ABSTRACT
This paper addresses partial information spreading among n nodes of a network. As opposed to traditional information spreading, where each node has a message that must be received by all nodes, we propose a relaxed requirement, where only n/c nodes need to receive each message, and every node should receive n/c messages, for some c ≥ 1.
As a key tool in our study we introduce the novel concept of weak conductance, a generalization of classic graph conductance which allows to analyze the time required for partial information spreading. We show the power of weak conductance as a measure of how well-knit the components of a graph are, by giving an example of a graph family for which the conductance is O(n-2), while the weak conductance is as large as 1/2. For such graphs, weak conductance can be used to show that partial information spreading requires time complexity of O(\logn).
Finally, we demonstrate the usefulness of partial information spreading in solving the maximum coverage problem, which naturally arises in circuit layout, job scheduling and facility location, as well as in distributed resource allocation with a global budget constraint. Our algorithm yields a constant approximation factor and a constant deviation from the given budget. For graphs with a constant weak conductance, this implies a scalable time complexity for solving a problem with a global constraint.
- N. Alon, C. Avin, M. Koucky, G. Kozma, Z. Lotker, and M. R. Tuttle. Many random walks are faster than one. In SPAA '08: Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures, pages 119--128, New York, NY, USA, 2008. ACM. Google ScholarDigital Library
- D. Amzallag, J. Naor, and D. Raz. Coping with interference: From maximum coverage to planning cellular networks. In WAOA, pages 29--42, 2006. Google ScholarDigital Library
- E. Ando, H. Ono, K. Sadakane, and M. Yamashita. The space complexity of the leader election in anonymous networks. In IPDPS, pages 1--8, 2008.Google ScholarCross Ref
- D. Angluin. Local and global properties in networks of processors (extended abstract). In STOC '80: Proceedings of the twelfth annual ACM symposium on Theory of computing, pages 82--93, New York, NY, USA, 1980. ACM. Google ScholarDigital Library
- C. Avin and C. Brito. Efficient and robust query processing in dynamic environments using random walk techniques. In IPSN '04: Proceedings of the 3rd international symposium on Information processing in sensor networks, pages 277--286, New York, NY, USA, 2004. ACM. Google ScholarDigital Library
- C. Avin and G. Ercal. Bounds on the mixing time and partial cover of ad-hoc and sensor networks. In Wireless Sensor Networks, 2005. Proceeedings of the Second European Workshop on, pages 1--12, 2005.Google ScholarCross Ref
- M. Borokhovich, C. Avin, and Z. Lotker. Tight bounds for algebraic gossip on graphs. arXiv:1001.3265v1 {cs.IT}, 2010.Google Scholar
- F. Chierichetti, S. Lattanzi, and A. Panconesi. Almost tight bounds for rumour spreading with conductance. In Proceedings of the 42nd ACM Symposium on Theory of Computing (STOC 2010), to appear, 2010. Google ScholarDigital Library
- F. Chierichetti, S. Lattanzi, and A. Panconesi. Rumour spreading and graph conductance. In Proceedings of the 21st ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 1657--1663, 2010. Google ScholarDigital Library
- M. Conforti and G. Cornuejols. Submodular set functions, matroids and the greedy algorithm: Tight worstcase bounds and some generalizations of the rado-edmonds theorem. Discrete Applied Math, 7:257--274, 1984.Google ScholarCross Ref
- A. Demers, D. Greene, C. Hauser, W. Irish, J. Larson, S. Shenker, H. Sturgis, D. Swinehart, and D. Terry. Epidemic algorithms for replicated database maintenance. In PODC '87: Proceedings of the sixth annual ACM Symposium on Principles of distributed computing, pages 1--12, New York, NY, USA, 1987. ACM. Google ScholarDigital Library
- U. Feige. A threshold of ln n for approximating set cover. J. ACM, 45(4):634--652, 1998. Google ScholarDigital Library
- U. Feige, D. Peleg, P. Raghavan, and E. Upfal. Randomized broadcast in networks. In SIGAL International Symposium on Algorithms, pages 128--137, 1990. Google ScholarDigital Library
- P. Fraigniaud, A. Pelc, D. Peleg, and S. Pérennes. Assigning labels in unknown anonymous networks (extended abstract). In PODC '00: Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing, pages 101--111, New York, NY, USA, 2000. ACM. Google ScholarDigital Library
- M. R. Garey and D. S. Johnson. "strong" NP-completeness results: Motivation, examples, and implications. J. ACM, 25(3):499--508, 1978. Google ScholarDigital Library
- C. Georgiou, S. Gilbert, R. Guerraoui, and D. R. Kowalski. On the complexity of asynchronous gossip. In PODC '08: Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing, pages 135--144, New York, NY, USA, 2008. ACM. Google ScholarDigital Library
- F. Grandoni, J. Könemann, and A. Panconesi. Distributed weighted vertex cover via maximal matchings. ACM Trans. Algorithms, 5(1):1--12, 2008. Google ScholarDigital Library
- D. S. Hochbaum. Approximating covering and packing problems: set cover, vertex cover, independent set, and related problems. In Approximation algorithms for NP-hard problems, pages 94--143, Boston, MA, USA, 1997. PWS Publishing Co. Google ScholarDigital Library
