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Approximating the Bandwidth of Caterpillars
[chapter]
2005
Lecture Notes in Computer Science
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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
2007
Algorithmica
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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
2006
Theoretical Computer Science
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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]
2005
Lecture Notes in Computer Science
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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]
2011
Lecture Notes in Computer Science
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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
2012
Information Processing Letters
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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]
1995
Lecture Notes in Computer Science
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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
2011
Journal of computer and system sciences (Print)
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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]
2014
Lecture Notes in Computer Science
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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
2021
Mathematics
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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]
2014
arXiv
pre-print
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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]
2014
arXiv
pre-print
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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
2007
Computing
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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]
2019
arXiv
pre-print
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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
2019
International Symposium on Parameterized and Exact Computation
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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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