Balancing Degree, Diameter and Weight in Euclidean Spanners

Abstract. In a seminal STOC'95 paper, Arya et al. [4] devised a construction that for any set S of n points in Rd and any > 0, provides a (1 + )-spanner with diameter O(log n), weight O(log2 n)w(MST(S)), and constant maximum degree. Another construction of [4] provides a (1 + )-spanner with O(n) edges and diameter (n), where stands for the inverse-Ackermann function. Das and Narasimhan [18] devised a construction with constant maximum degree and weight O(w(MST(S))), but whose diameter may be arbitrarily large. In another construction by Arya et al. [4] there is diameter O(log n) and weight O(log n)w(MST(S)), but it may have arbitrarily large maximum degree. These constructions fail to address situations in which we are prepared to compromise on one of the parameters, but cannot afford it to be arbitrarily large. In this paper we devise a novel unified construction that trades between maximum degree, diameter and weight gracefully. For a positive integer k, our construction pr...

• Type: Conference
• Year: 2010
• Where: ESA
• Authors: Shay Solomon, Michael Elkin
• Keywords: Algorithms, Arbitrarily Large, Constant Maximum Degree, ESA 2010, Maximum Degree