The sparsest additive spanner via multiple weighted BFS trees

Keren Censor-Hillel, Ami Paz, Noam Ravid

Research output: Contribution to journalArticlepeer-review


Spanners are fundamental graph structures that sparsify graphs at the cost of small stretch. In particular, in recent years, many sequential algorithms constructing additive all-pairs spanners were designed, providing very sparse small-stretch subgraphs. Remarkably, it was then shown that the known (+6)-spanner constructions are essentially the sparsest possible, that is, larger additive stretch cannot guarantee a sparser spanner, which brought the stretch-sparsity trade-off to its limit. Distributed constructions of spanners are also abundant. However, for additive spanners, while there were algorithms constructing (+2) and (+4)-all-pairs spanners, the sparsest case of (+6)-spanners remained elusive. We remedy this by designing a new sequential algorithm for constructing a (+6)-spanner with the essentially-optimal sparsity of O˜(n4/3) edges. We then show a distributed implementation of our algorithm, answering an open problem in [12]. A main ingredient in our distributed algorithm is an efficient construction of multiple weighted BFS trees. A weighted BFS tree is a BFS tree in a weighted graph, that consists of the lightest among all shortest paths from the root to each node. We present a distributed algorithm in the CONGEST model, that constructs multiple weighted BFS trees in |S|+D−1 rounds, where S is the set of sources and D is the diameter of the network graph.

Original languageEnglish
Pages (from-to)33-44
Number of pages12
JournalTheoretical Computer Science
StatePublished - 6 Nov 2020


  • Additive spanners
  • Congest model
  • Distributed graph algorithms
  • Weighted BFS trees

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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