Asynchronous leader election and MIS using abstract MAC layer

We study leader election (LE) and computation of a maximal independent set (MIS) in wireless ad-hoc networks. We use the abstract MAC layer proposed in [14] to divorce the algorithmic complexity of solving these problems from the low-level issues of contention and collisions. We demonstrate the advantages of such a MAC layer by presenting simple asynchronous deterministic algorithms to solve LE and MIS and proving their correctness. First, we present an LE algorithm for static single-hop networks in which each process sends no more than three messages to its neighbors in the system. Next, we present an algorithm to compute an MIS in a static multi-hop network in which each process sends a constant number of messages to each of its neighbors in the communication graph.

[1]  Nancy A. Lynch,et al.  MAC design for analog network coding , 2011, FOMC '11.

[2]  Jennifer L. Welch,et al.  An asynchronous leader election algorithm for dynamic networks , 2009, 2009 IEEE International Symposium on Parallel & Distributed Processing.

[3]  Dina Katabi,et al.  Zigzag decoding: combating hidden terminals in wireless networks , 2008, SIGCOMM '08.

[4]  Nancy A. Lynch,et al.  Leader Election Using Loneliness Detection , 2011, DISC.

[5]  Andrzej Pelc,et al.  Leader election in ad hoc radio networks: A keen ear helps , 2013, J. Comput. Syst. Sci..

[6]  Jennifer L. Welch,et al.  Neighbor discovery in mobile ad hoc networks using an abstract MAC layer , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[7]  Nancy A. Lynch,et al.  The abstract MAC layer , 2009, Distributed Computing.

[8]  Roger Wattenhofer,et al.  A log-star distributed maximal independent set algorithm for growth-bounded graphs , 2008, PODC '08.

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

[10]  Stephan Olariu,et al.  Uniform leader election protocols for radio networks , 2001, International Conference on Parallel Processing, 2001..

[11]  Roger Wattenhofer,et al.  Fast Deterministic Distributed Maximal Independent Set Computation on Growth-Bounded Graphs , 2005, DISC.

[12]  Miroslaw Kutylowski,et al.  Efficient algorithms for leader election in radio networks , 2002, PODC '02.

[13]  John Capetanakis,et al.  Tree algorithms for packet broadcast channels , 1979, IEEE Trans. Inf. Theory.

[14]  Andrzej Pelc,et al.  Broadcasting in undirected ad hoc radio networks , 2005, Distributed Computing.

[15]  Reuven Bar-Yehuda,et al.  On the time-complexity of broadcast in radio networks: an exponential gap between determinism randomization , 1987, PODC '87.

[16]  Hagit Attiya,et al.  Distributed Computing: Fundamentals, Simulations and Advanced Topics , 1998 .

[17]  Dan E. Willard,et al.  Log-Logarithmic Selection Resolution Protocols in a Multiple Access Channel , 1986, SIAM J. Comput..

[18]  Stephan Olariu,et al.  A survey on leader election protocols for radio networks , 2002, Proceedings International Symposium on Parallel Architectures, Algorithms and Networks. I-SPAN'02.

[19]  Koji Nakano,et al.  Randomized Leader Election Protocols in Noisy Radio Networks with a Single Transceiver , 2006, ISPA.

[20]  Stephan Olariu,et al.  Randomized Leader Election Protocols in Radio Networks with No Collision Detection , 2000, ISAAC.

[21]  Roger Wattenhofer,et al.  Maximal independent sets in radio networks , 2005, PODC '05.

[22]  Nancy A. Lynch,et al.  Decomposing broadcast algorithms using abstract MAC layers , 2010, DIALM-POMC '10.

[23]  Stephan Olariu,et al.  Leader election protocols for radio networks , 2002 .

[24]  Seif Haridi,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[25]  Roger Wattenhofer,et al.  What Is the Use of Collision Detection (in Wireless Networks)? , 2010, DISC.