Shuji Kijima

Asynchronous pattern formation by anonymous oblivious mobile robots

We present an oblivious pattern formation algorithm for anonymous mobile robots in the asynchronous model. The robots obeying the algorithm, starting from any initial configuration I, always form a given pattern F, if I and F do not contain multiplicities and ρ(I) divides ρ(F), where ρ(·) denotes the geometric symmetricity. Our algorithm substantially outdoes an algorithm by Dieudonne et al. proposed in DISC 2010, which is dedicated to ρ(I)=1. Our algorithm is best possible (as long as I and F do not contain multiplicities), since there is no algorithm that always forms F from I when ρ(F) is not divisible by ρ(I). All known pattern formation algorithms are constructed from scratch. We instead use a bipartite matching algorithm (between the robots and the points in F) we proposed in OPODIS 2011 as a core subroutine, to make the description of algorithm concise and easy to understand.

Plane Formation by Synchronous Mobile Robots in the Three-Dimensional Euclidean Space

Creating a swarm of mobile computing entities, frequently called robots, agents, or sensor nodes, with self-organization ability is a contemporary challenge in distributed computing. Motivated by this, we investigate the plane formation problem that requires a swarm of robots moving in the three-dimensional Euclidean space to land on a common plane. The robots are fully synchronous and endowed with visual perception. But they do not have identifiers, nor access to the global coordinate system, nor any means of explicit communication with each other. Though there are plenty of results on the agreement problem for robots in the two-dimensional plane, for example, the point formation problem, the pattern formation problem, and so on, this is the first result for robots in the three-dimensional space. This article presents a necessary and sufficient condition for fully synchronous robots to solve the plane formation problem that does not depend on obliviousness, i.e., the availability of local memory at robots. An implication of the result is somewhat counter-intuitive: The robots cannot form a plane from most of the semi-regular polyhedra, while they can form a plane from every regular polyhedron (except a regular icosahedron), whose symmetry is usually considered to be higher than any semi-regular polyhedron.

Polynomial Time Perfect Sampling Algorithm for Two-Rowed Contingency Tables

This paper proposesapolynomialtime perfect (exact)sampling algorithm for2 xn contingencytables.Our algorithm isa LasVegas type randomized algorithm and the expected running time is boundedby 0(n3InN) where n isthenumber of columnsandN is the total sum of whole entries ina table.The algorithm is based on monotone coupling from thepast(monotone CFTP) algorithm and new Markov chain for sampling two-rowed contingency tables uniformly. We employed thepathcoupling methodandshowed the mixing rate of our chain. Our result indicatesthatuniform generation of two-rowed contingency tables is easier than the corresponding counting problem,since the counting problem is known to be #P-complete.

Online prediction under submodular constraints

We consider an online prediction problem of combinatorial concepts where each combinatorial concept is represented as a vertex of a polyhedron described by a submodular function (base polyhedron). In general, there are exponentially many vertices in the base polyhedron. We propose polynomial time algorithms with regret bounds. In particular, for cardinality-based submodular functions, we give O(n2)-time algorithms.

Mobile Byzantine Agreement on Arbitrary Network

The mobile Byzantine agreement problem on general network is investigated for the first time. We first show that the problem is unsolvable on any network with the order n and the vertex connectivity d, if n ≤ 6t or d ≤ 4t, where t is an upper bound on the number of faulty processes. Assuming full synchronization and the existence of a permanently non-faulty process, we next propose two t-resilient mobile Byzantine agreement algorithms for some families of not fully connected networks. They are optimal on some networks, in the sense that they correctly work if n > 6t and d > 4t.

On space complexity of self-stabilizing leader election in mediated population protocol

Chatzigiannakis et al. (Lect Notes Comput Sci 5734:56–76, 2009) extended the Population Protocol (PP) of Angluin et al. (2004) and introduced the Mediated Population Protocol (MPP) by introducing an extra memory on every agent-to-agent communication link (i.e., edge), in order to model more powerful networks of mobile agents with limited resources. For a general distributed system of autonomous agents, Leader Election (LE) plays a key role in their efficient coordination. A Self-Stabilizing (SS) protocol has ideal properties required for distributed systems of huge numbers of not highly reliable agents typically modeled by PP or MPP; it does not require any initialization and tolerates a finite number of transient failures. Cai et al. (2009) showed that for a system of

Dominating set counting in graph classes

n

On Listing, Sampling, and Counting the Chordal Graphs with Edge Constraints

agents, any PP for SS-LE requires at least