An O(log n) algorithm for parallel update of minimum spanning trees

Pawagi, Shaunak; Ramakrishnan, I. V.

doi:10.1016/0020-0190(86)90098-0

Cited by 25 publications

(7 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This can be done in 0(1) time and at most (n + k) x ( n+ 2"" X ) processors on the CRCW PRAM using the MAXIMUM rule for resolving write conflicts. Variants of this algorithm are described in [10,21,28,29,32,35,36].…”

Section: Resultsmentioning

confidence: 99%

“…Within this framework, an interesting case arises in connection with the minimum-weight spanning tree problem when corrections to the weights of the edges currently in the MST are received in real time and must be taken into consideration. Sequential and parallel algorithms for this problem are described in [10,15,29]. However, while these algorithms update the MST as required, their analyses (much like those of the algorithms in [19]) do not allow for the corrections to arrive, or for the results to be produced, at a certain specified rate.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Parallel Real-Time Optimization: Beyond Speedup

Akl

Bruda

1999

Parallel Process. Lett.

View full text Add to dashboard Cite

Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for real-time optimization problems, a parallel computer can obtain a solution that is better than that obtained by a sequential one. Specifically, a sequential and a parallel algorithm are exhibited for the problem of computing the best-possible approximation to the minimum-weight spanning tree of a connected, undirected and weighted graph whose vertices and edges are not all available at the outset, but instead arrive in real time. While the parallel algorithm succeeds in computing the exact minimum-weight spanning tree, the sequential algorithm can only manage to obtain an approximate solution. In the worst case, the ratio of the weight of the solution obtained sequentially to that of the solution computed in parallel can be arbitrarily large.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Parallel Real-Time Optimization: Beyond Speedup

Akl

Bruda

1999

Parallel Process. Lett.

View full text Add to dashboard Cite

show abstract

“…There has been significant interest in parallelizing incremental and dynamic MSF. Some of this work studies how to implement single updates in parallel [43,52,53,36,51,14,20,21,16,38], and some studies batch updates [41,35,42,45,22,23]. The most recent and best result [38] requires O( √ n lg n) work per update on n vertices, and only allows single edge updates.…”

Section: Introductionmentioning

confidence: 99%

Work-efficient Batch-incremental Minimum Spanning Trees with Applications to the Sliding Window Model

Anderson,

Blelloch,

Tangwongsan

2020

Preprint

View full text Add to dashboard Cite

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 edges in O( lg(1 + n/ )) 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.

show abstract

“…Consequently, update algorithms for these properties involve updating a spanning tree for the new graph (see [11,131). Similarly, start-over algorithms for initial computation of properties of a DAG require its transitive closure to be computed.…”

Section: L-mentioning

confidence: 99%

An O(log n) algorithm for parallel update of minimum spanning trees

Cited by 25 publications

References 5 publications

Parallel Real-Time Optimization: Beyond Speedup

Parallel Real-Time Optimization: Beyond Speedup

Work-efficient Batch-incremental Minimum Spanning Trees with Applications to the Sliding Window Model

Updating Properties of Directed Acyclic Graphs on a Parallel Random Access Machine.

Contact Info

Product

Resources

About