Code scheduling and register allocation in large basic blocks
ICS '88 Proceedings of the 2nd international conference on Supercomputing
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
Register allocation via graph coloring
Register allocation via graph coloring
Coloring interval graphs with First-Fit
Discrete Mathematics
A coloring problem for weighted graphs
Information Processing Letters
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
Linear scan register allocation
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
Complete register allocation problems
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Register allocation & spilling via graph coloring
SIGPLAN '82 Proceedings of the 1982 SIGPLAN symposium on Compiler construction
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)
Buffer minimization using max-coloring
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
OPT Versus LOAD in Dynamic Storage Allocation
SIAM Journal on Computing
An improved algorithm for online coloring of intervals with bandwidth
Theoretical Computer Science - Computing and combinatorics
Batch Coloring Flat Graphs and Thin
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Weighted Coloring: further complexity and approximability results
Information Processing Letters
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
A short proof of the NP-completeness of minimum sum interval coloring
Operations Research Letters
Aliased register allocation for straight-line programs is NP-complete
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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
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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, &ldots;, Ck, minimize ∑i=1k maxv ∈ Ci w(v). 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. Though this problem seems similar to the dynamic storage allocation problem, there are fundamental differences. We make a connection between max-coloring and online 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 an 8-approximation algorithm. We show this result by proving that the first-fit algorithm for online coloring an interval graph G uses no more than 8 ċ χ(G) colors, significantly improving the bound of 26 ċ χ(G) by Kierstead and Qin [1995]. We also show that the max-coloring problem is NP-hard. The problem of online coloring of intervals with bandwidths is a simultaneous generalization of online interval coloring and online bin packing. The input is a set I of intervals, each interval i∈ I having an associated bandwidth b(i) ∈ (0, 1]. We seek an online algorithm that produces a coloring of the intervals such that for any color c and any real r, the sum of the bandwidths of intervals containing r and colored c is at most 1. Motivated by resource allocation problems, Adamy and Erlebach [2003] consider this problem and present an algorithm that uses at most 195 times the number of colors used by an optimal offline algorithm. Using the new analysis of first-fit coloring of interval graphs, we show that the Adamy-Erlebach algorithm is 35-competitive. Finally, we generalize the Adamy-Erlebach algorithm to a class of algorithms and show that a different instance from this class is 30-competitive.