TY - GEN

T1 - On approximating the achromatic number

AU - Kortsarz, Guy

AU - Krauthgamer, Robert

PY - 2001

Y1 - 2001

N2 - The achromatic number problem is to legally color the vertices of an input graph with the maximum number of colors, denoted &psgr;*, so that every two color classes share at least one edge. This problem is known to be NP-hard. For general graphs we give an algorithm that approximates the achromatic number within ratio of &Ogr;(n -log log n/ log n). This improves over the previously known approximation ratio of &Ogr; (n/Vlog n), due to Chaudhary and Vishwanathan [4]. For graphs of girth at least 5 we give an algorithm with approximation ratio &Ogr;(min{n1/3, V&psgr;*}). This improves over an approximation ratio &Ogr;(V&psgr;*) = &Ogr;(n3/8) for the more restricted case of graphs with girth at least 6, due to Krista and Lorys [13]. We also give the first hardness result for approximating the achromatic number. We show that for every fixed □ > 0 there in no 2 - D approximation algorithm, unless P = NP.

AB - The achromatic number problem is to legally color the vertices of an input graph with the maximum number of colors, denoted &psgr;*, so that every two color classes share at least one edge. This problem is known to be NP-hard. For general graphs we give an algorithm that approximates the achromatic number within ratio of &Ogr;(n -log log n/ log n). This improves over the previously known approximation ratio of &Ogr; (n/Vlog n), due to Chaudhary and Vishwanathan [4]. For graphs of girth at least 5 we give an algorithm with approximation ratio &Ogr;(min{n1/3, V&psgr;*}). This improves over an approximation ratio &Ogr;(V&psgr;*) = &Ogr;(n3/8) for the more restricted case of graphs with girth at least 6, due to Krista and Lorys [13]. We also give the first hardness result for approximating the achromatic number. We show that for every fixed □ > 0 there in no 2 - D approximation algorithm, unless P = NP.

KW - Algorithms

KW - Theory

KW - Verification

UR - http://www.scopus.com/inward/record.url?scp=65549121601&partnerID=8YFLogxK

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:65549121601

SN - 0898714907

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 309

EP - 318

BT - Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms

T2 - 2001 Operating Section Proceedings, American Gas Association

Y2 - 30 April 2001 through 1 May 2001

ER -