On-Line Maximum Matching in Complete Multipartite Graphs with Implications to the Minimum ADM Problem on a Star Topology

Abstract

Abstract. One of the basic problems in optical networks is assigning wavelengths to (namely, coloring of) a given set of lightpaths so as to minimize the number of ADM switches. In this paper we present a connection between maximum matching in complete multipartite graphs and ADM minimization in star networks. A tight 2/3 competitive ratio for finding a maximum matching implies a tight 10/9 competitive ratio for finding a coloring that minimizes the number of ADMs.

On-line maximum matching in complete multi-partite graphs with an application to optical networks

“…In this work, whose preliminary version is published in [15], we consider complete multipartite graphs. To the best of our knowledge, this is the first study of on-line maximum matching in these graphs.…”

Scalable Feature Matching Across Large Data Collections

“…subjects, digital images, or networks) based on common descriptor variables is an ubiquitous task in applied science. This problem, variously known as object matching, feature matching, data association, or assignment problem, is at the core of applications such as resource allocation [Pierskalla, 1968], object tracking [Thornbrue et al, 2010, Bar-Shalom et al, 2011, Dehghan et al, 2015, Rezatofighi et al, 2015, Smeulders et al, 2014, Wang et al, 2015, object recognition [Lowe, 2001, Belongie et al, 2002, Conte et al, 2004, navigation systems [Doherty et al, 2019], image registration [Le Moigne et al, 2011, Ashburner, 2007, optimization of communication networks [Shalom et al, 2010], connectomics in neuroscience [Haxby et al, 2011, Vogelstein et al, 2015, and more.…”