Local Search for Weighted Tree Augmentation and Steiner Tree
Vera Traub, Rico Zenklusen

TL;DR
This paper introduces a non-oblivious local search technique that improves approximation algorithms for Weighted Tree Augmentation and Steiner Tree, achieving better ratios without LP reliance.
Contribution
The authors develop a purely combinatorial local search method that enhances approximation ratios for Weighted Tree Augmentation and Steiner Tree problems.
Findings
Achieves a (1.5+ε)-approximation for Weighted Tree Augmentation.
Provides an alternative proof for the Steiner Tree approximation factor of ln 4 + ε.
Eliminates the need for LP solving in approximation algorithms, simplifying the approach.
Abstract
We present a technique that allows for improving on some relative greedy procedures by well-chosen (non-oblivious) local search algorithms. Relative greedy procedures are a particular type of greedy algorithm that start with a simple, though weak, solution, and iteratively replace parts of this starting solution by stronger components. Some well-known applications of relative greedy algorithms include approximation algorithms for Steiner Tree and, more recently, for connectivity augmentation problems. The main application of our technique leads to a -approximation for Weighted Tree Augmentation, improving on a recent relative greedy based method with approximation factor . Furthermore, we show how our local search technique can be applied to Steiner Tree, leading to an alternative way to obtain the currently best known approximation…
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Taxonomy
TopicsVLSI and FPGA Design Techniques · Complexity and Algorithms in Graphs · Constraint Satisfaction and Optimization
