Abstract
In this paper we focus on dynamic batch algorithms for single source shortest paths in graphs with positive real edge weights. A dynamic algorithm is called batch if it is able to handle graph changes that consist of multiple edge updates at a time, i.e. a batch. We propose a new algorithm to process a decremental batch (containing only delete and weight increase operations), a new algorithm to process an incremental batch (containing only insert and weight decrease operations), and a combination of these algorithms to process arbitrary sequences of incremental and decremental batches. These algorithms are update-sensitive, namely they are efficient w.r.t. to the number of nodes in the shortest paths tree that change the parent and/or the distance from the source as a consequence of the changes.
Research partially supported by the Research Grant 2010N5K7EB PRIN 2010 ”ARS TechnoMedia” from the Italian Ministry of University and Research.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-319-03578-9_29
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D’Andrea, A., D’Emidio, M., Frigioni, D., Leucci, S., Proietti, G. (2013). Dynamically Maintaining Shortest Path Trees under Batches of Updates. In: Moscibroda, T., Rescigno, A.A. (eds) Structural Information and Communication Complexity. SIROCCO 2013. Lecture Notes in Computer Science, vol 8179. Springer, Cham. https://doi.org/10.1007/978-3-319-03578-9_24
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