arXiv subjects

Seyed Naser Hashemi

Publications and source records attributed to Seyed Naser Hashemi.

5 recordsLinked to original sources

arXiv2019

An efficient approximation for point-set diameter in higher dimensions

In this paper, we study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\varepsilon)$-approximation algorithm with $O(n+ 1/\varepsilon^{d-1})$ time and $O(n)$ space, where $0 < \varepsilon\leqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(\varepsilon))$-approximation algorithm with $O(n+ 1/\varepsilon^{\frac{2d}{3}-\frac{1}{3}})$ running time. These results provide some improvements in comparison with existing algorithms in terms of simplicity and data structure.

cs.CG↗

arXiv2019

Approximation Algorithms for Multi-Multiway Cut and Multicut Problems on Directed Graphs

In this paper, we present two approximation algorithms for the directed multi-multiway cut and directed multicut problems. The so called region growing paradigm \cite{1} is modified and used for these two cut problems on directed graphs. By using this paradigm, we give for each problem an approximation algorithm such that both algorithms have the approximate factor $O(k)$ the same as the previous works done on these problems. However, the previous works need to solve $k$ linear programming, whereas our algorithms require only one linear programming. Therefore, our algorithms improve the running time of the previous algorithms.

cs.DS↗

arXiv2018

Better approximation algorithm for point-set diameter

We propose a new $(1+O(\varepsilon))$-approximation algorithm with $O(n+ 1/\varepsilon^{\frac{(d-1)}{2}})$ running time for computing the diameter of a set of $n$ points in the $d$-dimensional Euclidean space for a fixed dimension $d$, where $0 < \varepsilon\leqslant 1$. This result provides some improvements in the running time of this problem in comparison with previous algorithms.

cs.CG↗

arXiv2016

The coefficients of the reduced Bartholdi zeta function

In this paper, we establish a new zeta function based on the Bartholdi zeta function for an undirected graph G called the reduced Bartholdi zeta function. We study the relation between its coefficients and the structure of the graph, and demonstrate that the coefficients count the star subgraphs in the symmetric digraph D(G). Moreover, we investigate the properties of semi principle minors extracted from the adjacency matrix of the oriented line graph of G. We also present a general formula for calculating all the coefficients of the reduced Bartholdi zeta function.

math.CO↗

arXiv2013

New Algorithms on Rooted Triplet Consistency

An evolutionary tree (phylogenetic tree) is a binary, rooted, unordered tree that models the evolutionary history of currently living species in which leaves are labeled by species. In this paper, we investigate the problem of finding the maximum consensus evolutionary tree from a set of given rooted triplets. A rooted triplet is a phylogenetic tree on three leaves and shows the evolutionary relationship of the corresponding three species. The mentioned problem is known to be APX-hard. We present two new heuristic algorithms. For a given set of m triplets on n species, the FastTree algorithm runs in O(mn^2) which is faster than any other previously known algorithms, although, the outcome is less satisfactory. The BPMTR algorithm runs in O(mn^3) and in average performs better than any other previously known approximation algorithms for this problem.

q-bio.PE↗