TY - GEN
T1 - Hard metrics from Cayley graphs of abelian groups
AU - Newman, Ilan
AU - Rabinovich, Yuri
PY - 2007
Y1 - 2007
N2 - Hard metrics are the class of extremal metrics with respect to embedding into Euclidean Spaces: their distortion is as bad as it possibly gets, which is Ω(log n). Besides being very interesting objects akin to expanders and good codes, with rich structure of independent interest, such metrics are important for obtaining lower bounds in Combinatorial Optimization, e.g., on the value of MinCut/MaxFlow ratio for multicommodity flows. For more than a decade, a single family of hard metrics was known (see [10,3]). Recently, a different such family was found (see [8]), causing a certain excitement among the researchers in the area. In this paper we present another construction of hard metrics, different from [10,3], and more general yet clearer and simpler than [8]. Our results naturally extend to NEG and to ℓ1.
AB - Hard metrics are the class of extremal metrics with respect to embedding into Euclidean Spaces: their distortion is as bad as it possibly gets, which is Ω(log n). Besides being very interesting objects akin to expanders and good codes, with rich structure of independent interest, such metrics are important for obtaining lower bounds in Combinatorial Optimization, e.g., on the value of MinCut/MaxFlow ratio for multicommodity flows. For more than a decade, a single family of hard metrics was known (see [10,3]). Recently, a different such family was found (see [8]), causing a certain excitement among the researchers in the area. In this paper we present another construction of hard metrics, different from [10,3], and more general yet clearer and simpler than [8]. Our results naturally extend to NEG and to ℓ1.
UR - http://www.scopus.com/inward/record.url?scp=38049188234&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-70918-3_14
DO - 10.1007/978-3-540-70918-3_14
M3 - Conference contribution
AN - SCOPUS:38049188234
SN - 9783540709176
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 157
EP - 162
BT - STACS 2007 - 24th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings
PB - Springer Verlag
T2 - 24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007
Y2 - 22 February 2007 through 24 February 2007
ER -