
Approximation algorithms and an integer program for multilevel graph spanners
Given a weighted graph G(V,E) and t > 1, a subgraph H is a tspanner of...
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On additive spanners in weighted graphs with local error
An additive +β spanner of a graph G is a subgraph which preserves distan...
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Kruskalbased approximation algorithm for the multilevel Steiner tree problem
We study the multilevel Steiner tree problem: a generalization of the S...
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A General Framework for Multilevel Subsetwise Graph Sparsifiers
Given an undirected weighted graph $G(V,E)$, a subsetwise sparsifier ove...
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Fast Construction of 4Additive Spanners
A kadditive spanner of a graph is a subgraph that preserves the distanc...
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Minimum Weight Pairwise Distance Preservers
In this paper, we study the Minimum Weight Pairwise Distance Preservers ...
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Optimal MultiLevel Intervalbased Checkpointing for Exascale Stream Processing Systems
Stateoftheart stream processing platforms make use of checkpointing t...
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Multilevel Weighted Additive Spanners
Given a graph G = (V,E), a subgraph H is an additive +β spanner if _H(u,v) ≤_G(u,v) + β for all u, v ∈ V. A pairwise spanner is a spanner for which the above inequality only must hold for specific pairs P ⊆ V × V given on input, and when the pairs have the structure P = S × S for some subset S ⊆ V, it is specifically called a subsetwise spanner. Spanners in unweighted graphs have been studied extensively in the literature, but have only recently been generalized to weighted graphs. In this paper, we consider a multilevel version of the subsetwise spanner in weighted graphs, where the vertices in S possess varying level, priority, or quality of service (QoS) requirements, and the goal is to compute a nested sequence of spanners with the minimum number of total edges. We first generalize the +2 subsetwise spanner of [Pettie 2008, Cygan et al., 2013] to the weighted setting. We experimentally measure the performance of this and several other algorithms for weighted additive spanners, both in terms of runtime and sparsity of output spanner, when applied at each level of the multilevel problem. Spanner sparsity is compared to the sparsest possible spanner satisfying the given error budget, obtained using an integer programming formulation of the problem. We run our experiments with respect to input graphs generated by several different random graph generators: Erdős–Rényi, Watts–Strogatz, Barabási–Albert, and random geometric models. By analyzing our experimental results we developed a new technique of changing an initialization parameter value that provides better performance in practice.
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