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Spanning Tree, Minimum Weight

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Encyclopedia of Parallel Computing

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Definition

Given an undirected connected graph G with n vertices and m edges, the minimum-weight spanning tree (MST) problem consists in finding a spanning tree with the minimum sum of edge weights. A single graph can have multiple MSTs. If the graph is not connected, then it has a minimum spanning forest (MSF) that is a union of minimum spanning trees for its connected components. MST is one of the most studied combinatorial problems with practical applications in VLSI layout, wireless communication, and distributed networks, recent problems in biology and medicine such as cancer detection, medical imaging, and proteomics.

With regard to any MST of graph G, two properties hold: Cycle property: the heaviest edge (edge with the maximum weight) in any cycle of G does not appear in the MST. Cut property: if the weight of an edge e of any cut C of G is smaller than the weights of other edges of C, then this edge belongs to all MSTs of the graph.

When all edges of Gare of unique weights,...

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Bibliography

  1. Adler M, Dittrich W, Juurlink B, Kutyłowski M, Rieping I (1998) Communication-optimal parallel minimum spanning tree algorithms (extended abstract). In: SPAA ’98: proceedings of the tenth annual ACM symposium on parallel algorithms and architectures, Puerto Vallarta, Mexico. ACM, New York, pp 27–36

    Google Scholar 

  2. Arge L, Bender MA, Demaine ED, Holland-Minkley B, Munro JI (2002) Cache-oblivious priority queue and graph algorithm applications. In: Proceedings of the 34th annual ACM symposium on theory of computing, Montreal, Canada. ACM, New York, pp 268–276

    Google Scholar 

  3. Bader DA, Cong G (2006) Fast shared-memory algorithms for computing the minimum spanning forest of sparse graphs. J Parallel Distrib Comput 66:1366–1378

    MATH  Google Scholar 

  4. Charles P, Donawa C, Ebcioglu K, Grothoff C, Kielstra A, Van Praun C, Saraswat V, Sarkar V (2005) X10: an object-oriented approach to non-uniform cluster computing. In: Proceedings of the 2005 ACM SIGPLAN conference on object-oriented programming systems, languages and applications (OOPSLA), San Diego, CA, pp 519–538

    Google Scholar 

  5. Chong KW, Han Y, Lam TW (2001) Concurrent threads and optimal parallel minimum spanning tree algorithm. J ACM 48: 297–323

    MATH  MathSciNet  Google Scholar 

  6. Chung S, Condon A (1996) Parallel implementation of Bor˚uvka’s minimum spanning tree algorithm. In: Proceedings of the 10th international parallel processing symposium (IPPS’96), Honolulu, Hawaii, pp 302–315

    Google Scholar 

  7. Cole R, Klein PN, Tarjan RE (1996) Finding minimum spanning forests in logarithmic time and linear work using random sampling. In: Proceedings of the 8th annual symposium parallel algorithms and architectures (SPAA-96), Newport, RI. ACM, New York, pp 243–250

    Google Scholar 

  8. Cole R, Klein PN, Tarjan RE (1994) A linear-work parallel algorithm for finding minimum spanning trees. In: Proceedings of the 6th annual ACM symposium on parallel algorithms and architectures, Cape May, NJ, ACM, New York, pp 11–15

    Google Scholar 

  9. Cong G, Almasi G, Saraswat V (2010) Fast PGAS implementation of distributed graph algorithms. In: Proceedings of the 2010 ACM/IEEE international conference for high performance computing, networking, storage and analysis (SC ’10), IEEE Computer Society, Washington, DC, pp 1–11

    Google Scholar 

  10. Cong G, Bader DA (2004) Lock-free parallel algorithms: an experimental study. In: Proceeding of the 33rd international conference on high-performance computing (HiPC 2004), Banglore, India

    Google Scholar 

  11. Cong G, Sbaraglia S (2006) A study of the locality behavior of minimum spanning tree algorithms. In: The 13th international conference on high performance computing (HiPC 2006), Bangalore, India. IEEE Computer Society, pp 583–594

    Google Scholar 

  12. Dehne F, Götz S (1998) Practical parallel algorithms for minimum spanning trees. In: Proceedings of the seventeenth symposium on reliable distributed systems, West Lafayette, IN. IEEE Computer Society, pp 366–371

    Google Scholar 

  13. Gibbons PB, Matias Y, Ramachandran V (1997) Can shared-memory model serve as a bridging model for parallel computation? In: Proceedings 9th annual symposium parallel algorithms and architectures (SPAA-97), Newport, RI, ACM, New York pp 72–83

    Google Scholar 

  14. Graham RL, Hell P (1985) On the history of the minimum spanning tree problem. IEEE Ann History Comput 7(1):43–57

    MATH  MathSciNet  Google Scholar 

  15. Helman DR, JáJá J (1999) Designing practical efficient algorithms for symmetric multiprocessors. In: Algorithm engineering and experimentation (ALENEX’99), Baltimore, MD, Lecture notes in computer science, vol 1619. Springer-Verlag, Heidelberg, pp 37–56

    Google Scholar 

  16. JáJá J (1992) An Introduction to parallel algorithms. Addison-Wesley, New York

    MATH  Google Scholar 

  17. Kang S, Bader DA (2009) An efficient transactional memory algorithm for computing minimum spanning forest of sparse graphs. In: Proceedings of the 14th ACM SIGPLAN symposium on principles and practice of parallel programming (PPoPP), Raleigh, NC

    Google Scholar 

  18. Karger DR, Klein PN, Tarjan RE (1995) A randomized linear-time algorithm to find minimum spanning trees. J ACM 42(2):321–328

    MATH  MathSciNet  Google Scholar 

  19. Katriel I, Sanders P, Träff JL (2003) A practical minimum spanning tree algorithm using the cycle property. In: 11th Annual European symposium on algorithms (ESA 2003), Budapest, Hungary, Lecture notes in computer science, vol 2832. Springer-Verlag, Heidelberg, pp 679–690

    Google Scholar 

  20. Moret BME, Shapiro HD (1994) An empirical assessment of algorithms for constructing a minimal spanning tree. In: DIMACS monographs in discrete mathematics and theoretical computer science: computational support for discrete mathematics vol 15, American Mathematical Society, Providence, RI, pp 99–117

    Google Scholar 

  21. Pettie S, Ramachandran V (2002) A randomized time-work optimal parallel algorithm for finding a minimum spanning forest. SIAM J Comput 31(6):1879–1895

    MATH  MathSciNet  Google Scholar 

  22. Poon CK, Ramachandran V (1997) A randomized linear work EREW PRAM algorithm to find a minimum spanning forest. In: Proceedings of the 8th international symposium algorithms and computation (ISAAC’97), Lecture notes in computer science, vol 1350. Springer-Verlag, Heidelberg, pp 212–222

    Google Scholar 

  23. Carlson WW, Draper JM, Culler DE, Yelick K, Brooks E, Warren K (1999) Introduction to UPC and Language Specification. CCS-TR-99-157. IDA/CCS, Bowie, Maryland

    Google Scholar 

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Authors and Affiliations

  1. College of Computing, Georgia Institute of Technology, 30332, Atlanta, GA, USA

    David A Bader Professor & Guojing Cong Dr.

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  1. David A Bader Professor
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  2. Guojing Cong Dr.
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Editors and Affiliations

  1. University of Illinois at Urbana-Champaign, Urbana, IL, USA

    David Padua

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Bader, D.A., Cong, G. (2011). Spanning Tree, Minimum Weight. In: Padua, D. (eds) Encyclopedia of Parallel Computing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09766-4_104

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