Boundary-based interactive segmentation methods aim to build a closed contour, very often using minimum cost paths linking userprovided ordered landmark points. While discrete methods rely on a graph modeling of the image, continous models address the problem by means of curve optimization. Among them, the minimal path method [1] find curves of minimal length defined from an edge-based cost fun...

Def: A deterministic protocol computing a function f(x, y) is a binary tree T whose internal nodes specify which party speaks and the value of the bit they communicate, as a function of their input. The leaves of the tree are labelled with 0 or 1, in such a way that if Alice and Bob’s path through the tree given inputs (x, y) ends up in that leaf, the label on the leaf is f(x, y). The cost of s...

The problem of finding the minimum cost multi-commodity flow in an undirected and complete network is studied when the link costs are piecewise linear and convex. The arc-path model and overflow model are presented to formulate the problem. The results suggest that the new overflow model outperforms the classical arc-path model for this problem. The classical revised simplex, Frank and Wolf and...

The Hop-constrained Minimum Spanning Tree Problem (HMST) is defined as follows: given a graph G = (V,E) with node set V = {0, 1, . . . , n} and edge set E as well as a cost ce associated with each edge e of E and a natural number H , we wish to find a spanning tree T of the graph with minimum total cost and such that the unique path from a specified root node, node 0, to any other node has no m...

A new framework of a hierarchical vision-motion planning for a mobile robot under uncertainty is proposed. An optimal plan is generated by twolevel planning: global route selection and local path planning. In global route selection, a sequence of observation points to acquire sufficient information to reach a destination is determined. Both the cost and the uncertainty of vision are considered ...

In the minimum-cost k-hop spanning tree (k-hop MST) problem, we are given a set S of n points in a metric space, a positive small integer k and a root point r ∈ S. We are interested in computing a rooted spanning tree of minimum cost such that the longest root-leaf path in the tree has at most k edges. We present a polynomial-time approximation scheme for the plane. Our algorithm is based on Ar...