Years and Authors of Summarized Original Work
1981; Kierstead, Trotter
Problem Definition
Online interval coloring is a graph coloring problem. In such problems the vertices of a graph are presented one by one. Each vertex is presented in turn, along with a list of its edges in the graph, which are incident to previously presented vertices. The goal is to assign colors (which without loss of generality are assumed to be nonnegative integers) to the vertices, so that two vertices which share an edge receive different colors and the total number of colors used (or alternatively, the largest index of any color that is used) is minimized. The smallest number of colors, for which the graph still admits a valid coloring, is called the chromatic number of the graph.
The interval coloring problem is defined as follows. Intervals on the real line are presented one by one, and the online algorithm must assign each interval a color before the next interval arrives, so that no two intersecting...
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Recommended Reading
Adamy U, Erlebach T (2003) Online coloring of intervals with bandwidth. In: Proceedings of the first international workshop on approximation and online algorithms (WAOA2003), Budapest, Hungary, pp 1–12
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Epstein L, Levin A (2012) On the max coloring problem. Theor Comput Sci 462(1):23–38
Epstein L, Levy M (2005) Online interval coloring and variants. In: Proceedings of the 32nd international colloquium on automata, languages and programming (ICALP2005), Lisbon, Portugal, pp 602–613
Epstein L, Levy M (2008) Online interval coloring with packing constraints. Theor Comput Sci 407(1–3):203–212
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Kierstead HA, Smith DA, Trotter WT (2013) Manuscript. https://math.la.asu.edu/~halk/Publications/biwall6.pdf
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Nonner T (2011) Clique clustering yields a PTAS for max-coloring interval graphs. In: Proceedings of the 38th international colloquium on automata, languages and programming (ICALP2011), Zurich, Switzerland, pp 183–194
Pemmaraju S, Raman R, Varadarajan KS (2011) Max-coloring and online coloring with bandwidths on interval graphs. ACM Trans Algorithms 7(3):35
Trotter WT (2014) Current research problems: first fit colorings of interval graphs. http://people.math.gatech.edu/~trotter/rprob.html
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Epstein, L. (2014). Online Interval Coloring. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27848-8_264-2
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DOI: https://doi.org/10.1007/978-3-642-27848-8_264-2
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