Shayan Ranjbarzadeh | Searcharxiv

arXiv2026

A Simplified Analysis of the Good-Bad $3/2$-Approximation Algorithm for Some Minimum-Cost Graph Problems

In this paper, we consider an easy greedy approximation algorithm, the good-bad algorithm, introduced by Couëtoux for finding a minimum-cost set of edges such that every connected component has at least $k$ vertices. Couëtoux proves that the good-bad algorithm achieves a $3/2$-approximation for this problem. Davis and Williamson extend this result to the more general problem of finding a minimum-cost edge set that contains at least one edge from every cut $S\subseteq V$ satisfying $h(S) = 1$ where $h:2^V \rightarrow \{0,1\}$ is downward monotone; that is, $h(S) = 1$ implies $h(T) = 1$ for every nonempty subset $T \subseteq S$. The original problem corresponds to $h(S) =1$ when $|S|<k$. We give a simplified analysis of the good-bad algorithm for downward monotone functions.

cs.DS↗

arXiv2021

Multi-Feasibility Variable Selection

This paper is the report of the problem proposed for the !Optimizer 2021 competition, and the solutions of the gold medalist team, i.e., the Panda team. The competition was held in two stages, the research and development stage and a two-week contest stage, consisting of five rounds, and seven teams succeeded in finishing both stages to the end. In this joint report of the winner team Panda and the problem design committee coordinated by Mojtaba Tefagh, we first explain each of the five rounds and then provide the solutions proposed by our team (Panda) to fulfill the required tasks in the fastest and most accurate way. Afterward, some preprocessing and data manipulating ideas used to enhance the algorithms would be presented. All codes are written in the Julia language, which showed a better performance than Python on optimization problems in our comparisons during the R&D stage, and are publicly available in the Github repository: https://github.com/Optimizer-Competition-Panda

cs.DC↗