Satoko Moriguchi

Discrete Hessian Matrix for L-Convex Functions

L-convex functions are nonlinear discrete functions on integer points that are computationally tractable in optimization. In this paper, a discrete Hessian matrix and a local quadratic expansion are defined for L-convex functions. We characterize L-convex functions in terms of the discrete Hessian matrix and the local quadratic expansion.

On Hochbaum's Proximity-Scaling Algorithm for the General Resource Allocation Problem

It is pointed out that the polynomial-time scaling algorithm by Hochbaum does not work correctly for the general resource allocation problem. Hochbaums algorithm increases a variable by one unit if the variable cannot feasibly be increased by the scaling unit. We modify the algorithm to increase such a variable by the largest possible amount and show that with this modification the algorithm works correctly. The effect is to modify the factorF in the running time of Hochbaums algorithm for finding whether a certain solution is feasible by the factorF~ of finding the maximum feasible increment (also called the saturation capacity). Therefore, the corrected algorithm runs in O( n(logn +F~) log( B/n)) time.

A capacity scaling algorithm for M-convex submodular flow

Abstract.This paper presents a faster algorithm for the M-convex submodular flow problem, which is a generalization of the minimum-cost flow problem with an M-convex cost function for the flow-boundary, where an M-convex function is a nonlinear nonseparable discrete convex function on integer points. The algorithm extends the capacity scaling approach for the submodular flow problem by Fleischer, Iwata and McCormick (2002) with the aid of a novel technique of changing the potential by solving maximum submodular flow problems.

Capacity scaling algorithm for scalable M-convex submodular flow problems

An M-convex function is a nonlinear discrete function defined on integer points introduced by Murota in 1996, and the M-convex submodular flow problem is one of the most general frameworks of efficiently solvable combinatorial optimization problems. It includes the minimum cost flow and the submodular flow problems as its special cases. In this paper, we first devise a successive shortest path algorithm for the M-convex submodular flow problem. We then propose an efficient algorithm based on a capacity scaling framework for the scalable M-convex submodular flow problem. Here an M-convex function [Formula: See Text] is said to be scalable if [Formula: See Text] is also M-convex for any positive integer [Formula: See Text] and any integer vector b.

A Home Security Service Robot System Using the Network Service Platform and Its Implementation

We propose the Network Service Platform (NSP) as a framework which enables the development of integrated services between three service fields: Internet Services, Robot Services, and Ubiquitous Computing. In this paper, we outline the development of a Home Security Service Robot System, a prototype service which integrates Internet and Robot services using the NSP framework. In this prototype system, the robot monitors the home and uploads image and motion detection data. The server on the Internet stores these images, allows human face recognition and email notification, and provides user consoles for controlling and browsing functionalities from a web browser. We also discuss the possibility of providing integrated services using the NSP framework based on the results of our implementation.

The Digital Travel Diary System Using the Network Service Platform

In this paper, we propose the Network Service Platform (NSP), which is a framework to develop network services using real-world data efficiently, and implement its application. We implemented a prototype system based on NSP using GPS data and image data obtained from cell phones. This service integrates internet services with ubiquitous services by using the Robot Service Network Protocol (RSNP), an open standard protocol for robot services. Through the implementation of the prototype system, we confirm the effectiveness of NSP to develop network services.

Scaling, proximity, and optimization of integrally convex functions

In discrete convex analysis, the scaling and proximity properties for the class of L

Projection and convolution operations for integrally convex functions

^{\natural }