2020/02/13 by Daniel Anderson, Guy E. Blelloch, Kanat Tangwongsan
Computer Science · #Complexity and Algorithms in Graphs #Distributed minimum spanning tree #Graph #Graph Theory and Algorithms #Minimum spanning tree #Optimization and Search Problems #Pairwise comparison #Path (computing) #Reverse-delete algorithm #Spanning tree #Time complexity #Weight-balanced tree #cs.DC #cs.DS #k-minimum spanning tree
paper · pdf · doi:10.1145/3350755.3400241
published as Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA '20) (2020) 51-61
arxiv created 2020/02/13 · openalex created_date 2020/02/24 · openalex publication_date 2020/07/06 · arxiv updated 2020/10/27 · openalex updated_date 2026/08/06
Algorithms for dynamically maintaining minimum spanning trees (MSTs) have received much attention in both the parallel and sequential settings. While previous work has given optimal algorithms for dense graphs, all existing parallel batch-dynamic algorithms perform polynomial work per update in the worst case for sparse graphs. In this paper, we present the first work-efficient parallel batch-dynamic algorithm for incremental MST, which can insert l edges in O(l log(1+n/l) work in expectation and O(polylog(n)) span w.h.p. The key ingredient of our algorithm is an algorithm for constructing a compressed path tree of an edge-weighted tree, which is a smaller tree that contains all pairwise heaviest edges between a given set of marked vertices. Using our batch-incremental MST algorithm, we demonstrate a range of applications that become efficiently solvable in parallel in the sliding-window model, such as graph connectivity, approximate MSTs, testing bipartiteness, k-certificates, cycle-freeness, and maintaining sparsifiers.