Amortized efficiency of list update and paging rules
Communications of the ACM
The greedy algorithm is optimal for on-line edge coloring
Information Processing Letters
Randomized algorithms
Online computation and competitive analysis
Online computation and competitive analysis
Best-fit bin-packing with random order
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
The relative worst order ratio for online algorithms
ACM Transactions on Algorithms (TALG)
The relative worst-order ratio applied to paging
Journal of Computer and System Sciences
The relative worst order ratio applied to seat reservation
ACM Transactions on Algorithms (TALG)
Theoretical evidence for the superiority of LRU-2 over LRU for the paging problem
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
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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 -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 worst-order 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.