%0 Journal Article
%T $\alpha$-Gap Greedy Spanner
%J Journal of Algorithms and Computation
%I University of Tehran
%Z 2476-2776
%A Salami, Hosein
%A Nouri Baygi, Mostafa
%D 2021
%\ 06/01/2021
%V 53
%N 1
%P 41-60
%! $\alpha$-Gap Greedy Spanner
%K computational geometry
%K geometric spanners
%K gap greedy spanner
%K construction algorithms
%K algorithm complexity
%R 10.22059/jac.2021.81307
%X In this paper, we have introduced a new geometric spanner called $\alpha$-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 $O(n^2 \log n)$ time with$O(n)$ space, and $O(n \log n)$ expected time on the set of points placedrandomly in a unit square.Two algorithms have been proposed with running time $O(n^2 \log n)$ for constructing the $\alpha$-Gap greedy spanner. Space complexity of the first algorithm is $O(n^2)$, but it is reduced to $O(n)$ in the second one. %The proposed algorithms have a parameter, called $\alpha$, by which the similarity of the $\alpha$-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 $\alpha$-Gap greedy spanner can be constructed in the expected $O(n \log n)$ time.
%U https://jac.ut.ac.ir/article_81307_669c0a0df2c0484e4332a6e5ff9041b6.pdf