We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph which has a small number of connected components, either to improve the prediction performance, or to obtain better interpretable results. Existing regularization or penalty functions for this ...

The global states of complex systems often form pospaces, topological spaces equipped with compatible partial orders reflecting causal relationships between the states. The calculation of tractable invariants on such pospaces can reveal critical system behavior unseen by ordinary invariants on the underlying spaces, thereby sometimes cirumventing the state space problem bedevilling static analy...

An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. Asteroidal triples play a central role in a classical characterization of interval graphs by Lekkerkerker and Boland. Their result says that a chordal graph is an interval graph if and only if it does not contain an asteroidal triple. In this paper, we...

Given a digraph D, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in D an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. Gutin, Razgon and Kim (2008) proved that MinLOB is polynomial time solvable for acyclic digraphs which are exactly the digraphs of directed path-width (DAG-width, directed tree-width, respectively) 0. We in...

Motivated by Asynchronous Transfer Mode (ATM) in telecommunication networks, we investigate the problem of designing a directed virtual topology on a directed physical topology, which consists in nding a set of directed virtual paths (VPs) satisfying some constraints in terms of load (the number of VPs sharing a physical link) and hop count (the number of VPs used to establish a connection). Fo...

Path finding is an ubiquitous problem in optimization and graphs in general, for which fast algorithms exist. Yet, in many cases side constraints make these well known algorithms inapplicable. In this paper we study constraints to find shortest paths on a weighted directed graph with arbitrary side constraints. We use the conjunction of two directed tree constraints to model the path, and a bou...

We consider economical representations for the path information in a directed graph. A directed graph G is said to be a transitive reduction of the directed graph G provided that (i) G has a directed path from vertex u to vertex v if and only if G has a directed path from vertex u to vertex v, and (ii) there is no graph with fewer arcs than G satisfying condition (i). Though directed graphs wit...

We construct a locally compact Hausdorff topology on the path space of a directed graph E and identify its boundary-path space ∂E as the spectrum of a commutative C∗-subalgebra DE of C∗(E). We then show that ∂E is homeomorphic to a subset of the infinite-path space of any desingularisation F of E. Drinen and Tomforde showed that we can realise C∗(E) as a full corner of C∗(F ), and we deduce tha...

This article investigates the problem of designing virtual di-paths (VPs) in a directed ATM model, in which the ow of information in the two directions of a link are not identical. On top of a given physical network we construct directed VPs. Routing in the physical network is done using these VPs. Given the capacity of each physical link (the maximum number of VPs that can pass through the lin...