Abstract
A weighted graph can have weights associated with its edges or its vertices. The weight on an edge typically denotes the cost of traversing that edge and the weights of a vertex commonly show its capacity to perform some function. In this chapter, we review sequential, parallel, and distributed algorithms for weighted graphs for two specific tasks; the minimum spanning tree problem and the shortest path problem.
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Acar UA, Blelloch GE (2017) Algorithm design: parallel and sequential. Chapter 18, Draft book, Carnegie Mellon University, Dept. of Computer Science. https://www.parallel-algorithms-book.com/
Bellman R (1958) On a routing problem. Q Appl Math 16:87–90
Boruvka O (1926) About a certain minimal problem. Prce mor. prrodoved. spol. v Brne III (in Czech, German summary), 3:37–58
Chung S, Condon A (1996) Parallel implementation of Boruvka’s minimum spanning tree algorithm. Technical report 1297, Computer Sciences Dept., University of Wisconsin
Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to algorithms, 3rd edn. MIT Press, Cambridge, Chapter 23
Dijkstra EW (1959) A note on two problems in connexion with graphs. Numerische Mathematik 1:269–271
Erciyes K (2013) Distributed graph algorithms for computer networks. Chapter 6, Springer computer communications and networks series. Springer, Berlin
Gallager RG, Humblet PA, Spira PM (1983) Distributed algorithms for mininimum-weight spanning trees. ACM Trans Progrmm Lang Syst 5(1):66–77
Graham RL, Hell P (1985) On the history of the minimum spanning tree problem. Ann Hist Comput 7(1):4357
Grama A, Gupta A, Karypis G, Kumar V (2003) Introduction to parallel computing, 2nd edn. Chapter 10. Addison Wesley, Boston
Kleinberg J, Tardos E (2005) Algorithm design. Chapter 4. Pearson Int. Ed. ISBN-13: 978-0321295354 ISBN-10: 0321295358
Korte B, Vygen J (2008) Combinatorial optimization: theory and algorithms. Chapter 7, 4th edn. Springer, Berlin
Kruskal JB (1956) On the shortest spanning subtree of a graph and the traveling salesman problem. Proc Am Math Soc 7:4850
Loncar V, Skrbic S, Bala A (2013) Parallelization of minimum spanning tree algorithms using distributed memory architectures. Transaction on engineering technology. Special volume of the world congress on engineering, pp 543–554
Peleg D (1987) Distributed computing: a locality-sensitive approach SIAM monographs on discrete mathematics and applications. Chapter 5
Prim RC (1957) Shortest connection networks and some generalizations. Bell Syst Tech J 36(6):1389–1401
Tarjan RE (1987) Data structures and network algorithms. SIAM, CBMS-NSF regional conference series in applied mathematics (Book 44)
Thorup M (2000) Near-optimal fully-dynamic graph connectivity. In: Proceedings of the 32nd ACM symposium on theory of computing, pp 343–350
Toueg S (1980) An all-pairs shortest-path distributed algorithm. Technical report RC 8327, IBM TJ Watson Research Center, Yorktown Heights, NY 10598
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Erciyes, K. (2018). Weighted Graphs. In: Guide to Graph Algorithms. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-73235-0_7
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DOI: https://doi.org/10.1007/978-3-319-73235-0_7
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