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Graph Algorithms

Chapter
Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)

Abstract

The first of the three main chapters of this book deals with two graph algorithms. First, we consider the single-source shortest path problem. For this problem, we present our original twist on the balls-and-strings metaphor. We show how our metaphor directly corresponds to the execution of Dijkstra’s algorithm, and how it can be used to gain a deep insight into the inner workings of the algorithm. Second, we show how a similar metaphor can be used for a class of problems on trees, including finding and counting the longest paths.

Keywords

Short Path Longe Path Short Path Problem Negative Edge Minimum Span Tree Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bell, T., Fellows, M.R., Witten, I.: Computer Science Unplugged: Off-Line Activities and Games for All Ages. http://csunplugged.com/ (1998). Cited 8 Dec 2012
  2. 2.
    Bor\(\mathop {\rm {u}}\limits ^{\circ }\)vka, O.: O jistém problému minimálním (About a certain minimal problem). Práce mor. přírodověd. spol. 3, 37–58 (1926) (in Czech)Google Scholar
  3. 3.
    Bor\(\mathop {\rm {u}}\limits ^{\circ }\)vka, O.: Příspěvek k řešení otázky ekonomické stavby elektrovodních sítí (Contribution to the solution of a problem of economical construction of electrical networks). Elektronický obzor 15, 153–154 (1926) (in Czech)Google Scholar
  4. 4.
    Bulterman, R.W., van der Sommen, F.W., Zwaan, G., Verhoeff, T., van Gasteren, A.J.M., Feijen, W.H.J.: On computing a longest path in a tree. Inf. Process. Lett. 81, 93–96 (2002)zbMATHCrossRefGoogle Scholar
  5. 5.
    Cayley, A.: A theorem on trees. Q. J. Math. 23, 376–378 (1889)Google Scholar
  6. 6.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, Cambridge (2009)Google Scholar
  7. 7.
    Dasgupta, S., Papadimitriou, C., Vazirani, U.: Algorithms. McGraw-Hill, New York (2006)Google Scholar
  8. 8.
    Dewdney, A.K.: Computer recreations. Sci. Am. 252, 18–29 (1985)Google Scholar
  9. 9.
    Diks, K., Idziaszek, T., Łacky, J., Radoszewski, J.: Looking for a Challenge? The Ultimate Problem Set from the University of Warsaw Programming Competitions. Lotos Poligrafia Sp. z o.o. (2012)Google Scholar
  10. 10.
    van Emde Boas, P.: Preserving order in a forest in less than logarithmic time. In: Proceedings of the 16th Annual Symposium on Foundations of Computer Science (FOCS 1975), pp. 75–84. IEEE Computer Society (1975)Google Scholar
  11. 11.
    Jarník, V.: O jistém problému minimálním (About a certain minimal problem). Práce Mor. Přírodověd. Spol. 6, 57–63 (1930) (in Czech)Google Scholar
  12. 12.
    Moscovich, I.: The Monty Hall Problem & Other Puzzles. Sterling Publishing, New York (2004)Google Scholar
  13. 13.
    Narváez, P., Siu, K.Y., Tzeng, H.Y.: New dynamic SPT algorithm based on a ball-and-string model. IEEE/ACM Trans. Netw. 9(6), 706–718 (2001)CrossRefGoogle Scholar
  14. 14.
    Prüfer, H.: Neuer Beweis eines Satzes ber Permutationen (A new proof of a theorem about permutations). Arch. der Math. u. Phys. 27, 742–744 (1918) (in German)Google Scholar
  15. 15.
    Rokicki, T., Kociemba, H., Davidson, M., Dethridge, J.: God’s Number Is 20. http://www.cube20.org/ (2010). Cited 8 Dec 2012

Copyright information

© The Author(s) 2013

Authors and Affiliations

  1. 1.Department of Computer ScienceComenius UniversityBratislavaSlovakia
  2. 2.Department of Computer ScienceETH ZürichZürichSwitzerland

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