α-Gap Greedy Spanner

In this paper, we have introduced a new geometric spanner called α-Gap greedy spanner, which is a parametric approximation of the well-known Gap-greedy spanner. We will show theoretically and experimentally that this spanner is similar to the Gap-greedy spanner in terms of qualitative features such as weight and maximum degree of vertices. %Wehave shown that this spanner can be computed in O(n2logn) time withO(n) space, and O(nlogn) expected time on the set of points placedrandomly in a unit square. Two algorithms have been proposed with running time O(n2logn) for constructing the α-Gap greedy spanner. Space complexity of the first algorithm is O(n2), but it is reduced to O(n) in the second one. %The proposed algorithms have a parameter, called α, by which the similarity of the α-Gap greedy spanner to the Gap-greedy spanner, in terms of quality features mentioned above, can be determined. Also, we have shown on the points placed randomly in a unit square, the α-Gap greedy spanner can be constructed in the expected O(nlogn) time.