Fast Quasi-Threshold Editing

We introduce Quasi-Threshold Mover (QTM), an algorithm to solve the quasi-threshold (also called trivially perfect) graph editing problem with edge insertion and deletion. Given a graph it computes a quasi-threshold graph which is close in terms of edit count. This edit problem is NP-hard. We present an extensive experimental study, in which we show that QTM is the first algorithm that is able to scale to large real-world graphs in practice. As a side result we further present a simple linear-time algorithm for the quasi-threshold recognition problem.Comment: 26 pages, 4 figures, submitted to ESA 201

Analyses of the Watershed Transform

International audienceIn the framework of mathematical morphology, watershed transform (WT) represents a key step in image segmentation procedure. In this paper, we present a thorough analysis of some existing watershed approaches in the discrete case: WT based on flooding, WT based on path-cost minimization, watershed based on topology preservation, WT based on local condition and WT based on minimum spanning forest. For each approach, we present detailed description of processing procedure followed by mathematical foundations and algorithm of reference. Recent publications based on some approaches are also presented and discussed. Our study concludes with a classification of different watershed transform algorithms according to solution uniqueness, topology preservation, prerequisites minima computing and linearity

Branch-and-Bound Ranked Search by Minimizing Parabolic Polynomials

The Branch-and-Bound Ranked Search algorithm (BRS) is an efficient method for answering top-k queries based on R-trees using multivariate scoring functions. To make BRS effective with ascending rankings, the algorithm must be able to identify lower bounds of the scoring functions for exploring search partitions. This paper presents BRS supporting parabolic polynomials. These functions are common to minimize combined scores over different attributes and cover a variety of applications. To the best of our knowledge the problem to develop an algorithm for computing lower bounds for the BRS method has not been well addressed yet

A numerical approach to cyclic-service queueing models

Queueing Theory;operations research