TY - JOUR
T1 - Deterministic conflict-free coloring for intervals
T2 - From offline to online
AU - Bar-Noy, Amotz
AU - Cheilaris, Panagiotis
AU - Smorodinsky, Shakhar
PY - 2008/8/1
Y1 - 2008/8/1
N2 - We investigate deterministic algorithms for a frequency assignment problem in cellular networks. The problem can be modeled as a special vertex coloring problem for hypergraphs: In every hyperedge there must exist a vertex with a color that occurs exactly once in the hyperedge (the conflict-free property). We concentrate on a special case of the problem, called conflict-free coloring for intervals. We introduce a hierarchy of four models for the aforesaid problem: (i) static, (ii) dynamic offline, (iii) dynamic online with absolute positions, and (iv) dynamic online with relative positions. In the dynamic offline model, we give a deterministic algorithm that uses at most log3/2 n + 1 ≈ 1.71 log2 n colors and show inputs that force any algorithm to use at least 3 log5 n + 1 1.29 log2 n colors. For the online absolute-positions model, we give a deterministic algorithm that uses at most 3⌈log3 n⌉ 1.89 log2 n colors. To the best of our knowledge, this is the first deterministic online algorithm using O(log n) colors in a nontrivial online model. In the online relative-positions model, we resolve an open problem by showing a tight analysis on the number of colors used by the first-fit greedy online algorithm. We also consider conflict-free coloring only with respect to intervals that contain at least one of the two extreme points.
AB - We investigate deterministic algorithms for a frequency assignment problem in cellular networks. The problem can be modeled as a special vertex coloring problem for hypergraphs: In every hyperedge there must exist a vertex with a color that occurs exactly once in the hyperedge (the conflict-free property). We concentrate on a special case of the problem, called conflict-free coloring for intervals. We introduce a hierarchy of four models for the aforesaid problem: (i) static, (ii) dynamic offline, (iii) dynamic online with absolute positions, and (iv) dynamic online with relative positions. In the dynamic offline model, we give a deterministic algorithm that uses at most log3/2 n + 1 ≈ 1.71 log2 n colors and show inputs that force any algorithm to use at least 3 log5 n + 1 1.29 log2 n colors. For the online absolute-positions model, we give a deterministic algorithm that uses at most 3⌈log3 n⌉ 1.89 log2 n colors. To the best of our knowledge, this is the first deterministic online algorithm using O(log n) colors in a nontrivial online model. In the online relative-positions model, we resolve an open problem by showing a tight analysis on the number of colors used by the first-fit greedy online algorithm. We also consider conflict-free coloring only with respect to intervals that contain at least one of the two extreme points.
KW - Cellular networks
KW - Coloring
KW - Conflict free
KW - Frequency assignment
KW - Online algorithms
UR - http://www.scopus.com/inward/record.url?scp=50849116105&partnerID=8YFLogxK
U2 - 10.1145/1383369.1383375
DO - 10.1145/1383369.1383375
M3 - Article
AN - SCOPUS:50849116105
VL - 4
JO - ACM Transactions on Algorithms
JF - ACM Transactions on Algorithms
SN - 1549-6325
IS - 4
M1 - 44
ER -