Distributed MIS in 𝑂 ( log log 𝑛 ) Awake Complexity

Maximal Independent Set (MIS) is one of the fundamental and most well-studied problems in distributed graph algorithms. Even after four decades of intensive research, the best-known (randomized) MIS algorithms have 𝑂 ( log 𝑛 ) round complexity on general graphs [Luby, STOC 1986](where 𝑛 is the number of nodes), while the best-known lower bound is Ω ( p log 𝑛 / loglog 𝑛 ) [Kuhn, Moscibroda, Wattenhofer, JACM 2016]. Breaking past the 𝑂 ( log 𝑛 ) round complexity upper bound or showing stronger lower bounds have been longstanding open problems.

[1]  John E. Augustine,et al.  Brief Announcement: Distributed MST Computation in the Sleeping Model: Awake-Optimal Algorithms and Lower Bounds , 2022, PODC.

[2]  M. Ghaffari,et al.  Average Awake Complexity of MIS and Matching , 2022, SPAA.

[3]  Gopal Pandurangan,et al.  Awake-Efficient Distributed Algorithms for Maximal Independent Set , 2022, IEEE International Conference on Distributed Computing Systems.

[4]  Thomas P. Hayes,et al.  How to Wake Up Your Neighbors: Safe and Nearly Optimal Generic Energy Conservation in Radio Networks , 2022, DISC.

[5]  Leonid Barenboim,et al.  Deterministic Logarithmic Completeness in the Distributed Sleeping Model , 2021, DISC.

[6]  Fabian Kuhn,et al.  Improved Distributed Lower Bounds for MIS and Bounded (Out-)Degree Dominating Sets in Trees , 2021, PODC.

[7]  Thomas P. Hayes,et al.  Brief Announcement: Wake Up and Join Me! An Energy Efficient Algorithm for Maximal Matching in Radio Networks , 2021, Distributed Computing.

[8]  Thomas P. Hayes,et al.  The Energy Complexity of BFS in Radio Networks , 2020, PODC.

[9]  Mohsen Ghaffari,et al.  Improved Deterministic Network Decomposition , 2020, SODA.

[10]  Soumyottam Chatterjee,et al.  Sleeping is Efficient: MIS in O(1)-rounds Node-averaged Awake Complexity , 2020, PODC.

[11]  Václav Rozhon,et al.  Polylogarithmic-time deterministic network decomposition and distributed derandomization , 2019, STOC.

[12]  Jukka Suomela,et al.  Lower Bounds for Maximal Matchings and Maximal Independent Sets , 2019, 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS).

[13]  Christian Konrad,et al.  MIS in the Congested Clique Model in $O(\log \log \Delta)$ Rounds , 2018, 1802.07647.

[14]  Thomas P. Hayes,et al.  The Energy Complexity of Broadcast , 2017, PODC.

[15]  Manuela Fischer,et al.  Tight Analysis of Parallel Randomized Greedy MIS , 2017, SODA.

[16]  Seth Pettie,et al.  Exponential separations in the energy complexity of leader election , 2016, STOC.

[17]  Krzysztof Krzywdzinski,et al.  Distributed algorithms for random graphs , 2015, Theor. Comput. Sci..

[18]  Mohsen Ghaffari,et al.  An Improved Distributed Algorithm for Maximal Independent Set , 2015, SODA.

[19]  Wendi B. Heinzelman,et al.  An adaptive sensor sleeping solution based on sleeping multipath routing and duty-cycled MAC protocols , 2013, ACM Trans. Sens. Networks.

[20]  Marek Klonowski,et al.  Energy-Efficient Leader Election Protocols for Single-Hop Radio Networks , 2013, 2013 42nd International Conference on Parallel Processing.

[21]  Maxwell Young,et al.  Making evildoers pay: resource-competitive broadcast in sensor networks , 2012, PODC '12.

[22]  Guy E. Blelloch,et al.  Greedy sequential maximal independent set and matching are parallel on average , 2012, SPAA '12.

[23]  Leonid Barenboim,et al.  The Locality of Distributed Symmetry Breaking , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[24]  Cynthia A. Phillips,et al.  Sleeping on the Job: Energy-Efficient and Robust Broadcast for Radio Networks , 2011, Algorithmica.

[25]  Christoph Lenzen,et al.  MIS on trees , 2011, PODC '11.

[26]  Leonid Barenboim,et al.  Sublogarithmic distributed MIS algorithm for sparse graphs using Nash-Williams decomposition , 2008, PODC '08.

[27]  Rong Zheng,et al.  On-demand power management for ad hoc networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

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

[29]  Martin Nilsson,et al.  Investigating the energy consumption of a wireless network interface in an ad hoc networking environment , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

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

[31]  Prabhakar Raghavan,et al.  Parallel graph algorithms that are efficient on average , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[32]  Michael Luby,et al.  A simple parallel algorithm for the maximal independent set problem , 1985, STOC '85.

[33]  Noga Alon,et al.  A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem , 1985, J. Algorithms.

[34]  Roger Wattenhofer,et al.  Local Computation , 2010, J. ACM.

[35]  Qin Wang,et al.  A Realistic Power Consumption Model for Wireless Sensor Network Devices , 2006, 2006 3rd Annual IEEE Communications Society on Sensor and Ad Hoc Communications and Networks.

[36]  C. Siva Ram Murthy,et al.  Ad Hoc Wireless Networks: Architectures and Protocols , 2004 .

[37]  David Peleg,et al.  Distributed Computing: A Locality-Sensitive Approach , 1987 .