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Approximating the Bandwidth of Caterpillars [chapter]

Uriel Feige, Kunal Talwar
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  ... 
doi:10.1007/11538462_6 fatcat:kgoyniwfzbemzks2oafpddrpau

Approximating the Bandwidth of Caterpillars

Uriel Feige, Kunal Talwar
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  ... 
doi:10.1007/s00453-007-9002-0 fatcat:yzyokdyeujdpzf255qkxhlc62e

Graph bandwidth of weighted caterpillars

Mingen Lin, Zhiyong Lin, Jinhui Xu
2006 Theoretical Computer Science  
In this paper, we study 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.  ... 
doi:10.1016/j.tcs.2006.07.015 fatcat:jy5cdhe6zrglxdjm3mmnjrkkmm

Graph Bandwidth of Weighted Caterpillars [chapter]

Zhiyong Lin, Mingen Lin, Jinhui Xu
2005 Lecture Notes in Computer Science  
In this paper, we study 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.  ... 
doi:10.1007/11496199_40 fatcat:pq3m2xhoazdxjgpe3p62gzjp3i

Bandwidth of Convex Bipartite Graphs and Related Graphs [chapter]

Anish Man Singh Shrestha, Satoshi Tayu, Shuichi Ueno
2011 Lecture Notes in Computer Science  
We provide an O (n)-time, 4-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  ... 
doi:10.1007/978-3-642-22685-4_28 fatcat:i7ttbbqfnvdendjzgqyyn7szfq

Bandwidth of convex bipartite graphs and related graphs

Anish Man Singh Shrestha, Satoshi Tayu, Shuichi Ueno
2012 Information Processing Letters  
We provide an O (n)-time, 4-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  ... 
doi:10.1016/j.ipl.2012.02.012 fatcat:eblgddqcavff3falsvj75nl2p4

Approximating the bandwidth for asteroidal triple-free graphs [chapter]

T. Kloks, D. Kratsch, H. Müller
1995 Lecture Notes in Computer Science  
Alternatively, at 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  ... 
doi:10.1007/3-540-60313-1_161 fatcat:fe3ku6hczfhyvalakh42gx4bzy

Hardness results for approximating the bandwidth

Chandan Dubey, Uriel Feige, Walter Unger
2011 Journal of computer and system sciences (Print)  
For 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.  ... 
doi:10.1016/j.jcss.2010.06.006 fatcat:pt257rzgqjbovhlcrxxjauhlme

Parameterized Complexity of Bandwidth on Trees [chapter]

Markus Sortland Dregi, Daniel Lokshtanov
2014 Lecture Notes in Computer Science  
This is 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.  ... 
doi:10.1007/978-3-662-43948-7_34 fatcat:44yi2acrpfhajah47ie23qo4fe

On the Embed and Project Algorithm for the Graph Bandwidth Problem

Janez Povh
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] .  ... 
doi:10.3390/math9172030 fatcat:lr7u5zq6fzawtbxcypl7l6gw3i

Parameterized Complexity of Bandwidth on Trees [article]

Markus Sortland Dregi, Daniel Lokshtanov
2014 arXiv   pre-print
This is 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.  ... 
arXiv:1404.7810v1 fatcat:bxpb4rstdnbrnktbeb5vfheecu

Line-distortion, Bandwidth and Path-length of a graph [article]

Feodor F. Dragan and Ekkehard Köhler and Arne Leitert
2014 arXiv   pre-print
for 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] .  ... 
arXiv:1409.8389v1 fatcat:yu2y7ljeenacxhmtikpdhmggda

Path multicoloring with fewer colors in spiders and caterpillars

A. Pagourtzis, K. Potika, S. Zachos
2007 Computing  
Our algorithms achieve 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.  ... 
doi:10.1007/s00607-007-0234-2 fatcat:mbugrxqjavesbfbq7vpzr4m3pq

Hierarchy of Transportation Network Parameters and Hardness Results [article]

Johannes Blum
2019 arXiv   pre-print
Finally we prove that on graphs G=(V,E) 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.  ... 
arXiv:1905.11166v3 fatcat:v57zvme52zhqdablmtia7ukoum

Hierarchy of Transportation Network Parameters and Hardness Results

Johannes Blum, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
Finally we prove that on graphs G = (V, E) 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.  ... 
doi:10.4230/lipics.ipec.2019.4 dblp:conf/iwpec/000119 fatcat:72voa3cwlbbwvpwj34zszwynwe
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