@article{Karger2006OnAT,
title={On approximating the longest path in a graph},
author={D. Karger and R. Motwani and G. Ramkumar},
journal={Algorithmica},
year={2006},
volume={18},
pages={82-98}
}

AbstractWe consider the problem of approximating the longest path in undirected graphs. In an attempt to pin down the best achievable performance ratio of an approximation algorithm for this problem, we present both positive and negative results. First, a simple greedy algorithm is shown to find long paths in dense graphs. We then consider the problem of finding paths in graphs that are guaranteed to have extremely long paths. We devise an algorithm that finds paths of a logarithmic length in… Expand