Article

The price of being near-sighted

Authors:

Thomas Moscibroda,

Roger WattenhoferAuthors Info & Claims

SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm

Pages 980 - 989

Published: 22 January 2006 Publication History

Abstract

Achieving a global goal based on local information is challenging, especially in complex and large-scale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible trade-off between the amount of local information and the quality of the global solution for general covering and packing problems. Specifically, we give a distributed algorithm using only small messages which obtains an (ρΔ)^1/k-approximation for general covering and packing problems in time O(k²), where ρ depends on the LP's coefficients. If message size is unbounded, we present a second algorithm that achieves an O(n^1/k) approximation in O(k) rounds. Finally, we prove that these algorithms are close to optimal by giving a lower bound on the approximability of packing problems given that each node has to base its decision on information from its k-neighborhood.

References

[1]

N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. Algorithms, 7(4):567--583, 1986.

Digital Library

[2]

Y. Bartal, J. W. Byers, and D. Raz. Global Optimization Using Local Information with Applications to Flow Control. In Proc. of the 38th Symp. on Foundations of Computer Science (FOCS), pages 303--312, 1997.

Digital Library

[3]

D. Dubhashi, A. Mei, A. Panconesi, J. Radhakrishnan, and A. Srinivasan. Fast Distributed Algorithms for (Weakly) Connected Dominating Sets and Linear-Size Skeletons. In Proc. of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 717--724, 2003.

Digital Library

[4]

M. Elkin. Unconditional Lower Bounds on the Time-Approximation Tradeoffs for the Distributed Minimum Spanning Tree Problem. In Proc. of the 36th ACM Symposium on Theory of Computing (STOC), 2004.

Digital Library

[5]

F. Fich and E. Ruppert. Hundreds of impossibility results for distributed computing. Distributed Computing, 16(2--3):121--163, 2003.

Digital Library

[6]

L. Fleischer. Approximating Fractional Multicommodity Flow Independent of the Number of Commodities. SIAM Journal on Discrete Math., 13(4):505--520, 2000.

Digital Library

[7]

A. Israeli and A. Itai. A Fast and Simple Randomized Parallel Algorithm for Maximal Matching. Information Processing Letters, 22:77--80, 1986.

Digital Library

[8]

L. Jia, R. Rajaraman, and R. Suel. An Efficient Distributed Algorithm for Constructing Small Dominating Sets. In Proc. of the 20th Symposium on Principles of Distributed Computing (PODC), pages 33--42, 2001.

[9]

F. Kuhn, T. Moscibroda, and R. Wattenhofer. What Cannot Be Computed Locally! In Proc. of the 23rd ACM Symp. on Principles of Distributed Computing (PODC), pages 300--309, 2004.

Digital Library

[10]

F. Kuhn and R. Wattenhofer. Constant-Time Distributed Dominating Set Approximation. In Proc. of the 22nd ACM Symposium on Principles of Distributed Computing (PODC), pages 25--32, 2003.

Digital Library

[11]

N. Linial. Locality in Distributed Graph Algorithms. SIAM Journal on Computing, 21(1):193--201, 1992.

Digital Library

[12]

N. Linial and M. Saks. Low Diameter Graph Decompositions. Combinatorica, 13(4):441--454, 1993.

[13]

M. Luby. A Simple Parallel Algorithm for the Maximal Independent Set Problem. SIAM Journal on Computing, 15:1036--1053, 1986.

Digital Library

[14]

M. Luby and N. Nisan. A Parallel Approximation Algorithm for Positive Linear Programming. In Proc. of the 25th ACM Symposium on Theory of Computing (STOC), pages 448--457, 1993.

Digital Library

[15]

M. Naor and L. Stockmeyer. What can be computed locally? SIAM Journal on Computing, 24(6):1259--1277, 1995.

Digital Library

[16]

C. Papadimitriou and M. Yannakakis. Linear Programming without the Matrix. In Proc. of the 25th Symp. on Theory of Computing (STOC), pages 121--129, 1993.

Digital Library

[17]

D. Peleg. Distributed Computing: A Locality-Sensitive Approach. SIAM, 2000.

Digital Library

[18]

S. Plotkin, D. Shmoys, and E. Tardos. Fast Approximation Algorithms for Fractional Packing and Covering Problems. Mathematics of Operations Research, 20:257--301, 1995.

Digital Library

[19]

S. Rajagopalan and V. Vazirani. Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs. SIAM Journal on Computing, 28:525--540, 1998.

Digital Library

[20]

T. Roughgarden and E. Tardos. How Bad is Selfish Routing? In Proc. of the 41th Symp. on Foundations of Computer Science (FOCS), pages 93--102, 2000.

Digital Library

[21]

N. Young. Randomized Rounding without Solving the Linear Program. In Proc. of the 6th Symposium on Discrete Algorithms (SODA), pages 170--178, 1995.

Digital Library

[22]

N. Young. Sequential and Parallel Algorithms for Mixed Packing and Covering. In Proc. of the 42nd Symposium on Foundations of Computer Science (FOCS), pages 538--546, 2001.

