The linearity of first-fit coloring of interval graphs
SIAM Journal on Discrete Mathematics
A polynomial time approximation algorithm for Dynamic Storage Allocation
Discrete Mathematics
On-Line Coloring and Recursive Graph Theory
SIAM Journal on Discrete Mathematics
Radius two trees specify &khgr;-bounded classes
Journal of Graph Theory
Coloring interval graphs with First-Fit
Discrete Mathematics
On-line chain partitions of orders
Ordal'94 Selected papers from the conference on Orders, algorithms and applications
Buffer minimization using max-coloring
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
First-Fit Algorithm for the On-Line Chain Partitioning Problem
SIAM Journal on Discrete Mathematics
The Sub-exponential Upper Bound for On-Line Chain Partitioning
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
First-Fit coloring of bounded tolerance graphs
Discrete Applied Mathematics
The first-fit algorithm uses many colors on some interval graphs
The first-fit algorithm uses many colors on some interval graphs
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Bosek and Krawczyk exhibited an on-line algorithm for partitioning an on-line poset of width w into w^1^4^l^g^w chains. They also observed that the problem of on-line chain partitioning of general posets of width w could be reduced to First-Fit chain partitioning of 2w^2+1-ladder-free posets of width w, where an m-ladder is the transitive closure of the union of two incomparable chains x"1@?...@?x"m, y"1@?...@?y"m and the set of comparabilities {x"1@?y"1,...,x"m@?y"m}. Here, we provide a subexponential upper bound (in terms of w with m fixed) for the performance of First-Fit chain partitioning on m-ladder-free posets, as well as an exact quadratic bound when m=2, and an upper bound linear in m when w=2. Using the Bosek-Krawczyk observation, this yields an on-line chain partitioning algorithm with a somewhat improved performance bound. More importantly, the algorithm and the proof of its performance bound are much simpler.