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

Comparing First-Fit and Next-Fit for Online Edge Coloring

We 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-Fi...

A Note on Circular Arc Online Coloring using First Fit

In [1] using a column construction technique it is proved that every interval graph can be colored online with First Fit with at most 8w(G) colors, where w(G) is the size of the maximum clique of G. Since the column construction can not be adapted to circular arc graphs we give a different proof to establish an upper bound of 9w(G) for online coloring a circular arc graph G with the First Fit a...

Parallel First-Fit Graph Coloring in Java

We implemented an existing parallel First-Fit graph coloring algorithm using JCSP in Java and present the results of its execution on a 32 core machine. An average speedup of 12.31 was observed with 32 cores and 140 parallel CSP processes as compared to the sequential execution. The algorithm was found to perform best when the number of processes exceeded the number of cores by an order of magn...

When are best fit and first fit optimal?

First Fit Level Tetris