Separating codes and traffic monitoring

International audienceThis paper studies the problem of traffic monitoring which consists of differentiating a set of walks on a directed graph by placing sensors on as few arcs as possible. The problem of characterising a set of individuals by testing as few attributes as possible is already well-known, but traffic monitoring presents new challenges that the previous models of separation fall short from modelling such as taking into account the multiplicity and order of the arcs in a walk. We introduce a new and stronger model of separation based on languages that generalises the traffic monitoring problem. We study three subproblems with practical applications and develop methods to solve them by combining integer linear programming, separating codes and language theory

The Complexity of Connectivity Problems in Forbidden-Transition Graphs And Edge-Colored Graphs

The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs of consecutive edges on the walk are permitted. Forbidden-transition graphs and related models have found applications in a variety of fields, such as routing in optical telecommunication networks, road networks, and bio-informatics. We initiate the study of fundamental connectivity problems from the point of view of parameterized complexity, including an in-depth study of tractability with regards to various graph-width parameters. Among several results, we prove that finding a simple compatible path between given endpoints in a forbidden-transition graph is W[1]-hard when parameterized by the vertex-deletion distance to a linear forest (so it is also hard when parameterized by pathwidth or treewidth). On the other hand, we show an algebraic trick that yields tractability when parameterized by treewidth of finding a properly colored Hamiltonian cycle in an edge-colored graph; properly colored walks in edge-colored graphs is one of the most studied special cases of compatible walks in forbidden-transition graphs

Algorithmic Aspects in Information and Management [electronic resource] : 11th International Conference, AAIM 2016, Bergamo, Italy, July 18-20, 2016, Proceedings /

This volume constitutes the proceedings of the 11th International Conference on Algorithmic Aspects in Information and Management, AAIM 2016, held in Bergamo, Italy, in July 2016. The 18 revised full papers presented were carefully reviewed and selected from 41 submissions. The papers deal with current trends of research on algorithms, data structures, operation research, combinatorial optimization and their applications.Item Pricing for Combinatorial Public Projects -- Norm-Based Locality Measures of Two-Dimensional Hilbert Curves -- On the Complexity of Clustering with Relaxed Size Constraints -- Superstring Graph: A New Approach for Genome Assembly -- Efficient FPT Algorithms for (Strict) Compatibility of Unrooted Phylogenetic Trees -- A Very Fast String Matching Algorithm Based on Condensed Alphabets -- Minimum-Density Identifying Codes in Square Grids -- Separating Codes and Traffic Monitoring -- Know When to Persist: Deriving Value from a Stream Buffer -- Algorithmic Aspects of Upper Domination: A Parameterised Perspective -- On Network Formation Games with Heterogeneous Players and Basic Network Creation Games -- Parameterized Complexity of Team Formation in Social Networks -- Reconstructing Cactus Graphs from Shortest Path Information -- Near-Optimal Dominating Sets via Random Sampling -- A Multivariate Approach for Checking Resiliency in Access Control -- Efficient Algorithms for the Order Preserving Pattern Matching Problem -- Computing the Line-Constrained k-Center in the Plane for Small k -- Online k-max Search Algorithm with Applications to the Secretary Problem.This volume constitutes the proceedings of the 11th International Conference on Algorithmic Aspects in Information and Management, AAIM 2016, held in Bergamo, Italy, in July 2016. The 18 revised full papers presented were carefully reviewed and selected from 41 submissions. The papers deal with current trends of research on algorithms, data structures, operation research, combinatorial optimization and their applications