Digital Library

Cited By

Izumi TKitamura NNaruse TSchwartzman GAgrawal KLee I(2022)Fully Polynomial-Time Distributed Computation in Low-Treewidth GraphsProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538590(11-22)Online publication date: 11-Jul-2022
https://dl.acm.org/doi/10.1145/3490148.3538590
Abboud ACensor-Hillel KKhoury SPaz A(2021)Smaller Cuts, Higher Lower BoundsACM Transactions on Algorithms10.1145/346983417:4(1-40)Online publication date: 4-Oct-2021
https://dl.acm.org/doi/10.1145/3469834
Suomela J(2020)Using Round Elimination to Understand LocalityACM SIGACT News10.1145/3427361.342737451:3(63-81)Online publication date: 29-Sep-2020
https://dl.acm.org/doi/10.1145/3427361.3427374
Show More Cited By

Index Terms

The price of being near-sighted
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
  2. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
2. Theory of computation
  1. Design and analysis of algorithms

Recommendations

Memoryless near-collisions, revisited

In this paper we discuss the problem of generically finding near-collisions for cryptographic hash functions in a memoryless way. A common approach is to truncate several output bits of the hash function and to look for collisions of this modified ...
Known-key distinguishers on type-1 Feistel scheme and near-collision attacks on its hashing modes

We present some known-key distinguishers for a type-1 Feistel scheme with a permutation as the round function. To be more specific, the 29-round known-key truncated differential distinguishers are given for the 256-bit type-1 Feistel scheme with an SP (...
The price of bandit information for online optimization
NIPS'07: Proceedings of the 20th International Conference on Neural Information Processing Systems

In the online linear optimization problem, a learner must choose, in each round, a decision from a set D ⊂ ℝⁿ in order to minimize an (unknown and changing) linear cost function. We present sharp rates of convergence (with respect to additive regret) ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm

January 2006

1261 pages

ISBN:0898716055

Sponsors

SIAM Activity Group on Discrete Mathematics
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 22 January 2006

Check for updates

Qualifiers

Article

Acceptance Rates

Overall Acceptance Rate 411 of 1,322 submissions, 31%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

79
Total Citations
View Citations
606
Total Downloads

Downloads (Last 12 months)13
Downloads (Last 6 weeks)4

Reflects downloads up to 12 Aug 2024

Other Metrics

View Author Metrics

Citations

Cited By

Izumi TKitamura NNaruse TSchwartzman GAgrawal KLee I(2022)Fully Polynomial-Time Distributed Computation in Low-Treewidth GraphsProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538590(11-22)Online publication date: 11-Jul-2022
https://dl.acm.org/doi/10.1145/3490148.3538590
Abboud ACensor-Hillel KKhoury SPaz A(2021)Smaller Cuts, Higher Lower BoundsACM Transactions on Algorithms10.1145/346983417:4(1-40)Online publication date: 4-Oct-2021
https://dl.acm.org/doi/10.1145/3469834
Suomela J(2020)Using Round Elimination to Understand LocalityACM SIGACT News10.1145/3427361.342737451:3(63-81)Online publication date: 29-Sep-2020
https://dl.acm.org/doi/10.1145/3427361.3427374
Deurer JKuhn FMaus YRobinson PEllen F(2019)Deterministic Distributed Dominating Set Approximation in the CONGEST ModelProceedings of the 2019 ACM Symposium on Principles of Distributed Computing10.1145/3293611.3331626(94-103)Online publication date: 16-Jul-2019
https://dl.acm.org/doi/10.1145/3293611.3331626
Ben Basat REven GKawarabayashi KSchwartzman GRobinson PEllen F(2019)Optimal Distributed Covering AlgorithmsProceedings of the 2019 ACM Symposium on Principles of Distributed Computing10.1145/3293611.3331577(104-106)Online publication date: 16-Jul-2019
https://dl.acm.org/doi/10.1145/3293611.3331577
Deng HZhao THou I(2019)Online Routing and Scheduling With Capacity Redundancy for Timely Delivery Guarantees in Multihop NetworksIEEE/ACM Transactions on Networking10.1109/TNET.2019.291739327:3(1258-1271)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1109/TNET.2019.2917393
Indyk PMahabadi SRubinfeld RVakilian AYodpinyanee ACzumaj A(2018)Set cover in sub-linear timeProceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3174304.3175463(2467-2486)Online publication date: 7-Jan-2018
https://dl.acm.org/doi/10.5555/3174304.3175463
Czumaj AŁącki JMądry AMitrović SOnak KSankowski PDiakonikolas IKempe DHenzinger M(2018)Round compression for parallel matching algorithmsProceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3188745.3188764(471-484)Online publication date: 20-Jun-2018
https://dl.acm.org/doi/10.1145/3188745.3188764
Agarwal AChakaravarthy VChoudhury ARoy SSabharwal Y(2018)Set Cover Problems with Small Neighborhood CoversTheory of Computing Systems10.1007/s00224-017-9842-162:8(1763-1797)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.1007/s00224-017-9842-1
Mansour YPatt-Shamir BVardi S(2018)Constant-Time Local Computation AlgorithmsTheory of Computing Systems10.1007/s00224-017-9788-362:2(249-267)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1007/s00224-017-9788-3
Show More Cited By

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents