Tadao Takaoka

A new upper bound on the complexity of the all pairs shortest path problem

Abstract A new algorithm is invented for the all pairs shortest path problem with O (n 3 ( log log n log n ) 1 2 ) time on a unifor RAM. This is an improvement of Fredmans result for this problem by a factor of ( log n log log n ) 1 6 . A parallel algorithm for this problem on a PRAM-EREW is also presented.

Efficient Algorithms for the Maximum Subarray Problem by Distance Matrix Multiplication

Abstract We design an efficient algorithm that maximizes the sum of array elements of a subarray of a two-dimensional array. The solution can be used to find the most promising array portion that correlates two parameters involved in data, such as ages and income for the amount of sales per some period. The previous subcubic time algorithm is simplified, and the time complexity is improved for the worst case. We also give a more practical algorithm whose expected time is better than the worst case time.

An all pairs shortest path algorithm with expected time O ( n 2 log n )

An algorithm is described that solves the all pairs shortest path problem for a nonnegatively weighted directed graph of n vertices in average time

Subcubic cost algorithms for the all pairs shortest path problem

O(n^2 \log n)

A technique for two-dimensional pattern matching

. The algorithm is a blend of two previous shortest path algorithms, those of Dantzig [Management Sci., 6 (1960), pp. 187–190] and Spira [SIAM J. Comput., 2 (1973), pp. 28–32]. Bloniarz [SIAM J. Comput., 12 (1983), pp. 588–600] categorised a class of random graphs called endpoint independent graphs; the new algorithm executes in the stated time on endpoint independent graphs and represents an asymptotic improvement over the

Algorithms for the problem of K maximum sums and a VLSI algorithm for the K maximum subarrays problem

O(n^2 \log n\log ^ * n)

A New Upper Bound on the Complexity of the All Pairs Shortest Path Problem

algorithm given by Bloniarz for this class of random graphs.

Theory of 2-3 heaps

Abstract. In this paper we give three subcubic cost algorithms for the all pairs shortest distance (APSD) and path (APSP) problems. The first is a parallel algorithm that solves the APSD problem for a directed graph with unit edge costs in O(log2n) time with

A Faster Algorithm for the All-Pairs Shortest Path Problem and Its Application

O(n^\mu/\sqrt{\log n})

N-Fail-Safe Logical Systems

processors where μ = 2.688 on an EREW PRAM. The second parallel algorithm solves the APSP, and consequently APSD, problem for a directed graph with nonnegative general costs (real numbers) in O(log2n) time with o(n3) subcubic cost. Previously this cost was greater than O(n3) . Finally we improve with respect to M the complexity O((Mn)μ) of a sequential algorithm for a graph with edge costs up to M to O(M1/3n(6+ω)/3(log n)2/3(log log n)1/3) in the APSD problem, where ω = 2.376 .