Naoki Katoh

Resource Allocation Problems

The resource allocation problem seeks to find an optimal allocation of a fixed amount of resources to activities so as to minimize the cost incurred by the allocation. A simplest form of the problem is to minimize a separable convex function under a single constraint concerning the total amount of resources to be allocated. The amount of resources to be allocated to each activity is treated as a continuous or integer variable, depending on the cases. This can be viewed as a special case of the nonlinear programming problem or the nonlinear integer programming problem.

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.

Finding k points with minimum diameter and related problems

Abstract Let S be a set consisting of n points in the plane. We consider the problem of finding k points of S that form a “small” set under some given measure, and present efficient algorithms for several natural measures including the diameter and the variance.

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

Algorithms and Computations

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

Semi-definite programming for topology optimization of trusses under multiple eigenvalue constraints

and the space is

Mining Pharmacy Data Helps to Make Profits

O(K + m)

Group Symmetry in Interior-Point Methods for Semidefinite Program

, 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

Efficient algorithms for optimization-based image segmentation

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

A parametric characterization and an e-approximating scheme for the minimization of a quasiconcave program

steps, where