A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2007; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Approximating the Bandwidth of Caterpillars
[chapter]

2005
*
Lecture Notes in Computer Science
*

*The*previous best

*approximation*ratio for

*the*

*bandwidth*

*of*

*caterpillars*was O(log n). ... We also show how to obtain a (1 + )

*approximation*for

*the*

*bandwidth*

*of*

*caterpillars*in time 2Õ ( √ n/ ) . ... Given an algorithm A for

*approximating*

*the*

*bandwidth*

*of*

*caterpillars*, for every

*caterpillar*G we consider

*the*following four quantities: its local density ρ G ; its

*bandwidth*b G ; its unfolded

*bandwidth*...

##
###
Approximating the Bandwidth of Caterpillars

2007
*
Algorithmica
*

*The*previous best

*approximation*ratio for

*the*

*bandwidth*

*of*

*caterpillars*was O(log n). ... We also show how to obtain a (1 + )

*approximation*for

*the*

*bandwidth*

*of*

*caterpillars*in time 2Õ ( √ n/ ) . ... Given an algorithm A for

*approximating*

*the*

*bandwidth*

*of*

*caterpillars*, for every

*caterpillar*G we consider

*the*following four quantities: its local density ρ G ; its

*bandwidth*b G ; its unfolded

*bandwidth*...

##
###
Graph bandwidth of weighted caterpillars

2006
*
Theoretical Computer Science
*

In this paper, we study

doi:10.1016/j.tcs.2006.07.015
fatcat:jy5cdhe6zrglxdjm3mmnjrkkmm
*the**bandwidth*minimization problem*of*weighted*caterpillars*, and propose several algorithms for solving various types*of**caterpillars*and general graphs. ... More specifically, we show that*the*GBM problem on*caterpillars*with hair-length at most 2 and*the*GBM problem on star-shape*caterpillars*are NP-complete, and give a lower bound*of**the*graph*bandwidth*... Acknowledgments*The*authors would like to thank two anonymous referees for their thoughtful suggestions for improving*the*presentation*of*this paper. ...##
###
Graph Bandwidth of Weighted Caterpillars
[chapter]

2005
*
Lecture Notes in Computer Science
*

In this paper, we study

doi:10.1007/11496199_40
fatcat:pq3m2xhoazdxjgpe3p62gzjp3i
*the**bandwidth*minimization problem*of*weighted*caterpillars*, and propose several algorithms for solving various types*of**caterpillars*and general graphs. ... More specifically, we show that*the*GBM problem on*caterpillars*with hair-length at most 2 and*the*GBM problem on star-shape*caterpillars*are NP-complete, and give a lower bound*of**the*graph*bandwidth*... Acknowledgments*The*authors would like to thank two anonymous referees for their thoughtful suggestions for improving*the*presentation*of*this paper. ...##
###
Bandwidth of Convex Bipartite Graphs and Related Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

We provide an O (n)-time, 4-

doi:10.1007/978-3-642-22685-4_28
fatcat:i7ttbbqfnvdendjzgqyyn7szfq
*approximation*algorithm and an O (n log 2 n)-time, 2-*approximation*algorithm to compute*the**bandwidth**of*convex bipartite graphs with n vertices. ... We show that*the**bandwidth*problem is NP-complete for convex bipartite graphs. ...*Approximation*algorithms*Approximation*algorithms for convex bipartite graphs We will present two algorithms that*approximate**the**bandwidth**of*convex graphs with worst-case performance ratios*of*2 and ...##
###
Bandwidth of convex bipartite graphs and related graphs

2012
*
Information Processing Letters
*

We provide an O (n)-time, 4-

doi:10.1016/j.ipl.2012.02.012
fatcat:eblgddqcavff3falsvj75nl2p4
*approximation*algorithm and an O (n log 2 n)-time, 2-*approximation*algorithm to compute*the**bandwidth**of*convex bipartite graphs with n vertices. ... We show that*the**bandwidth*problem is NP-complete for convex bipartite graphs. ...*Approximation*algorithms*Approximation*algorithms for convex bipartite graphs We will present two algorithms that*approximate**the**bandwidth**of*convex graphs with worst-case performance ratios*of*2 and ...##
###
Approximating the bandwidth for asteroidal triple-free graphs
[chapter]

1995
*
Lecture Notes in Computer Science
*

Alternatively, at

doi:10.1007/3-540-60313-1_161
fatcat:fe3ku6hczfhyvalakh42gx4bzy
*the*cost*of**the**approximation*factor, we can also obtain an O(e + nlog n) algorithm to*approximate**the**bandwidth**of*an AT-free graph within a factor 4 and an O(n + e) algorithm with a ... We show that there is an O(n 3 ) algorithm to*approximate**the**bandwidth**of*an AT-free graph with worst case performance ratio 2. ... connected component*of*T V n B] is a path with at most k vertices (a hair*of**the**caterpillar*). 2 2 We describe a simple O(n) time*approximation*algorithm for*the**bandwidth**of**caterpillars*with worst ...##
###
Hardness results for approximating the bandwidth

2011
*
Journal of computer and system sciences (Print)
*

For

doi:10.1016/j.jcss.2010.06.006
fatcat:pt257rzgqjbovhlcrxxjauhlme
*caterpillars*(trees in which all vertices*of*degree larger than two lie on one path) we show that it is NP-hard to*approximate**the**bandwidth*within any constant, and that an*approximation*ratio*of*...*The**bandwidth**of**caterpillars*received a lot*of*attention. For*caterpillars**of*strand length at most 2,*the**bandwidth*problem can be solved in polynomial time [1] . ... Acknowledgments We thank Shimon Kogan for*the*simple proof*of*Proposition 3, and an anonymous referee for numerous helpful comments on an earlier version*of*this manuscript. ...##
###
Parameterized Complexity of Bandwidth on Trees
[chapter]

