In contrast to the previous work, this analysis avoids consideration of fractional matchings and yields a significantly shorter and more direct proof of the approximation factor for the basic algorithm.
Abstract
We show that a simple extension of the randomized greedy maximal independent set algorithm yields a constant approximation for the maximum matching problem. The algorithm is a simplification of an algorithm used by Assadi et al. [JACM 2026] in the context of processing data streams in the dynamic setting where edges may be inserted and deleted. In contrast to the previous work, our analysis avoids consideration of fractional matchings and yields a significantly shorter and more direct proof of the approximation factor for the basic algorithm.
A new $O(\log n)$ approximation algorithm for Node Weighted Steiner Tree and Node Weighted Steiner Forest that matches the bounds of Klein&Ravi, but has the advantage that they work in the online setting when the terminal pairs are revealed in random order.
Joseph Koutsoutis, Jessica Lerner, Roie Levin et al.· 0 citations
We study Greedy for online metric matching with $n$ servers and $n$ requests sampled independently and uniformly from $[0,1]^d$. Servers are available initially, and Greedy irrevocably matches each arriving request to its closest available server, incurring a cost of their distance. We prove that Greedy has competitive...
This paper studies how well LLMs can simplify algorithms by evaluating three different LLMs on ten different algorithmic problems, and results in the discovery of two novel algorithms.
Antoine El-Hayek, Monika Henzinger, D. Zheng· 1 citation
We consider the problem of approximately maximizing a weakly submodular function using the standard greedy algorithm, which is known to give tight approximation results for such functions under a cardinality constraint. We show that this is not the case for general matroid constraints. For any $\gamma<1$, we give a fam...
In this work we establish a connection between the min-max optimal matching in the critical dimension $d=2$ and a simpler, geometrically linear, action of random curves in a Brownian potential. This is done by following Leighton and Shor and working with the dual formulation, which we approximate by a problem of isoper...
Xiao-Peng Cheng, Felix Otto, Matteo Palmieri et al.· 2 citations
