Work-Efficient Batch-Incremental Minimum Spanning Trees with Applications to the Sliding-Window Model
Year: 2020
Type: conference-paper
Abstract: 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.
Authors: Daniel Anderson, Guy E. Blelloch, Kanat Tangwongsan
Institutions: Carnegie Mellon University, Mahidol University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
Awards: SHF: Medium: Collaborative Research: Automatic Locality Management for Dynamically Scheduled Parallelism, AF: Small: Shared-Memory Parallel Algorithms: Theory and Practice, SHF: Medium: Algorithmic lambda-Calculus for the Design, Analysis, and Implementation of Parallel Algorithms, SPX: Parallel Models and Algorithms for Emerging Memory Systems
OpenAlex ID: W3006157595