New Bounds for Old Algorithms: On the Average-Case Behavior of Classic Single-Source Shortest-Paths Approaches

Meyer, Ulrich; Negoescu, Andrei; Weichert, Volker

doi:10.1007/978-3-642-19754-3_22

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…As each thread caches a local worklist threadws (a subset of ws), they can process it independently of each other. Thus, a local set of new actived nodes (relaxedws) is built by the running threads, and finally, each relaxedws is merged into the global worklist (lines [20][21][22]. The size of the bunch of nodes picked up by each thread is dynamically defined in the algorithm.…”

Section: Work Chunkingmentioning

confidence: 99%

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Parallel Implementations of RCM Algorithm for Bandwidth Reduction of Sparse Matrices

Rodrigues

Bóeres

Catabriga

2018

Tend. Mat. Apl. Comput.

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ABSTRACT. The Reverse Cuthill-McKee (RCM) algorithm is a well-known heuristic for reordering sparse matrices. It is typically used to speed up the computation of sparse linear systems of equations. This paper describes two parallel approaches for the RCM algorithm as well as an optimized version of each one based on some proposed enhancements. The first one exploits a strategy for reducing lazy threads, while the second one makes use of a static bucket array as the main data structure and suppress some steps performed by the original algorithm. These related changes led to outstanding reordering time results and significant bandwidth reductions. The performance of two algorithms is compared with the respective implementation made available by Boost library. The OpenMP framework is used for supporting the parallelism and both versions of the algorithm are tested with large sparse and structural symmetric matrices.

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Section: Work Chunkingmentioning

confidence: 99%

“…In this phase, each thread takes a bucket and stored the children mapped to it in the final permutation array (lines [21][22]. This way of traversing the processed nodes, i.e.…”

Section: Optimized Leveled Parallel Rcmmentioning

confidence: 99%

Parallel Implementations of RCM Algorithm for Bandwidth Reduction of Sparse Matrices

Rodrigues

Bóeres

Catabriga

2018

Tend. Mat. Apl. Comput.

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“…Because it demands multiple paths as output, this lower bound does not apply to algorithms that compute only a single shortest path. -Meyer et al [17] study a version of the Bellman-Ford algorithm, in which edges are relaxed in a specific (adaptive) order. They construct sparse graphs, with O(n) edges, on which this algorithm takes Ω(n 2 ) time, even in the average case for edge weights uniformly drawn from a unit interval.…”

Section: Related Workmentioning

confidence: 99%

Finding the k shortest paths

Eppstein

Proceedings 35th Annual Symposium on Foundations of Computer Science

456

463

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We consider single-source shortest path algorithms that perform a sequence of relaxation steps whose ordering depends only on the input graph structure and not on its weights or the results of prior steps. Each step examines one edge of the graph, and replaces the tentative distance to the endpoint of the edge by its minimum with the tentative distance to the start of the edge, plus the edge length. As we prove, among such algorithms, the Bellman-Ford algorithm has optimal complexity for dense graphs and near-optimal complexity for sparse graphs, as a function of the number of edges and vertices in the given graph. Our analysis holds both for deterministic algorithms and for randomized algorithms that find shortest path distances with high probability.

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Lower Bounds for Non-adaptive Shortest Path Relaxation

Eppstein¹

2023

Lecture Notes in Computer Science

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New Bounds for Old Algorithms: On the Average-Case Behavior of Classic Single-Source Shortest-Paths Approaches

Cited by 3 publications

References 14 publications

Parallel Implementations of RCM Algorithm for Bandwidth Reduction of Sparse Matrices

Parallel Implementations of RCM Algorithm for Bandwidth Reduction of Sparse Matrices

Finding the k shortest paths

Lower Bounds for Non-adaptive Shortest Path Relaxation

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