The longest path problem is polynomial on cocomparability graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
A linear-time algorithm for the longest path problem in rectangular grid graphs
Discrete Applied Mathematics
An efficient parallel algorithm for the longest path problem in meshes
The Journal of Supercomputing
| Hi-index | 0.00 |
We present a polynomial-time algorithm to find a cycle of length$\exp(\Omega(\sqrt{\log \ell}))$ in an undirected graph having acycle of length ≥ ℓ. This is a slight improvement overpreviously known bounds. In addition the algorithm is more general,since it can similarly approximate the longest circuit, as well asthe longest S-circuit (i.e., for S an arbitrarysubset of vertices, a circuit that can visit each vertex inS at most once). We also show that any algorithm forapproximating the longest cycle can approximate the longestcircuit, with a square root reduction in length. For digraphs, weshow that the long cycle and long circuit problems have the sameapproximation ratio up to a constant factor. We also give analgorithm to find a vw-path of length ≥logn/loglogn if one exists; this is within aloglogn factor of a hardness result.