Formalization of the Necessary and Sufficient Connectivity Conditions to the Distributed Mutual Exclusion Problem in Dynamic Networks

Nowadays there exist many networks with dynamic characteristics (e.g. MANETs, DTNs, opportunistic networks, etc.). Our aim is thus to determine the necessary and sufficient connectivity conditions which allow the correct execution of some distributed algorithms on top of them. To this end, we use a framework proposed by Casteigts et al. [1] that exploits the evolving graphs theory, which models the topology of the network as well as the graph relabeling approach, which abstracts communication. In particular, we provide necessary and sufficient conditions for two important distributed problems: mutual exclusion and K-mutual exclusion.

[1]  Ashok K. Agrawala,et al.  An optimal algorithm for mutual exclusion in computer networks , 1981, CACM.

[2]  Boaz Patt-Shamir,et al.  Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing , 2008, PODC 2008.

[3]  Tomasz Imielinski,et al.  Structuring distributed algorithms for mobile hosts , 1994, 14th International Conference on Distributed Computing Systems.

[4]  Pierre Fraigniaud,et al.  Parsimonious flooding in dynamic graphs , 2009, PODC '09.

[5]  Kerry Raymond,et al.  A tree-based algorithm for distributed mutual exclusion , 1989, TOCS.

[6]  Yves Métivier,et al.  Graph relabelling systems and distributed algorithms , 1999 .

[7]  Afonso Ferreira,et al.  Building a reference combinatorial model for MANETs , 2004, IEEE Network.

[8]  Shmuel Zaks,et al.  Opportunistic Information Dissemination in Mobile Ad-hoc Networks: The Profit of Global Synchrony , 2010, DISC.

[9]  Achour Mostéfaoui,et al.  From static distributed systems to dynamic systems , 2005, 24th IEEE Symposium on Reliable Distributed Systems (SRDS'05).

[10]  Roberto Baldoni,et al.  A distributed mutual exclusion algorithm for mobile ad-hoc networks , 2002, Proceedings ISCC 2002 Seventh International Symposium on Computers and Communications.

[11]  Leslie Lamport,et al.  Time, clocks, and the ordering of events in a distributed system , 1978, CACM.

[12]  Mohamed Naimi,et al.  A Log(N) Distributed Mutual Exclusion Algorithm Based on Path Reversal , 1996, J. Parallel Distributed Comput..

[13]  Andrea E. F. Clementi,et al.  Flooding time in edge-Markovian dynamic graphs , 2008, PODC '08.

[14]  Nitin H. Vaidya,et al.  A Mutual Exclusion Algorithm for Ad Hoc Mobile Networks , 2001, Wirel. Networks.

[15]  Pierre Sens,et al.  Partition Participant Detector with Dynamic Paths in Mobile Networks , 2010, 2010 Ninth IEEE International Symposium on Network Computing and Applications.

[16]  Michel Raynal,et al.  A Distributed Algorithm for Mutual Exclusion in an Arbitrary Network , 1988, Comput. J..

[17]  Ichiro Suzuki,et al.  A distributed mutual exclusion algorithm , 1985, TOCS.

[18]  Andrea E. F. Clementi,et al.  Information Spreading in Stationary Markovian Evolving Graphs , 2011 .

[19]  Michel Raynal,et al.  Looking for a Definition of Dynamic Distributed Systems , 2007, PaCT.

[20]  Kerry Raymond.  A Distributed Algorithm for Multiple Entries to a Critical Section , 1989, Inf. Process. Lett..

[21]  Serge Chaumette,et al.  Characterizing Topological Assumptions of Distributed Algorithms in Dynamic Networks , 2009, SIROCCO.