathering) by two robots. However, the gathering problem for two semi-synchronous robots without memory is trivially solvable when their local coordinate systems are consistent, and the impossibility proof essentially uses the inconsistencies in their coordinate systems. Motivated by this, this paper investigates the magnitude of consistency between the local coordinate systems necessary and sufficient to solve the gathering problem for two oblivious robots under semi-synchronous and asynchronous models. To discuss the magnitude of consistency, we assume that each robot is equipped with an unreliable compass, the bearings of which may deviate from an absolute reference direction, and that the local coordinate system of each robot is determined by its compass. We consider two families of unreliable compasses, namely,static compasses with constant bearings, and dynamic compasses the bearings of which can change arbitrarily. For each of the combinations of robot and compass models, we establish the condition on deviation ϕthat allows an algorithm to solve the gathering problem, where the deviation is measured by the largest angle formed between the x-axis of a compass and the reference direction of the global coordinate system: ϕ< π/2 for semi-synchronous and asynchronous robots with static compasses, ϕ< π/4 for semi-synchronous robots with dynamic compasses, and ϕ< π/6 for asynchronous robots with dynamic compasses. Except for asynchronous robots with dynamic compasses, these sufficient conditions are also necessary.

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arXiv2011

On the Approximability and Hardness of Minimum Topic Connected Overlay and Its Special Instances

In the context of designing a scalable overlay network to support decentralized topic-based pub/sub communication, the Minimum Topic-Connected Overlay problem (Min-TCO in short) has been investigated: Given a set of t topics and a collection of n users together with the lists of topics they are interested in, the aim is to connect these users to a network by a minimum number of edges such that every graph induced by users interested in a common topic is connected. It is known that Min-TCO is NP-hard and approximable within O(log t) in polynomial time. In this paper, we further investigate the problem and some of its special instances. We give various hardness results for instances where the number of topics in which an user is interested in is bounded by a constant, and also for the instances where the number of users interested in a common topic is constant. For the latter case, we present a first constant approximation algorithm. We also present some polynomial-time algorithms for very restricted instances of Min-TCO.

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arXiv2011

Minimum Certificate Dispersal with Tree Structures

Given an n-vertex graph G=(V,E) and a set R \subseteq {{x,y} | x,y \in V} of requests, we consider to assign a set of edges to each vertex in G so that for every request {u, v} in R the union of the edge sets assigned to u and v contains a path from u to v. The Minimum Certificate Dispersal Problem (MCD) is defined as one to find an assignment that minimizes the sum of the cardinality of the edge set assigned to each vertex. This problem has been shown to be LOGAPX-complete for the most general setting, and APX-hard and 2-approximable in polynomial time for dense request sets, where R forms a clique. In this paper, we investigate the complexity of MCD with sparse (tree) structures. We first show that MCD is APX-hard when R is a tree, even a star. We then explore the problem from the viewpoint of the maximum degree Δof the tree: MCD for tree request set with constant Δis solvable in polynomial time, while that with Δ=Ω(n) is 2.56-approximable in polynomial time but hard to approximate within 1.01 unless P=NP. As for the structure of G itself, we show that the problem can be solved in polynomial time if G is a tree.

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arXiv2011

The BG-simulation for Byzantine Mobile Robots

This paper investigates the task solvability of mobile robot systems subject to Byzantine faults. We first consider the gathering problem, which requires all robots to meet in finite time at a non-predefined location. It is known that the solvability of Byzantine gathering strongly depends on a number of system attributes, such as synchrony, the number of Byzantine robots, scheduling strategy, obliviousness, orientation of local coordinate systems and so on. However, the complete characterization of the attributes making Byzantine gathering solvable still remains open. In this paper, we show strong impossibility results of Byzantine gathering. Namely, we prove that Byzantine gathering is impossible even if we assume one Byzantine fault, an atomic execution system, the n-bounded centralized scheduler, non-oblivious robots, instantaneous movements and a common orientation of local coordinate systems (where n denote the number of correct robots). Those hypotheses are much weaker than used in previous work, inducing a much stronger impossibility result. At the core of our impossibility result is a reduction from the distributed consensus problem in asynchronous shared-memory systems. In more details, we newly construct a generic reduction scheme based on the distributed BG-simulation. Interestingly, because of its versatility, we can easily extend our impossibility result for general pattern formation problems.

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