Section: Research Program
Graph and Combinatorial Algorithms
We focus on two approaches for designing algorithms for large graphs: decomposing the graph and relying on simple graph traversals.
We more deeply study multi-sweep graph searches. In this domain a graph search only yields a total ordering of the vertices which can be used by the subsequent graph searches. This technique can be used on huge graphs and does not need extra memory. We have already obtained preliminary results in this direction and many well-known graph algorithms can be put in this framework. The idea behind this approach is that each sweep discovers some structure of the graph. At the end of the process either we have found the underlying structure (for example an interval representation for an interval graph) or an approximation of it (for example in hard discrete optimization problems). We envision applications to exact computations of centers in huge graphs, to underlying combinatorial optimization problems, but also to networks arising in biology.
In order to summarize a graph into a more compact and more human-readable form, we introduced the hub-laminar decomposition. It is suitable for graphs that are dominated by long isometric cycles or shortest paths, called laminar, which meet only at their extremities, called hubs. Computing this decomposition is NP-hard but a canonical approximation may be computed under some hypotheses on the distances between hubs. It provides a distance labelling for the decomposable graphs. We also investigated the case were the decomposition is reduced to a single cycle, yielding the problem of fining the longest isometric cycle, which is NP-complete and for which a first approximation algorithm was proposed in ENTCS.
In the course of graph exploration, a mobile agent is expected to regularly visit all the nodes of an unknown network, trying to discover all its nodes as quickly as possible. Our research focuses on the design and analysis of agent-based algorithms for exploration-type problems, which operate efficiently in a dynamic network environment, and satisfy imposed constraints on local computational resources, performance, and resilience. Our recent contributions in this area concern the design of fast deterministic algorithms for teams of agents operating in parallel in a graph, with limited or no persistent state information available at nodes. We plan further studies to better understand the impact of memory constraints and of the availability of true randomness on efficiency of the graph exploration process.