Hisashi Mine

An efficient algorithm for K shortest simple paths

This article gives an efficient algorithm for obtaining K shortest simple paths between two specified nodes in an undirected graph G with non-negative edge lengths. Letting n be the number of nodes and m be the number of edges in G, its running time is O(Kc(n, m)) if the shortest paths from one node to all the other nodes are obtained in c(n, m) [≥O(m)] time, and the required space is O(Kn + m). This time bound is better than those realized by existing algorithms, the best of which, proposed by Yen, requires O(Kn3) time, since c(n, m) ≤min[O(n2), O(m log n)] is known.

A Solvable Case of the One-Machine Scheduling Problem with Ready and Due Times

We consider a class of n-job one-machine scheduling problems with ready time ri, processing time pi, and due time di for each job i. Preemption is not allowed, and precedence constraints among jobs are not assumed. For this problem we show that there is a 0n2-time algorithm to find a schedule that minimizes the number of tardy jobs, under the assumption that ri

A generalized proximal point algorithm for certain non-convex minimization problems

An algorithm is presented for minimizing a function which is the sum of a continuously differentiable function and a convex function. The class of such problems contains as a special case that of minimizing a continuously differentiable function over a closed convex set. This algorithm may be viewed as a generalization of the proximal point algorithm to cope with non-convexity of the objective function by linearizing the differentiable term at each iteration. Convergence of the algorithm is proved and the rate of convergence is analysed.

An Algorithm for Finding K Minimum Spanning Trees

This paper presents an algorithm for finding K minimum spanning trees in an undirected graph. The required time is

AN OPTIMAL INSPECTION AND REPLACEMENT POLICY FOR A DETERIORATING SYSTEM

O(Km + \min (n^2 ,m\log \log n))

A minimization method for the sum of a convex function and a continuously differentiable function

and the space is

Fractional knapsack problems

O(K + m)

An Optimal Inspection and Replacement Policy

, where n is the number of vertices and m is the number of edges. The algorithm is based on three subroutines. The first two subroutines are used to obtain the second minimum spanning tree in

N-Fail-Safe Logical Systems

O(\min (n^2 ,m\alpha (m,n)))

Linear programming algorithms for semi-Markovian decision processes

steps, where