Multi-Level Graph Sketches via Single-Level Solvers
Reyan Ahmed, Keaton Hamm, Mohammad Javad Latifi Jebelli, Stephen, Kobourov, Faryad Darabi Sahneh, Richard Spence

TL;DR
This paper introduces a flexible, modular approach to compute multi-level graph sketches, including spanners and Steiner trees, using single-level solvers with approximation guarantees and demonstrates a new subsetwise spanner algorithm with proven weight bounds.
Contribution
It presents a novel modular procedure for multi-level graph sketches that leverages single-level solvers, along with a new polynomial-time subsetwise spanner algorithm with weight guarantees.
Findings
Logarithmic number of solver queries for multi-level sketches.
First weight guarantee for multiplicative subsetwise spanners in nonplanar graphs.
Effective algorithms demonstrated through numerical experiments.
Abstract
Given an undirected weighted graph , a constrained sketch over a terminal set is a subgraph that connects the terminal vertices while satisfying a given set of constraints. Examples include Steiner trees (preserving connectivity among ) and subsetwise spanners (preserving shortest path distances up to a stretch factor). Multi-level constrained terminal sketches are generalizations in which terminal vertices require different levels or grades of service and each terminal pair is connected with edges of at least the minimum required level of the two terminals. This paper gives a flexible procedure for computing a broad class of multi-level graph sketches, which encompasses multi-level graph spanners, Steiner trees, and --connected subgraphs as a few special cases. The proposed procedure is modular, i.e., it relies on availability of a single-level solver…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Graph Theory and Algorithms · Computer Graphics and Visualization Techniques
