Metric Sublinear Algorithms via Linear Sampling

We provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a sublinear number of edge weight queries, provides a linear sampling, where each edge is (roughly speaking) sampled proportionally to its weight. For several natural problems, such as densest subgraph and max cut, we show that by sparsifying the graph using this sampling process, we can run a suitable approximation algorithm on the sparsified graph and the result remains a good approximation for the original problem. Our results have several interesting implications, such as providing the first sublinear time approximation algorithm for densest subgraph in a metric space, and improving the running time of estimating the average distance.

Authors

• Hossein Esfandiari
• Michael Mitzenmacher

Keywords

• Approximation algorithms
• Extraterrestrial measurements
• Heuristic algorithms
• Computer science
• Information theory
• Sampling methods
• Estimation Algorithm
• Sampling Approach
• Edge Weights
• Algorithm For Problem
• Graph Metrics
• Point In The Graph
• Max-Cut
• Graph Problems
• High Probability
• Approximate Solution
• Constant Factor
• Sampling Efficiency
• Maximum Weight
• Probability Of Failure
• Original Graph
• Constant Probability
• Weighted Graph
• Facility Location Problem
• Subgraph Of Graph
• Sublinear Algorithm
• Metric Space
• Densest Subgraph
• Diversity Maximization
• Linear Sampling