The linearity of first-fit coloring of interval graphs
SIAM Journal on Discrete Mathematics
An on-line graph coloring algorithm with sublinear performance ratio
Discrete Mathematics
A polynomial time approximation algorithm for Dynamic Storage Allocation
Discrete Mathematics
Coloring interval graphs with First-Fit
Discrete Mathematics
The ultimate interval graph recognition algorithm?
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for compile-time memory optimization
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Routing with Minimum Wire Length in the Dogleg-Free Manhattan Model is $\cal NP$-Complete
SIAM Journal on Computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation Algorithms for Dynamic Storage Allocations
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
OPT versus LOAD in dynamic storage allocation
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Buffer Allocation in Regular Dataflow Networks: An Approach Based on Coloring Circular-Arc Graphs
HIPC '96 Proceedings of the Third International Conference on High-Performance Computing (HiPC '96)
Three dozen papers on online algorithms
ACM SIGACT News
Weighted coloring: further complexity and approximability results
Information Processing Letters
Approximating interval coloring and max-coloring in chordal graphs
Journal of Experimental Algorithmics (JEA)
Online unit clustering: Variations on a theme
Theoretical Computer Science
Online interval coloring with packing constraints
Theoretical Computer Science
On the Maximum Edge Coloring Problem
Approximation and Online Algorithms
Weighted coloring on planar, bipartite and split graphs: Complexity and approximation
Discrete Applied Mathematics
Minimum Entropy Combinatorial Optimization Problems
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Weighted Coloring: further complexity and approximability results
Information Processing Letters
On-line partitioning for on-line scheduling with resource conflicts
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Approximating the max-edge-coloring problem
Theoretical Computer Science
On the max-weight edge coloring problem
Journal of Combinatorial Optimization
Energy efficient transmission scheduling for infrastructure sensor nodes in location systems
Computer Networks: The International Journal of Computer and Telecommunications Networking
First-Fit coloring of bounded tolerance graphs
Discrete Applied Mathematics
Max-coloring and online coloring with bandwidths on interval graphs
ACM Transactions on Algorithms (TALG)
Improved approximation algorithms for the max-edge coloring problem
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Clique clustering yields a PTAS for max-coloring interval graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Variable sized online interval coloring with bandwidth
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Weighted coloring: further complexity and approximability results
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Online interval coloring and variants
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Approximation algorithms for the max-coloring problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Online interval coloring with packing constraints
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Capacitated max -batching with interval graph compatibilities
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
A one-to-one correspondence between colorings and stable sets
Operations Research Letters
Theoretical Computer Science
Online capacitated interval coloring
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
On the complexity of the max-edge-coloring problem with its variants
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
On first-fit coloring of ladder-free posets
European Journal of Combinatorics
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Given a graph G = (V,E) and positive integral vertex weights w : V → N, the max-coloring problem seeks to find a proper vertex coloring of G whose color classes C1, C2,...,Ck, minimize Σki = 1 maxν∈Ciw(ν). This problem, restricted to interval graphs, arises whenever there is a need to design dedicated memory managers that provide better performance than the general purpose memory management of the operating system. Specifically, companies have tried to solve this problem in the design of memory managers for wireless protocol stacks such as GPRS or 3G.Though this problem seems similar to the wellknown dynamic storage allocation problem, we point out fundamental differences. We make a connection between max-coloring and on-line graph coloring and use this to devise a simple 2-approximation algorithm for max-coloring on interval graphs. We also show that a simple first-fit strategy, that is a natural choice for this problem, yields a 10-approximation algorithm. We show this result by proving that the first-fit algorithm for on-line coloring an interval graph G uses no more than 10.x(G) colors, significantly improving the bound of 26.x(G) by Kierstead and Qin (Discrete Math., 144, 1995). We also show that the max-coloring problem is NP-hard.