TY - JOUR
T1 - The interval constrained 3-coloring problem
AU - Byrka, Jaroslaw
AU - Karrenbauer, Andreas
AU - Sanità, Laura
PY - 2015/8/16
Y1 - 2015/8/16
N2 - In this paper, we settle the open complexity status of interval constrained coloring with a fixed number of colors. We prove that the problem is already NP-complete if the number of different colors is 3. Previously, it has only been known that it is NP-complete, if the number of colors is part of the input and that the problem is solvable in polynomial time, if the number of colors is at most 2. We also show that it is hard to satisfy almost all of the constraints for a feasible instance (even in the restricted case where each interval is used at most once). This implies APX-hardness of maximizing the number of simultaneously satisfiable intervals.
AB - In this paper, we settle the open complexity status of interval constrained coloring with a fixed number of colors. We prove that the problem is already NP-complete if the number of different colors is 3. Previously, it has only been known that it is NP-complete, if the number of colors is part of the input and that the problem is solvable in polynomial time, if the number of colors is at most 2. We also show that it is hard to satisfy almost all of the constraints for a feasible instance (even in the restricted case where each interval is used at most once). This implies APX-hardness of maximizing the number of simultaneously satisfiable intervals.
KW - APX-hardness
KW - Interval constrained coloring
UR - http://www.scopus.com/inward/record.url?scp=84944916804&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2015.04.037
DO - 10.1016/j.tcs.2015.04.037
M3 - Article
AN - SCOPUS:84944916804
SN - 0304-3975
VL - 593
SP - 42
EP - 50
JO - Theoretical Computer Science
JF - Theoretical Computer Science
ER -