scholarly journals On the Inapproximability of Disjoint Paths and Minimum Steiner Forest with Bandwidth Constraints

2000 ◽  
Vol 60 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Bin Ma ◽  
Lusheng Wang
Keyword(s):  
Disjoint Paths ◽  
Steiner Forest

Disjoint paths of bounded length in large generalized cycles

1999 ◽  
Vol 197-198 (1-3) ◽  
pp. 285-298 ◽  
Author(s):  
D Ferrero
Keyword(s):  
Disjoint Paths

An approximation algorithm for the k-generalized Steiner forest problem

2021 ◽  
Author(s):  
Jiawen Gao ◽  
Suogang Gao ◽  
Wen Liu ◽  
Weili Wu ◽  
Ding-Zhu Du ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Steiner Forest

scholarly journals Cycle partitions of regular graphs

2020 ◽  
pp. 1-24
Author(s):  
Vytautas Gruslys ◽  
Shoham Letzter
Keyword(s):  
Regular Graph ◽  
Bipartite Graphs ◽  
Disjoint Paths ◽  
Regular Graphs ◽  
Simple Construction ◽  
Vertex Set ◽  
Almost All ◽  
Vertex Disjoint

Abstract Magnant and Martin conjectured that the vertex set of any d-regular graph G on n vertices can be partitioned into $n / (d+1)$ paths (there exists a simple construction showing that this bound would be best possible). We prove this conjecture when $d = \Omega(n)$ , improving a result of Han, who showed that in this range almost all vertices of G can be covered by $n / (d+1) + 1$ vertex-disjoint paths. In fact our proof gives a partition of V(G) into cycles. We also show that, if $d = \Omega(n)$ and G is bipartite, then V(G) can be partitioned into n/(2d) paths (this bound is tight for bipartite graphs).

scholarly journals On Structural Parameterizations of the Edge Disjoint Paths Problem

Algorithmica ◽  
2021 ◽  
Author(s):  
Robert Ganian ◽  
Sebastian Ordyniak ◽  
M. S. Ramanujan
Keyword(s):  
Polynomial Time ◽  
Disjoint Paths ◽  
Structural Parameter ◽  
Input Graph ◽  
Feedback Vertex Set ◽  
Fpt Algorithms ◽  
Edge Disjoint ◽  
Fpt Algorithm ◽  
Vertex Set ◽  
Terminal Pair

AbstractIn this paper we revisit the classical edge disjoint paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our focus lies on structural parameterizations for the problem that allow for efficient (polynomial-time or FPT) algorithms. As our first result, we answer an open question stated in Fleszar et al. (Proceedings of the ESA, 2016), by showing that the problem can be solved in polynomial time if the input graph has a feedback vertex set of size one. We also show that EDP parameterized by the treewidth and the maximum degree of the input graph is fixed-parameter tractable. Having developed two novel algorithms for EDP using structural restrictions on the input graph, we then turn our attention towards the augmented graph, i.e., the graph obtained from the input graph after adding one edge between every terminal pair. In constrast to the input graph, where EDP is known to remain -hard even for treewidth two, a result by Zhou et al. (Algorithmica 26(1):3--30, 2000) shows that EDP can be solved in non-uniform polynomial time if the augmented graph has constant treewidth; we note that the possible improvement of this result to an FPT-algorithm has remained open since then. We show that this is highly unlikely by establishing the [1]-hardness of the problem parameterized by the treewidth (and even feedback vertex set) of the augmented graph. Finally, we develop an FPT-algorithm for EDP by exploiting a novel structural parameter of the augmented graph.

scholarly journals Bandwidth scheduling for big data transfer with two variable node-disjoint paths

2020 ◽  
Vol 22 (2) ◽  
pp. 130-144
Author(s):  
Aiqin Hou ◽  
Chase Qishi Wu ◽  
Liudong Zuo ◽  
Xiaoyang Zhang ◽  
Tao Wang ◽  
...  
Keyword(s):  
Big Data ◽  
Data Transfer ◽  
Disjoint Paths ◽  
Bandwidth Scheduling ◽  
Variable Node

scholarly journals On randomly 3-axial graphs

1982 ◽  
Vol 25 (2) ◽  
pp. 187-206
Author(s):  
Yousef Alavi ◽  
Sabra S. Anderson ◽  
Gary Chartrand ◽  
S.F. Kapoor
Keyword(s):  
Bipartite Graphs ◽  
Disjoint Paths ◽  
Complete Graphs ◽  
Initial Vertex ◽  
Complete Bipartite Graphs

A graph G, every vertex of which has degree at least three, is randomly 3-axial if for each vertex v of G, any ordered collection of three paths in G of length one with initial vertex v can be cyclically randomly extended to produce three internally disjoint paths which contain all the vertices of G. Randomly 3-axial graphs of order p > 4 are characterized for p ≢ 1 (mod 3), and are shown to be either complete graphs or certain regular complete bipartite graphs.

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