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We prove that to find optimal positional strategies for stochastic mean payoff games when the value of every state of the game is known, in general, is as hard as solving such games tout court. This answers a question posed by Daniel Andersson and Peter Bro Miltersen. In this note, we consider perfect information 0-sum stochastic games, which, for short, we will just call stochastic games. For ...

In this paper, we propose a new method of recognizing mathematical formulae. The method is robust against the recognition errors of characters and the variation of the printing styles of the documents. The outline is as follows: we first construct a network with vertices representing the characters (symbols), linked each other by several edges with labels and costs representing the possible rel...

We describe an O(min(m,n3/2)m1/2)-time algorithm for finding maximum flows in undirected networks with unit capacities and no parallel edges. This improves upon the previous bound of Karzanov and Even and Tarjan when m = ω(n3/2), and upon a randomized bound of Karger when v = Ω(n7/4/m1/2).

First I want to say a few words about my graph terminology. If I want to allow loops, I use the adjective reflexive. If I want to allow multiple edges, I use multigraph. Thus, a graph has no loops and no multiple edges. I use valency rather than degree. If we say a graph is 4-valent (or tetravalent), it means it is regular of valency 4, for example. A decomposition of a graph X is a partition o...

A c-edge-colored multigraph has each edge colored with one of the c available colors and no two parallel edges have the same color. A proper Hamiltonian cycle is a cycle containing all the vertices of the multigraph such that no two adjacent edges have the same color. In this work we establish sufficient conditions for a multigraph to have a proper Hamiltonian cycle, depending on several parame...

We consider only finite undirected graphs without loops or multiple edges. For terminology and notation not defined here we refer the reader to Bondy and Murty’s textbook [6]. In this note we investigate irregularity measures of graphs. A graph is regular if all its vertices have the same degree, otherwise it is irregular. However, it is of interest to measure how irregular it is. Several appro...

Multi-Edge type Low-Density Parity-Check codes (METLDPC codes) introduced by Richardson and Urbanke are generalized LDPC codes which can be seen as LDPC codes obtained by concatenating several standard (ir)regular LDPC codes. We prove in this paper that MET-LDPC code ensembles possess a certain symmetry with respect to their Average Coset Weight Distributions (ACWD). Using this symmetry, we dri...

As in the foreseeable future a human will be expected to remain as part of the object extraction system, semi-automated road extraction methods are still important. Following this trend, this paper presents a semi-automated method for extracting road segments from mediumand high-resolution images based on active testing and edge analysis. The method is based on two sequential and independent st...

We prove that, if a graph G (without multiple edges) has maximum degree d and edge-chromatic number d + 1, then G contains two distinct vertices x, y and a collection of d pairwise edge-disjoint paths between x and y. In particular, the line graph of G satisfies Hajós’ conjecture. © 2006 Elsevier Inc. All rights reserved.