Publications with Ahmad Biniaz
Spanning trees in multipartite geometric graphs.
A. Biniaz, P. Bose, D. Eppstein, A. Maheshwari, P. Morin, and M. Smid.
arXiv:1611.01661.
Algorithmica 80 (11): 3177–3191, 2018.We provide near-linear-time algorithms for minimum and maximum spanning trees on Euclidean graphs given by multicolored point sets, where each point forms a vertex, and each bichromatic pair of points forms an edge with length equal to their Euclidean distance.
Maximum plane trees in multipartite geometric graphs.
A. Biniaz, P. Bose, J.-L. De Carufel, K. Crosbie, D. Eppstein, A. Maheshwari, M. Smid.
15th Algorithms and Data Structures Symp. (WADS 2017), St. John's, Newfoundland.
Springer, Lecture Notes in Comp. Sci. (2017), pp. 193–204.
Algorithmica 81 (4): 1512–1534, 2019.We consider problems of constructing the maximum-length plane (non-self-crossing) spanning tree on Euclidean graphs given by multicolored point sets, where each point forms a vertex, and each bichromatic pair of points forms an edge with length equal to their Euclidean distance. We show that several such problems can be efficiently approximated.
Noncrossing longest paths and cycles.
G. Aloupis, A. Biniaz, P. Bose, J.-L. De Carufel, D. Eppstein, A. Maheshwari, S. Odak, M. Smid, C. Tóth, and P. Valtr.
32nd International Symposium on Graph Drawing and Network Visualization.
Leibniz International Proceedings in Informatics (LIPIcs) 320, 2024, pp. 36:1–36:17.
arXiv:2410.05580.
Graphs and Combinatorics 41, article 122 (25pp), 2025.The shortest path or cycle through given planar points (the solution to the traveling salesperson problem) never crosses itself: any crossing can be eliminated by a local move that shortens the tour. One might think that, correspondingly, the longest path or cycle through enough planar points always crosses itself. We show that this is not the case: there exist arbitrarily large point sets for which the longest path or cycle has no crossing.