# Tag: graphs

## (Reported to unkwown date) The Bron-Kerbosch algorithm with vertex ordering is output sensitive.

summary: The Bron-Kerbosch algorithm is a well known maximal clique enumeration algorithm. So far it was unknown whether it was output sensitive or not. In this paper we partially answer this question by proving that the Bron-Kerbosch Algorithm with vertex ordering, first introduced and studied by Eppstein, Löffler and Strash ...

## L-orientations of graphs

summary: An orientation of an (undirected) graph G is an assignment of directions to each edge of G. In this talk, we consider an orientation such that the out-degree of each vertex is contained in a given list. We introduce several relations to graph theory topics and pose our main ...

## PHD defense: A guide book for the traveller on graphs full of blockages

summary: We study NP-hard problems dealing with graphs containing blockages.

We analyze cut problems via the parameterized complexity framework. The size p of the cut is the parameter. Given a set of sources {s_1,...,s_k} and a target t, we propose an algorithm deciding whether a cut of size at ...

## Overcoming interference in the beeping communication model

summary: Small inexpensive inter-communicating electronic devices have become widely available. Although the individual device has severely limited capabilities (e.g., basic communication, constant-size memory or limited mobility), multitudes of such weak devices communicating together are able to form low-cost, easily deployable, yet highly performant networks. Such distributed systems present significant ...

## Scalable Load Balancing - Distributed Algorithms and the Packing Model

summary: Load imbalance is a recurring problem in High Performance Computing (HPC), which leads to suboptimal performance via the under-use of available resources. As computing systems grow larger, resource management and load balancing become a costly process, especially for dynamic applications that demand periodical workload balance. With this in mind ...

## graph algorithms to help molecular construction

**Summary:**
In organic chemistry, when a new molecule is designed, it is necessary to determine chemical reactions that can be used to synthesize this target molecule from available compounds. Finding such chemical reactions consists usually in searching in a reaction database (such as REAXYS or ChEBI) for a molecule that ...

## Fighting epidemics with the maximum spectral subgraph

**Summary:** Recent developments in mathematical epidemiology have identified a relationship between the time to extinction of an epidemic spreading over a network and the spectral radius of the underlying graph i.e. the largest eigenvalue of its adjacency matrix. At the same time, new generation networking technologies such as NFV ...

## Reconfiguration Distribuée de Problèmes de Graphes

**Summary:** En théorie des graphes, un problème de configuration est le suivant : est-il possible d'aller d'une solution valide d'un problème à une autre, en passant par un chemin de solutions acceptables ? Quelle est la longueur minimale d'un chemin ? Quelle est la complexité ? Par exemple, un problème ...

## Some recent results on the integer linear programming formulation for the Max-Cut problem

**Summary:** Given an undirected graph G=(V,E) where the edges are weighted by an arbitrary cost vector c, a cut S in G associated with a node subset S is the edge subset of E which contains all the edges having exactly one end-node in S.
The Maximum Cut ...

## Maximum Independent Set in H-free graphs

**Summary:** Maximum Independent Set (MIS) in graphs without a connected H as an induced subgraph (that is, H-free) is NP-complete when H is not a tree with at most one vertex of degree at least 3. For the other graphs H, which are paths and subdivisions of the claw (K_1 ...

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