A Tight Lower Bound for Parity in Noisy Communication Networks

被引:0
|
作者
Dutta, Chinmoy [1 ]
Kanoria, Yashodhan [2 ]
Manjunath, D. [3 ]
Radhakrishnan, Jaikumar [1 ]
机构
[1] Tata Inst Fundamental Res, Homi Bhabha Rd, Bombay 400005, Maharashtra, India
[2] Stanford Univ, Stanford, CA 94305 USA
[3] Indian Inst Technol, Madras, Tamil Nadu, India
来源
PROCEEDINGS OF THE NINETEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS | 2008年
关键词
D O I
暂无
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
We show a tight lower bound of Omega(N log log N) on the number of transmission required to compute the parity of N bits (with constant error) in a network of N randomly placed sensors, communicating using local transmissions, and operating with power near the connectivity threshold. This result settles a question left open by Ying, Srikant and Dullerud (WiOpt 06), who showed how the sum of all N bits can be computed using 0(N log log N) transmissions. Earlier works on lower bounds for communication networks worked with the full broadcast model without using the fact that the communication in real networks is local, determined by the power of the transmitters. In fact, in full broadcast networks parity can he computed using 0(N) transmissions. To obtain our lower bound we employ techniques developed by Goyal, Kindler and Saks (FOCS 05), who showed lower bounds in the full broadcast model by reducing the problem to a model of noisy decision trees. However, in order to capture the limited range of transmissions in real sensor networks, we define and work with a localized version of noisy decision trees. Our lower bound is obtained by exploiting special properties of parity computations in such decision trees.
引用
收藏
页码:1056 / +
页数:2
相关论文
共 50 条
  • [1] ON A LOWER BOUND FOR THE REDUNDANCY OF RELIABLE NETWORKS WITH NOISY GATES
    PIPPENGER, N
    STAMOULIS, GD
    TSITSIKLIS, JN
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1991, 37 (03) : 639 - 643
  • [2] A TIGHT LOWER BOUND ON THE SIZE OF PLANAR PERMUTATION NETWORKS
    KLAWE, M
    LEIGHTON, T
    LECTURE NOTES IN COMPUTER SCIENCE, 1990, 450 : 281 - 287
  • [3] A TIGHT LOWER BOUND ON THE SIZE OF PLANAR PERMUTATION NETWORKS
    KLAWE, M
    LEIGHTON, T
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 1992, 5 (04) : 558 - 563
  • [4] A Tight Lower Bound on the Controllability of Networks with Multiple Leaders
    Yazicioglu, A. Yasin
    Abbas, Waseem
    Egerstedt, Magnus
    2012 IEEE 51ST ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2012, : 1978 - 1983
  • [5] Distinguishing views in symmetric networks: A tight lower bound
    Dereniowski, Dariusz
    Kosowski, Adrian
    Pajak, Dominik
    THEORETICAL COMPUTER SCIENCE, 2015, 582 : 27 - 34
  • [6] A tight lower bound on the classical communication cost of entanglement dilution
    Harrow, AW
    Lo, HK
    2003 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS, 2003, : 429 - 429
  • [7] A tight lower bound on the classical communication cost of entanglement dilution
    Harrow, AW
    Lo, HK
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2004, 50 (02) : 319 - 327
  • [8] On Exponential Lower Bound for Protocols for Reliable Communication in Networks
    Srinathan, K.
    Rangan, C. Pandu
    Kumaresan, R.
    INFORMATION THEORETIC SECURITY, 2009, 4883 : 89 - +
  • [9] A NEW LOWER BOUND FOR PARITY CIRCUITS
    DU, DZ
    COMBINATORICS, COMPUTING AND COMPLEXITY, 1989, : 132 - 141
  • [10] A tight lower bound for the hardness of clutters
    Mkrtchyan, Vahan
    Sargsyan, Hovhannes
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2018, 35 (01) : 21 - 25