2014
*
Lecture Notes in Computer Science
*

This is

doi:10.1007/978-3-662-43948-7_34
fatcat:44yi2acrpfhajah47ie23qo4fe
*the*first parameterized*approximation*algorithm for*the**bandwidth**of*trees. 1 constant*the*matrix operations discussed above can be implemented in linear time. ...*The**bandwidth**of*a n-vertex graph G is*the*smallest integer b such that there exists a bijective function f : V (G) → {1, ..., n}, called a layout*of*G, such that for every edge In*the**Bandwidth*problem ... An FPT-*Approximation*for*the**Bandwidth**of**Caterpillars**The**bandwidth**of**caterpillars*is, somewhat surprisingly, a well-studied problem. Assmann et al. ...##
###
On the Embed and Project Algorithm for the Graph Bandwidth Problem

2021
*
Mathematics
*

*The*graph

*bandwidth*problem, where one looks for a labeling

*of*graph vertices that gives

*the*minimum difference between

*the*labels over all edges, is a classical NP-hard problem that has drawn a lot

*of*... methods or with

*the*bundle method. ... A polynomial time

*approximation*algorithm for

*caterpillars*that computes

*the*

*bandwidth*, which is at most O(log n/(log log n)) times

*the*local density, was given by Feige and Talwar [22] . ...

##
###
Parameterized Complexity of Bandwidth on Trees
[article]

2014
*
arXiv
*
pre-print

This is

arXiv:1404.7810v1
fatcat:bxpb4rstdnbrnktbeb5vfheecu
*the*first parameterized*approximation*algorithm for*the**bandwidth**of*trees. ... In*the**Bandwidth*problem we are given as input a graph G and integer b, and asked whether*the**bandwidth**of*G is at most b. ... An FPT-*Approximation*for*the**Bandwidth**of**Caterpillars**The**bandwidth**of**caterpillars*is, somewhat surprisingly, a well-studied problem. Assmann et al. ...##
###
Line-distortion, Bandwidth and Path-length of a graph
[article]

2014
*
arXiv
*
pre-print

for

arXiv:1409.8389v1
fatcat:yu2y7ljeenacxhmtikpdhmggda
*the*minimum*bandwidth*problem; - there is an efficient 2-*approximation*algorithm for computing*the*path-length*of*an arbitrary graph; - AT-free graphs and some intersection families*of*graphs have ... path-length at most 2; - for AT-free graphs, there exist a linear time 8-*approximation*algorithm for*the*minimum line-distortion problem and a linear time 4-*approximation*algorithm for*the*minimum*bandwidth*... For n-vertex*caterpillars*with arbitrary hair-lengths,*the*minimum*bandwidth*can be*approximated*to within a factor*of*O(log n/ log log n) [16] . ...##
###
Path multicoloring with fewer colors in spiders and caterpillars

2007
*
Computing
*

Our algorithms achieve

doi:10.1007/s00607-007-0234-2
fatcat:mbugrxqjavesbfbq7vpzr4m3pq
*approximation*ratio*of*2 in spiders and 3 in*caterpillars*, whereas*the*best algorithm for trees so far, achieves an*approximation*ratio*of*4. ... We also study*the*directed version*of**the*problem and show that it admits a 3-*approximation*algorithm in*caterpillars*, while it can be solved exactly in spiders. ... Special thanks go to one*of**the*referees for suggesting*the*exact algorithm for Directed Min-Colors-PMC in spiders. ...##
###
Hierarchy of Transportation Network Parameters and Hardness Results
[article]

2019
*
arXiv
*
pre-print

Finally we prove that on graphs G=(V,E)

arXiv:1905.11166v3
fatcat:v57zvme52zhqdablmtia7ukoum
*of*skeleton dimension O(log^2 | V |) it is NP-hard to*approximate**the*k-Center problem within a factor less than 2. ... We show that*the*skeleton dimension is incomparable to any*of**the*parameters distance to linear forest,*bandwidth*, treewidth and highway dimension and hence, it is worthwhile to study mentioned problems ... We will use*the*fact that*the**caterpillar*tree C b on b backbone vertices*of*degree 3 has a distance to linear forest*of*b = n /2 − 1*Bandwidth*.*The**caterpillar*C b has*bandwidth*2. ...##
###
Hierarchy of Transportation Network Parameters and Hardness Results

2019
*
International Symposium on Parameterized and Exact Computation
*

Finally we prove that on graphs G = (V, E)

doi:10.4230/lipics.ipec.2019.4
dblp:conf/iwpec/000119
fatcat:72voa3cwlbbwvpwj34zszwynwe
*of*skeleton dimension O(log 2 |V |) it is NP-hard to*approximate**the*k-Center problem within a factor less than 2. ... We show that*the*skeleton dimension is incomparable to any*of**the*parameters distance to linear forest,*bandwidth*, treewidth and highway dimension and hence, it is worthwhile to study mentioned problems ... This raises*the*question whether there is a (2 − )-*approximation*algorithm for graphs*of*constant skeleton dimension. ...
« Previous

*Showing results 1 — 15 out of 515 results*