TY - JOUR

T1 - Unexplored Steiner ratios in geometric networks

AU - Carmi, Paz

AU - Chaitman-Yerushalmi, Lilach

N1 - Funding Information:
Research is partially supported by Lynn and William Frankel Center for Computer Science and by grant 2240-2100.6/2009 from the German Israeli Foundation for scientific research and development (GIF) and by grant 680/11 from the Israel Science Foundation (ISF).

PY - 2012/9/6

Y1 - 2012/9/6

N2 - In this paper we extend the context of Steiner ratio and examine the influence of Steiner points on the weight of a graph in two generalizations of the Euclidean minimum weight connected graph (MST). The studied generalizations are with respect to the weight function and the connectivity condition. First, we consider the Steiner ratio of Euclidean minimum weight connected graph under the budget allocation model. The budget allocation model is a geometric version of a new model for weighted graphs introduced by Ben-Moshe et al. in [4]. It is known that adding auxiliary points, called Steiner points, to the initial point set may result in a lighter Euclidean minimum spanning tree. We show that this behavior changes under the budget allocation model. Apparently, Steiner points are not helpful in weight reduction of the geometric minimum spanning trees under the budget allocation model (BMST), as opposed to the traditional model. An interesting relation between the BMST and the Euclidean square root metric reveals a somewhat surprising result: Steiner points are also redundant in weight reduction of the minimum spanning tree in the Euclidean square root metric. Finally, we consider the Steiner ratio of geometric t-spanners. We show that the influence of Steiner points on reducing the weight of Euclidean spanner networks goes much further than what is known for trees.

AB - In this paper we extend the context of Steiner ratio and examine the influence of Steiner points on the weight of a graph in two generalizations of the Euclidean minimum weight connected graph (MST). The studied generalizations are with respect to the weight function and the connectivity condition. First, we consider the Steiner ratio of Euclidean minimum weight connected graph under the budget allocation model. The budget allocation model is a geometric version of a new model for weighted graphs introduced by Ben-Moshe et al. in [4]. It is known that adding auxiliary points, called Steiner points, to the initial point set may result in a lighter Euclidean minimum spanning tree. We show that this behavior changes under the budget allocation model. Apparently, Steiner points are not helpful in weight reduction of the geometric minimum spanning trees under the budget allocation model (BMST), as opposed to the traditional model. An interesting relation between the BMST and the Euclidean square root metric reveals a somewhat surprising result: Steiner points are also redundant in weight reduction of the minimum spanning tree in the Euclidean square root metric. Finally, we consider the Steiner ratio of geometric t-spanners. We show that the influence of Steiner points on reducing the weight of Euclidean spanner networks goes much further than what is known for trees.

UR - http://www.scopus.com/inward/record.url?scp=84865639045&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-32241-9_24

DO - 10.1007/978-3-642-32241-9_24

M3 - Conference article

AN - SCOPUS:84865639045

SN - 0302-9743

VL - 7434 LNCS

SP - 275

EP - 286

JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

T2 - 18th Annual International Computing and Combinatorics Conference, COCOON 2012

Y2 - 20 August 2012 through 22 August 2012

ER -