University of TehranJournal of Algorithms and Computation2476-277653120210601$\alpha$-Gap Greedy Spanner41608130710.22059/jac.2021.81307ENHoseinSalamiDepartment of Computer Engineering, Ferdowsi University of MashhadMostafaNouri BaygiDepartment of Computer Engineering, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20210514In 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.<br />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. <br />%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. <br />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.https://jac.ut.ac.ir/article_81307_669c0a0df2c0484e4332a6e5ff9041b6.pdf