Aohan Mei

An efficient strategy for robot navigation in unknown environment

Abstract 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 1 + 3 5 f , 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.

Optimal Time Broadcasting in Faulty Star Networks

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 — 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 to design our broadcasting scheme. This technique is useful to improve the efficiency of broadcasting in star networks. We analyze the reliability of the broadcasting scheme in the case where faults are randomly distributed in the n-star network. The broadcasting scheme in the n-star network can tolerate (n!)* random faults with a high probability, where α is any constant less than 1.

Efficient Strategies for Robot Navigation in Unknown Environment

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.

Broadcasting in Star Graphs with Byzantine Failures

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 n≤d!. The broadcasting time of the scheme is logarithmic in the number of nodes of the n-star graph.

Efficient Broadcasting on Faulty Star Networks

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.

Embeddings of Hyper-Rings in Hypercubes

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 show a greedy embedding with dilation 2 and congestion n+1 and a modified greedy embedding with dilation 4 and congestion 6.

A shortest path algorithm for banded matrices by a mesh connection without processor penalty

We give an efficient shortest path algorithm on a mesh-connected processor array for n/spl times/n banded matrices with bandwidth b. We use a [b/2]/spl times/[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.<<ETX>>

Average competitive ratios of on-line spanning trees

Abstract 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 1 4 In n − 1 2 .