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Approximating the Diameter

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 200 Accesses

Years and Authors of Summarized Original Work

  • 1999; Aingworth, Chekuri, Indyk, Motwani

  • 2013; Roditty, Vassilevska Williams

  • 2014; Chechik, Larkin, Roditty, Schoenebeck, Tarjan, Vassilevska Williams

Problem Definition

The diameter of a graph is the largest distance between its vertices. Closely related to the diameter is the radius of the graph. The center of a graph is a vertex that minimizes the maximum distance to all other nodes, and the radius is the distance from the center to the node furthest from it. Being able to compute the diameter, center, and radius of a graph efficiently has become an increasingly important problem in the analysis of large networks [11]. For general weighted graphs the only known way to compute the exact diameter and radius is by solving the all-pairs shortest paths problem (APSP). Therefore, a natural question is whether it is possible to get faster diameter and radius algorithms by settling for an approximation. For a graph G with diameter D, a c-approxi...

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Recommended Reading

  1. Aingworth D, Chekuri C, Indyk P, Motwani R (1999) Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM J Comput 28(4):1167–1181

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  2. Berman P, Kasiviswanathan SP (2007) Faster approximation of distances in graphs. In: Proceedings of the WADS, Halifax, pp 541–552

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  3. Chechik S, Larkin D, Roditty L, Schoenebeck G, Tarjan RE, Williams VV (2014) Better approximation algorithms for the graph diameter. In: SODA, Portland, pp 1041–1052

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  4. Coppersmith D, Winograd S (1990) Matrix multiplication via arithmetic progressions. J Symb Comput 9(3):251–280

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  5. Cygan M, Gabow HN, Sankowski P (2012) Algorithmic applications of Baur-strassen’s theorem: shortest cycles, diameter and matchings. In: Proceedings of the FOCS, New Brunswick

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  6. Dor D, Halperin S, Zwick U (2000) All-pairs almost shortest paths. SIAM J Comput 29(5):1740–1759

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  8. Roditty L, Vassilevska Williams V (2013) Fast approximation algorithms for the diameter and radius of sparse graphs. In: Proceedings of the 45th annual ACM symposium on theory of computing, STOC ’13, Palo Alto. ACM, New York, pp 515–524. doi:10.1145/2488608.2488673, http://doi.acm.org/10.1145/2488608.2488673

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  10. Vassilevska Williams V (2012, to appear) Multiplying matrices faster than Coppersmith-Winograd. In: Proceedings of the STOC, New York

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  11. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442

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Author information

Authors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Liam Roditty

Authors
  1. Liam Roditty
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Roditty, L. (2016). Approximating the Diameter. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_566

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