- D. S. Hochbaum and A. Pathria. Analysis of the greedy approach in problems of maximum k-coverage. Naval Research Logistics, 45(6):615--627, 1998.Google ScholarCross Ref
- R. Kannan, L. Lovász, and R. Montenegro. Blocking conductance and mixing in random walks. Comb. Probab. Comput., 15(4):541--570, 2006. Google ScholarDigital Library
- R. Karp, C. Schindelhauer, S. Shenker, and B. Vocking. Randomized rumor spreading. In FOCS '00: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, page 565, Washington, DC, USA, 2000. IEEE Computer Society. Google ScholarDigital Library
- D. Kempe, A. Dobra, and J. Gehrke. Gossip-based computation of aggregate information. In Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS), page 482, Washington, DC, USA, 2003. IEEE Computer Society. Google ScholarDigital Library
- S. Khuller, A. Moss, and J. S. Naor. The budgeted maximum coverage problem. Inf. Process. Lett., 70(1):39--45, 1999. Google ScholarDigital Library
- C. Koufogiannakis and N. E. Young. Distributed and parallel algorithms for weighted vertex cover and other covering problems. In PODC '09: Proceedings of the 28th ACM symposium on Principles of distributed computing, pages 171--179, New York, NY, USA, 2009. ACM. Google ScholarDigital Library
- F. Kuhn, T. Moscibroda, and R. Wattenhofer. What cannot be computed locally! In PODC '04: Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing, pages 300--309, New York, NY, USA, 2004. ACM. Google ScholarDigital Library
- F. Kuhn, T. Moscibroda, and R. Wattenhofer. The price of being near-sighted. In SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, pages 980--989, New York, NY, USA, 2006. ACM. Google ScholarDigital Library
- L. Lovász and R. Kannan. Faster mixing via average conductance. In STOC '99: Proceedings of the thirty-first annual ACM symposium on Theory of computing, pages 282--287, New York, NY, USA, 1999. ACM. Google ScholarDigital Library
- D. Mosk-Aoyama and D. Shah. Computing separable functions via gossip. In Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing (PODC), pages 113--122, New York, NY, USA, 2006. ACM. Google ScholarDigital Library
- D. Mosk-Aoyama and D. Shah. Information dissemination via network coding. In 2006 IEEE International Symposium on Information Theory, pages 1748--1752, July 2006.Google ScholarCross Ref
- G. Nemhauser and L. Wolsey. Maximizing submodular set functions: Formulations and studies of algorithms. Studies on Graphs and Discrete Programming, pages 279--301, 1981.Google ScholarCross Ref
- R. G. Shlomi Dolev, Seth Gilbert and C. Newport. Gossiping in a multi-channel radio network (an oblivious approach to coping with malicious interference). In Proceedings of the 21st International Symposium on Distributed Computing (DISC), pages 208--222, 2007. Google ScholarDigital Library
- A. Sinclair. Algorithms for random generation and counting: a Markov chain approach. Birkhauser Verlag, Basel, Switzerland, Switzerland, 1993. Google ScholarDigital Library
- D. Subhadrabandhu, F. Anjum, S. Kannan, and S. Sarkar. Domination and coverage guarantees through distributed computation. In Proceedings of 43d Annual Allerton Conference on Communication, Control and Computing, Allerton, Monticello, Illinois, September 28--30, 2005.Google Scholar
- K. Suh, Y. Guo, J. Kurose, and D. Towsley. Locating network monitors: Complexity, heuristics, and coverage. Comput. Commun., 29(10):1564--1577, 2006. Google ScholarDigital Library
- R. V. Vohra and N. G. Hall. A probabilistic analysis of the maximal covering location problem. Discrete Appl. Math., 43(2):175--183, 1993. Google ScholarDigital Library
- M. Yamashita and T. Kameda. Computing on an anonymous network. In PODC '88: Proceedings of the seventh annual ACM Symposium on Principles of distributed computing, pages 117--130, New York, NY, USA, 1988. ACM. Google ScholarDigital Library
Index Terms
- Partial information spreading with application to distributed maximum coverage
Recommendations
Fast information spreading in graphs with large weak conductance
SODA '11: Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithmsGathering data from nodes in a network is at the heart of many distributed applications, most notably, while performing a global task. We consider information spreading among n nodes of a network, where each node v has a message m(v) which must be ...
Fast Information Spreading in Graphs with Large Weak Conductance
† Special Section on the Forty-First Annual ACM Symposium on Theory of Computing (STOC 2009)Gathering data from nodes in a network is at the heart of many distributed applications, most notably while performing a global task. We consider information spreading among $n$ nodes of a network, where each node $v$ has a message $m(v)$ which must be ...
Near-Optimal Distributed Dominating Set in Bounded Arboricity Graphs
PODC'22: Proceedings of the 2022 ACM Symposium on Principles of Distributed ComputingWe describe a simple deterministic O(ε-1 log Δ) round distributed algorithm for (2α+ 1) (1 + ε) approximation of minimum weighted dominating set on graphs with arboricity at most α. Here Δ denotes the maximum degree. We also show a lower bound proving ...
Comments