Incremental distance products via faulty shortest paths

Research output: Contribution to journalArticlepeer-review


Given a constant number d of n×n matrices with total m non-infinity entries, we show how to construct in (essentially optimal) O˜(mn+n2) time a data structure that can compute in (essentially optimal) O˜(n2) time the distance product of these matrices after incrementing the value (possibly to infinity) of a constant number k of entries. Our result is obtained by designing an oracle for single source replacement paths that is suited for short distances: Given a graph G=(V,E), a source vertex s, and a shortest paths tree T of depth d rooted at s, the oracle can be constructed in O˜(mdk) time for any constant k. Then, given an arbitrary set S of at most k=O(1) edges and an arbitrary vertex t, the oracle in O˜(1) time either reports the length of the shortest s-to-t path in (V,E∖S) or otherwise reports that any such shortest path must use more than d edges.

Original languageEnglish
Article number105977
JournalInformation Processing Letters
StatePublished - Sep 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.


  • Data structures
  • Distance product
  • Fault tolerance
  • Graph algorithms
  • Shortest paths

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications


Dive into the research topics of 'Incremental distance products via faulty shortest paths'. Together they form a unique fingerprint.

Cite this