Finding monotone paths in edge-ordered graphs

Authors:
J. Katrenič;G. Semanišin
Affiliations:
Institute of Computer Science, P.J. Šafárik University, Faculty of Science, Jesenná 5, 041 54 Košice, Slovak Republic;Institute of Computer Science, P.J. Šafárik University, Faculty of Science, Jesenná 5, 041 54 Košice, Slovak Republic
Venue:
Discrete Applied Mathematics
Year:
2010

Citing 8
Cited 0

Introduction to algorithms

Introduction to algorithms
On linear time minor tests with depth-first search

Journal of Algorithms
Color-coding

Journal of the ACM (JACM)
Monotone paths in edge-ordered sparse graphs

Discrete Mathematics
Splitters and near-optimal derandomization

FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
How (and why) to introduce Monte Carlo randomized algorithms into a basic algorithms course?

Journal of Computing Sciences in Colleges
Improved algorithms for path, matching, and packing problems

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Divide-and-color

WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science

Quantified Score

Hi-index	0.04

Visualization

Abstract

An edge-ordering of a graph G=(V,E) is a one-to-one function f from E to a subset of the set of positive integers. A path P in G is called an f-ascent if f increases along the edge sequence of P. The heighth(f) of f is the maximum length of an f-ascent in G. In this paper we deal with computational problems concerning finding ascents in graphs. We prove that for a given edge-ordering f of a graph G the problem of determining the value of h(f) is NP-hard. In particular, the problem of deciding whether there is an f-ascent containing all the vertices of G is NP-complete. We also study several variants of this problem, discuss randomized and deterministic approaches and provide an algorithm for the finding of ascents of order at least k in graphs of order n in running time O(4^kn^O^(^1^)).