Aohan Mei's research while affiliated with Gunma University and other places

this paper we assume that nodes in a graph aresync hronized with a global co c k. Star graphs were proposed asattrac--- e intercK necK9 networks [1], and they have been muc h stud ied [2], [3], [7], [8], [12], [14], [21]--[23]. Known results re lated to this paper are as follows. The n-star

. This paper investigates fault-tolerant broadcasting in star networks. We propose a non-adaptive single-port broadcasting scheme in the n-star network such that it tolerates n 0 2 faults in the worst case and completes the broadcasting in O(n log n) time. The existence of such a broadcasting scheme was not known before. A new technique, called diffusing-and-disseminating, is introduced into the scheme. This technique is useful to overcome the difficulty due to the special topology of star networks. We also analyze the reliability of the broadcasting scheme in the case where faults are randomly distributed in the n-star network. We show that the broadcasting scheme in the n-star network can tolerate (n!) ff random faults with a high probability, where ff is any constant less than 1. 1 Introduction Broadcasting is one of the fundamental tasks in network communications. It is the process of disseminating a message from the source node to all other nodes in the network. It can be acco...

We study the average competitive ratio of on-line spanning trees with the same distribution of points in the Euclidean plane. We show a distribution of n points such that the average competitive ratio of on-line spanning trees by any on-line algorithm cannot be less than 14 In n − 12.

We study broadcasting in star graphs containing faulty nodes and/or edges of the Byzantine type. We propose a single-port broadcasting scheme that tolerates up to n–3d–1/2 Byzantine failures in the n-star graph, where d is the smallest positive integer satisfying nd!. The broadcasting time of the scheme is logarithmic in the number of nodes of the n-star graph.

We propose a non-adaptive single-port broadcasting scheme for star graphs. Broadcasting in the n-star graph by the scheme can tolerate O(n log n) faults, and it is completed in O(n log n) time.

A graph G = (V, E) with N nodes is called an N-hyper-ring if V = {0, ···, N-1} and E = {(u, v)|(u - v) modulo N is a power of 2}. We study embeddings of the 2n-hyper-ring in the n-dimensional hypercube. We first show a greedy embedding with dilation 2 and congestion n+1. We next modify the greedy embedding, and then we obtain an embedding with dilation 4 and congestion 6.

We give an efficient shortest path algorithm on a mesh-connected processor array for n×n banded matrices with bandwidth b. We use a [b/2]×[b/2] semisystolic processor array. The input data is supplied to the processors array from the host computer. The output from the processor array can be also supplied to itself through the host computer. This algorithm computes all pair shortest distances within the band in 7n-4[b/2]-1 steps

We study the ratio of the dead-free path length made by a new strategy to the shortest path length in unknown environment containing rectangular and rectilinear obstacles satisfying some limitations on their aspect ratios and side lengths. We show that the ratio is at most arbitrarily close to , as n grows, if the start point and the target are at the same horizontal level, where the aspect ratio of each obstacle is at most f. We also study the ratio for unknown environment where the start point and the target may be at different levels.

We propose two strategies called the adaptive- bias heuristic and the adjusted- bias heuristic for navigating a robot in unknown environment containing rectangular and rectilinear obstacles. For each of these strategies we study the ratio of the dead-free path length made by the strategy to the shortest path length between the start point and the target point when all obstacles satisfy some limitations on their aspect ratios and side lengths. For the adaptive- bias heuristic and the adjusted-bias heuristic we show that the ratios are at most arbitrarily close to 1+3/5k and 1+3/5f, respectively, as n grows, if the start point and the target are at the same horizontal level, where any side length of each obstacle is at most k and the aspect ratio of any obstacle is at most f, respectively. We also study the ratios for unknown environment where the start point and the target may be at different levels. These ratios are better than the ratios obtained by strategies previously known for the classes of scenes considered in this paper.

We study robot navigation in unknown environment with rectangular obstacles aligned with the x and y axes. We propose a strategy called the modified-bian heuristic, and analyze its efficiency. Let n be the distance between the start point and the target of robot navigation, and let k be the maximum side length among the obstacles in a scene. We show that if k = (o(√n) and if the summation of the widths of the obstacles on the line crossing the target and along the y axis is o(n), then the ratio of the total distance walked by the robot to the shortest path length between the start point and the target is at most arbitrarily close to 1+k/2, as n grows. For the same restrictions as above on the sizes of the obstacles, the ratio is also at most arbitrarily close to 1+3 h̄/4n, as n grows, where h̄ is the summation of the lengths of the obstacles in y axis direction.