Abstract
The process number is the minimum number of requests that have to be simultaneously disturbed during a routing reconfiguration phase of a connection oriented network. From a graph theory point of view, it is similar to the node search number, and thus to the pathwidth, however they are not always equal. In general determining these parameters is NP-complete.
We present a distributed algorithm to compute these parameters and the edge search number, in trees. It can be executed in an asynchronous environment, requires n steps, an overall computation time of O(nlogn), and n messages of size log3 n + 2. Then, we propose a distributed algorithm to update these parameters on each component of a forest after addition or deletion of any tree edge. This second algorithm requires O(D) steps, an overall computation time of O(Dlogn), and O(D) messages of size log3 n + 3, where D is the diameter of the new connected component.
This work was partially funded by the European projects ist fet Aeolus and COST 293 Graal, ARC CARMA, ANR JC OSERA, CRC CORSO and Région PACA.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Robertson, N., Seymour, P.D.: Graph minors. I. Excluding a forest. J. Combin. Theory Ser. B 35, 39–61 (1983)
Ellis, J., Sudborough, I., Turner, J.: The vertex separation and search number of a graph. Information and Computation 113, 50–79 (1994)
Scheffler, P.: A linear algorithm for the pathwidth of trees. In: Bodendiek, R., Henn, R. (eds.) Topics in Combinatorics and Graph Theory, pp. 613–620. Physica-Verlag, Heidelberg (1990)
Skodinis, K.: Construction of linear tree-layouts which are optimal with respect to vertex separation in linear time. Journal of Algorithms 47, 40–59 (2003)
Kirousis, M., Papadimitriou, C.: Searching and pebbling. Theoretical Computer Science 47, 205–218 (1986)
Fomin, F., Thilikos, D.: An annotated bibliography on guaranteed graph searching. Theor. Comput. Sci. 399, 236–245 (2008)
Díaz, J., Petit, J., Serna, M.: A survey on graph layout problems. ACM Computing Surveys 34, 313–356 (2002)
Coudert, D., Perennes, S., Pham, Q.C., Sereni, J.S.: Rerouting requests in wdm networks. In: AlgoTel 2005, Presqu’île de Giens, France, pp. 17–20 (2005)
Coudert, D., Sereni, J.S.: Characterization of graphs and digraphs with small process number. Research Report 6285, INRIA (2007)
Megiddo, N., Hakimi, S.L., Garey, M.R., Johnson, D.S., Papadimitriou, C.H.: The complexity of searching a graph. J. Assoc. Comput. Mach. 35, 18–44 (1988)
Kinnersley, N.G.: The vertex separation number of a graph equals its pathwidth. Information Processing Letters 42, 345–350 (1992)
Coudert, D., Huc, F., Mazauric, D.: A distributed algorithm for computing and updating the process number of a forest. Research Report 6560, INRIA (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Coudert, D., Huc, F., Mazauric, D. (2008). Computing and Updating the Process Number in Trees. In: Baker, T.P., Bui, A., Tixeuil, S. (eds) Principles of Distributed Systems. OPODIS 2008. Lecture Notes in Computer Science, vol 5401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92221-6_37
Download citation
DOI: https://doi.org/10.1007/978-3-540-92221-6_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92220-9
Online ISBN: 978-3-540-92221-6
eBook Packages: Computer ScienceComputer Science (R0)