Probabilistic Algorithms for the Wake-Up Problem in Single-Hop Radio Networks

AbstractWe consider the problem of waking up n processors in a completely broadcast system. We analyze this problem in both globally and locally synchronous models, with or without n being known to the processors and with or without labeling of the processors. The main question we answer is: how fast we can wake up all the processors with probability 1 - ε in each of these eight models? In [12] a logarithmic waking algorithm for the strongest set of assumptions is described, while for weaker models only linear and quadratic algorithms were obtained. We prove that in the weakest model (local synchronization, no knowledge of n or labeling) the best waking time is O(n/log n). We also show logarithmic or polylogarithmic probabilistic waking algorithms for all stronger models, which in some cases gives an exponential improvement over previous results.

[1]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[2]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[3]  Peter March,et al.  On the stability of the Ethernet , 1985, STOC '85.

[4]  Imrich Chlamtac,et al.  On Broadcasting in Radio Networks - Problem Analysis and Protocol Design , 1985, IEEE Transactions on Communications.

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

[6]  Frank Thomson Leighton,et al.  Analysis of backoff protocols for multiple access channels , 1987, STOC '87.

[7]  Michael J. Fischer,et al.  The wakeup problem , 1990, STOC '90.

[8]  Noga Alon,et al.  A Lower Bound for Radio Broadcast , 1991, J. Comput. Syst. Sci..

[9]  Reuven Bar-Yehuda,et al.  On the Time-Complexity of Broadcast in Multi-hop Radio Networks: An Exponential Gap Between Determinism and Randomization , 1992, J. Comput. Syst. Sci..

[10]  Eyal Kushilevitz,et al.  An Ω(D log(N/D)) lower bound for broadcast in radio networks , 1993, PODC '93.

[11]  Michael J. Fischer,et al.  The Wakeup Problem , 1996, SIAM J. Comput..

[12]  Jacques Mazoyer.  On Optimal Solutions to the Firing Squad Synchronization Problem , 1996, Theor. Comput. Sci..

[13]  C. SIAMJ..  AN Ω(D log(N/D)) LOWER BOUND FOR BROADCAST IN RADIO NETWORKS∗ , 1998 .

[14]  Eyal Kushilevitz,et al.  An Omega(D log (N/D)) Lower Bound for Broadcast in Radio Networks , 1998, SIAM J. Comput..

[15]  Wojciech Rytter,et al.  Fast broadcasting and gossiping in radio networks , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[16]  Andrzej Pelc,et al.  Assigning Labels in Unknown Anonymous Networks , 2000 .

[17]  Stephan Olariu,et al.  Energy-Efficient Initialization Protocols for Single-Hop Radio Networks with No Collision Detection , 2000, IEEE Trans. Parallel Distributed Syst..

[18]  Andrzej Pelc,et al.  The Wakeup Problem in Synchronous Broadcast Systems , 2000, SIAM J. Discret. Math..

[19]  Andrzej Lingas,et al.  Oblivious gossiping in ad-hoc radio networks , 2001, DIALM '01.

[20]  Piotr Indyk,et al.  Explicit constructions of selectors and related combinatorial structures, with applications , 2002, SODA '02.

[21]  Shimon Even,et al.  Unison, canon, and sluggish clocks in networks controlled by a synchronizer , 1995, Mathematical systems theory.

[22]  Reuven Bar-Yehuda,et al.  Efficient emulation of single-hop radio network with collision detection on multi-hop radio network with no collision detection , 1989, Distributed Computing.

[23]  Igor Potapov,et al.  Deterministic Communication in Radio Networks with Large Labels , 2006, Algorithmica.