Theoretical Computer Science
The complexity of searching a graph
Journal of the ACM (JACM)
The vertex separation and search number of a graph
Information and Computation
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Approximating Minimum Feedback Sets and Multi-Cuts in Directed Graphs
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Reconfiguration of the routing in WDM networks with two classes of services
ONDM'09 Proceedings of the 13th international conference on Optical Network Design and Modeling
Analyzing two different objectives of the WDM lightpath reconfiguration problem
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Tradeoffs in process strategy games with application in the WDM reconfiguration problem
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Characterization of graphs and digraphs with small process numbers
Discrete Applied Mathematics
Exact and Approximate Solutions for the Gate Matrix Layout Problem
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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We consider a variant of the graph searching games that models the routing reconfiguration problem in WDM networks. In the digraph processing game, a team of agents aims at processing, or clearing, the vertices of a digraph D. We are interested in two different measures: (1) the total number of agents used, and (2) the total number of vertices occupied by an agent during the processing of D. These measures, respectively, correspond to the maximum number of simultaneous connections interrupted and to the total number of interruptions during a routing reconfiguration in a WDM network. Previous works have studied the problem of independently minimizing each of these parameters. In particular, the corresponding minimization problems are APX-hard, and the first one is known not to be in APX. In this paper, we give several complexity results and study tradeoffs between these conflicting objectives. In particular, we show that minimizing one of these parameters while the other is constrained is NP-complete. Then, we prove that there exist some digraphs for which minimizing one of these objectives arbitrarily impairs the quality of the solution for the other one. We show that such bad tradeoffs may happen even for a basic class of digraphs. On the other hand, we exhibit classes of graphs for which good tradeoffs can be achieved. We finally detail the relationship between this game and the routing reconfiguration problem. In particular, we prove that any instance of the processing game, i.e. any digraph, corresponds to an instance of the routing reconfiguration problem.