# Coloring inductive graphs on-line

@article{Irani1990ColoringIG,
title={Coloring inductive graphs on-line},
author={Sandy Irani},
journal={Algorithmica},
year={1990},
volume={11},
pages={53-72}
}
• S. Irani
• Published 22 October 1990
• Mathematics
• Algorithmica
In this paper we consider the problem of on-line graph coloring. In an instance of on-line graph coloring, the nodes are presented one at a time. As each node is presented, its edges to previously presented nodes are also given. Each node must be assigned a color, different from the colors of its neighbors, before the next node is given. LetA(G) be the number of colors used by algorithmA on a graphG and letx(G) be the chromatic number ofG. The performance ratio of an on-line graph coloring…
ONLINE COLORING CO-INTERVAL GRAPHS
It is proved that for the class of general co-interval graphs no randomized algorithm has competitive ratio better than 3/2, and that no deterministic online algorithm for coloring unit co- Interval graphs can be better than3/2-competitive.
Online Coloring Co-interval Graphs ∗
It is proved that for the class of general co-interval graphs no randomized algorithm has competitive ratio better than 3/2, and that no deterministic online algorithm for coloring unit co- Interval graphs can be better than3/2-competitive.
Conflict-free coloring
• Mathematics, Computer Science
• 2009
For the problem of conlict-free coloring points with respect to a given set of intervals, an efficient algorithm is described that computes a coloring with at most twice the number of colors of an optimal coloring, and it is shown that there is a family of inputs that force the algorithm to use two times the number to use an optimal solution.
Lower bounds for on-line graph problems with application to on-line circuit and optical routing
• Computer Science
STOC '96
• 1996
An Ω(nǫ) lower bound on the competitive ratio of randomized online algorithms for virtual circuit routing on general networks is obtained, in contrast to the known results for some specific networks.
On the First-Fit Chromatic Number of Graphs
• Mathematics
SIAM J. Discret. Math.
• 2008
This paper studies the first-fit chromatic number of outerplanar and planar graphs as well as Cartesian products of graphs, and in particular it is given asymptotically tight results forouterplanar graphs.
Online graph coloring with bichromatic exchanges
• Mathematics, Computer Science
• 2019
This work considers a variation of greedy algorithms in which the algorithm is allowed to make modifications to previously colored vertices by performing local bichromatic exchanges, and shows that such algorithms can be used to find an optimal coloring in the case of bipartite graphs, chordal graphs and outerplanar graphs.
Tight Bounds for Online Coloring of Basic Graph Classes
• Computer Science, Mathematics
Algorithmica
• 2020
For all of the above mentioned graph classes except bipartite graphs, the natural First Fit coloring algorithm achieves an optimal performance, up to constant factors, among deterministic and randomized online algorithms.
Randomized Algorithm for Conflict-Free Coloring of Graphs & Hypergraphs
• Mathematics, Computer Science
• 2012
This work provides a framework for randomized conflict-free coloring (CF-coloring) any k-degenerate hypergraph and uses O(log n) colors with high probability, motivated by frequency assignment in wireless cellular networks.
Online conflict-free coloring for geometric hypergraphs
• Computer Science, Mathematics
• 2007
An efficient randomized online algorithm is obtained for CF-coloring any k-degenerate hypergraph using O(log n) colors and O(n) recolorings and this bound is asymptotically optimal for any constant k.

## References

SHOWING 1-10 OF 14 REFERENCES
On-line and first fit colorings of graphs
• Mathematics
J. Graph Theory
• 1988
An upper bound for the performance ratio of the first fit coloring on interval graphs is proved and it is shown that there are simple families resisting any on-line algorithm: no on- line algorithm can color all trees by a bounded number of colors.
A Dynamic location problem for graphs
• Mathematics
Comb.
• 1989
A new parameter of graphs is defined, called the window indexWX(G), that measures how large a “window” into the future is needed to solve every instance of the dynamic location problem on G optimally on-line.
The Linearity of First-Fit Coloring of Interval Graphs
It is shown that First-Fit coloring requires at most $40\omega$ colors to color an interval graph with clique size $\omega$, and it follows that a polynomial time approximation algorithm for Dynamic Storage Allocation has a constant performance ratio of 80.
Register allocation and spilling via graph coloring
This work has discovered how to extend the graph coloring approach so that it naturally solves the spilling problem, and produces better object code and takes much less compile time.
Register allocation & spilling via graph coloring
This work has discovered how to extend the graph coloring approach so that it naturally solves the spilling problem, and produces better object code and takes much less compile time.
On the performance of on-line algorithms for partition problems
• Computer Science, Mathematics
Acta Cybern.
• 1989
The performance of the greedy algorithm and of on-line algorithms for partition problems in combinatorial optimization and the power of non-adaptive adversaries for proving lower bounds are considered.
Amortized efficiency of list update and paging rules
• Computer Science
CACM
• 1985
This article shows that move-to-front is within a constant factor of optimum among a wide class of list maintenance rules, and analyzes the amortized complexity of LRU, showing that its efficiency differs from that of the off-line paging rule by a factor that depends on the size of fast memory.
Search problems in the decision tree model
• Computer Science
[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science
• 1991
It is shown that the CNF search problem is complete for all the variants of decision trees and that the gaps between the nondeterministic, the randomized, and the deterministic complexities can be arbitrarily large for search problems.
Reduced instruction set computers
Optimize compilers are used to compile programming languages down to instructions that are as unencumbered as microinstructions in a large virtual address space, and to make the instruction cycle time as fast as possible.