Partial cubes are defined as isometric subgraphs of hypercubes. For a partial cube G, its crossing graph G# is introduced as the graph whose vertices are the equivalence classes of the Djoković–Winkler relation Θ, two vertices being adjacent if they cross on a common cycle. It is shown that every graph is the crossing graph of some median graph and that a partial cube G is 2-connected if and on...

In this paper, we present GMG-BCU — a local search algorithm based on block coordinate update for estimating generalized median graph given collection of labeled or unlabeled input graphs. Unlike all competitors, is designed both discrete and continuous label spaces can be configured to run in linear time w. r. t. the size whenever node edge labels are computable time. These properties make usa...

A set of vertices S in a graph is called geodetic if every vertex of this graph lies on some shortest path between two vertices from S. In this paper, minimum geodetic sets in median graphs are studied with respect to the operation of peripheral expansion. Along the way geodetic sets of median prisms are considered and median graphs that possess a geodetic set of size two are characterized. © 2...

A profile π = (x1, ..., xk), of length k, in a finite connected graph G is a sequence of vertices of G, with repetitions allowed. A median x of π is a vertex for which the sum of the distances from x to the vertices in the profile is minimum. The median function finds the set of all medians of a profile. Medians are important in location theory and consensus theory. A median graph is a graph fo...

In the quest to better understand the connection between median graphs, triangle-free graphs and partial cubes, a hierarchy of subclasses of partial cubes has been introduced. In this article, we study the role of tiled partial cubes in this scheme. For instance, we prove that

Tree-like isometric subgraphs of hypercubes, or tree-like partial cubes as we shall call them, are a generalization of median graphs. Just as median graphs they capture numerous properties of trees, but encompass a larger class of graphs that may be easier to recognize than the class of median graphs. We investigate the structure of tree-like partial cubes, characterize them, and provide exampl...

In the computer security task of anomaly detection, we wish to measure not only the classi cation accuracy of a detector but also the average time to detection. This quantity represents either the average time between false alarms (for a valid user) or the average time until a hostile user is detected. We examine the use of noise suppression lters as componants of a learning classi cation syste...

In evolutionary biology, biologists often face the problem of constructing a phylogenetic tree on a set X of species from a multiset Π of partitions corresponding to various attributes of these species. One approach that is used to solve this problem is to try instead to associate a tree (or even a network) to the multiset ΣΠ consisting of all those bipartitions {A,X − A} with A a part of some ...