On-Line Edge-Coloring with a Fixed Number of Colors

Favrholdt, Lene M.; Nielsen, Morten

doi:10.1007/3-540-44450-5_8

Cited by 5 publications

(5 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Among the bad superstars, let S be the superstars with the most frequently occurring majority coloring. If |S| < 1 3 n, add the bad superstars with the most frequently occurring majority coloring among the superstars not in S. Continue doing this until S reaches a size between 1 3 n and 2 3 n. This is possible, since we consider the case where there are at least 2 3 n bad superstars.…”

Section: Proposition 14 If Two Neighboring Superstars Have Differentmentioning

confidence: 95%

“…The max-problem was studied in [1]. For k-colorable graphs, First-Fit and Next-Fit have very similar competitive ratios of 1/2 and k/(2k − 1).…”

Section: Introductionmentioning

confidence: 99%

“…For the min-coloring problem, we define the class of Any-Fit algorithms that do not take a new color into use, unless necessary. In [1], the term ''parsimonious'' was used for this type of algorithm. In this paper, we use the term ''Any-Fit'' because of the similarity with the class of Any-Fit algorithms for bin packing.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comparing First-Fit and Next-Fit for online edge coloring

Ehmsen

Favrholdt

Kohrt

et al. 2010

Theoretical Computer Science

View full text Add to dashboard Cite

a b s t r a c tWe study the performance of the algorithms First-Fit and Next-Fit for two online edge coloring problems. In the min-coloring problem, all edges must be colored using as few colors as possible. In the max-coloring problem, a fixed number of colors is given, and as many edges as possible should be colored. Previous analysis using the competitive ratio has not separated the performance of First-Fit and Next-Fit, but intuition suggests that First-Fit should be better than Next-Fit. We compare First-Fit and Next-Fit using the relative worstorder ratio, and show that First-Fit is better than Next-Fit for the min-coloring problem. For the max-coloring problem, we show that First-Fit and Next-Fit are not strictly comparable, i.e., there are graphs for which First-Fit is significantly better than Next-Fit and graphs where Next-Fit is slightly better than First-Fit.

show abstract

Section: Proposition 14 If Two Neighboring Superstars Have Differentmentioning

confidence: 95%

“…The max-problem was studied in [1]. For k-colorable graphs, First-Fit and Next-Fit have very similar competitive ratios of 1/2 and k/(2k − 1).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Comparing First-Fit and Next-Fit for online edge coloring

Ehmsen

Favrholdt

Kohrt

et al. 2010

Theoretical Computer Science

View full text Add to dashboard Cite

show abstract

“…Favrholdt et al [9] investigated a variant of on-line edgecoloring in which there are a fixed number of colors available and for each edge the algorithm must either color the edge with one of the colors, or reject it, before seeing the next edge. The aim is to color as many edges as possible.…”

Section: Related Workmentioning

confidence: 99%

Distributed dynamic channel assignment in wireless networks

Kari

Shashidhar

Kentros

2014

2014 International Conference on Computing, Networking and Communications (ICNC)

View full text Add to dashboard Cite

This paper studies the online channel assignment problem arising in dynamic wireless networks. The goal is to assign channels to communication links such that interference (or the number of conflicts) in the network is minimized. We model the problem as an online edge coloring problem. This problem is NP-hard by a reduction from EDGE COLORING. We present an online distributed greedy algorithm that gives a solution with at most 2(1 1 k )|E| more conflicts than the optimal solution, which implies a (2 1 k )-approximation. We then show that this ratio is tight by proving a lower bound that matches the above ratio.

show abstract

“…, k}, where k is a number given at input. This problem was recently considered by Favrholdt and Nielsen [6], who introduced the class of fair on-line algorithms, i.e. on-line algorithms which at every step consider a single edge e for coloring, and are required to assign some color from the range {1, .…”

Section: An On-line 647-approximation Algorithmmentioning

confidence: 99%

The maximum edge-disjoint paths problem in complete graphs

Kosowski

2008

Theoretical Computer Science

View full text Add to dashboard Cite

In this paper, we consider the undirected version of the well known maximum edge-disjoint paths problem, restricted to complete graphs. We propose an off-line 3.75-approximation algorithm and an on-line 6.47-approximation algorithm, improving the earlier 9-approximation algorithm proposed by Carmi, Erlebach, and Okamoto [P. Carmi, T. Erlebach, Y. Okamoto, Greedy edge-disjoint paths in complete graphs, in: ]. Moreover, we show that for the general case, no on-line algorithm is better than a (2 − ε)-approximation, for all ε > 0. For the special case when the number of paths is within a linear factor of the number of vertices of the graph, it is established that the problem can be optimally solved in polynomial time by an off-line algorithm, but that no on-line algorithm is better than a (1.5 − ε)-approximation. Finally, the proposed techniques are used to obtain off-line and on-line algorithms with a constant approximation ratio for the related problems of edge congestion routing and wavelength routing in complete graphs.

show abstract

On-Line Edge-Coloring with a Fixed Number of Colors

Cited by 5 publications

References 5 publications

Comparing First-Fit and Next-Fit for online edge coloring

Comparing First-Fit and Next-Fit for online edge coloring

Distributed dynamic channel assignment in wireless networks

The maximum edge-disjoint paths problem in complete graphs

Contact Info

Product

Resources

About