Trees and Graph Traversals

Chapter
Part of the Texts in Computer Science book series (TCS)

Abstract

A tree is a connected acyclic graph and a forest consists of trees. In this chapter, we first describe the tree structure, algorithms to construct a spanning tree of a graph, and tree traversal algorithms. Two main methods of graph traversal are depth-first search and breadth-first search. We review sequential, parallel, and distributed algorithms for these traversals along with their various applications.

References

  1. 1.
    Awerbuch A (1985) A new distributed depth first search algorithm. Inf Process Lett 20:147150CrossRefGoogle Scholar
  2. 2.
    Bader DA, Madduri K (2006) Designing multithreaded algorithms for breadth-First search and st-connectivity on the Cray MTA-2. In: Proceedings of the 35th international conference on parallel processing (ICPP 2006), pp 523–530Google Scholar
  3. 3.
    Buluc A, Madduri K (2011) Parallel breadth-first search on distributed memory systems. In: International conference for high performance computing, networking, storage and analysis (SC’11), Article 65Google Scholar
  4. 4.
    Cayley A (1857) On the theory of analytical forms called trees. Philos Mag 4(13):172176Google Scholar
  5. 5.
    Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to algorithms, 3rd edn. MIT Press, Cambridge, Chapter 22Google Scholar
  6. 6.
    Erciyes K (2013) Distributed graph algorithms for computer networks, Chaps. 4 and 5. Springer computer communications and networks series. Springer, Berlin (2013). ISBN- 10:1447151720CrossRefGoogle Scholar
  7. 7.
    Even S, Tarjan RE (1975) Network flow and testing graph connectivity. SIAM J Comput 4(4):507–518MathSciNetCrossRefGoogle Scholar
  8. 8.
    Grama A, Gupta A, Karypis G, Kumar V (2003) Introduction to parallel computing, 2nd edn. Chapter 11. Addison Wesley, BostonGoogle Scholar
  9. 9.
    Hopcroft JE, Karp RM (1973) An \(n^{5/2}\) algorithm for maximum matching in bipartite graphs. SIAM J Comput 2(4):225–231MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hopcroft JE, Karp RM (1974) Efficient planarity testing. J ACM 21(4):549–568MathSciNetCrossRefGoogle Scholar
  11. 11.
    Peleg D (2000) Distributed computing: a locality-sensitive approach. SIAM monographs on discrete mathematics and applications, Chapter 5Google Scholar
  12. 12.
    Yoo A, Chow E, Henderson K, McLendon W, Hendrickson B, Catalyuurek UV (2005) A scalable distributed parallel breadth-First search algorithm on BlueGene/L. In: Proceedings of the ACM/IEEE conference on high performance computing (SC2005)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.International Computer InstituteEge UniversityIzmirTurkey

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