Saeed Amiri | Razi University of Kermanshah, Iran (original) (raw)

Papers by Saeed Amiri

Information Processing Letters, 2019

We study the version of the k-disjoint paths problem where k demand pairs (s 1 , t 1),. .. , (s k... more We study the version of the k-disjoint paths problem where k demand pairs (s 1 , t 1),. .. , (s k , t k) are specified in the input and the paths in the solution are allowed to intersect, but such that no vertex is on more than c paths. We show that on directed acyclic graphs the problem is solvable in time n O(d) if we allow congestion k − d for k paths. Furthermore, we show that, under a suitable complexity theoretic assumption, the problem cannot be solved in time f (k)n o(d/ log d) for any computable function f. Digital Object Identifier 10.4230/LIPIcs...

Theoretical Computer Science, 2016

Berwanger et al. show in Berwanger et al. (2012) that for every graph G of size n and DAG-width k... more Berwanger et al. show in Berwanger et al. (2012) that for every graph G of size n and DAG-width k there is a DAG decomposition of width k and size n O(k). This gives a polynomial time algorithm for determining the DAG-width of a graph for any fixed k. However, if the DAG-width of the graphs from a class is not bounded, such algorithms become exponential. This raises the question whether we can always find a DAG decomposition of size polynomial in n as it is the case for tree width and all generalisations of tree width similar to DAG-width. We show that there is an infinite class of graphs such that every DAG decomposition of optimal width has size super-polynomial in n and, moreover, there is no polynomial size DAG decomposition which would approximate an optimal decomposition up to an additive constant. In the second part we use our construction to prove that deciding whether the DAG-width of a given graph is at most a given constant is PSpace-complete.

Lecture Notes in Computer Science, 2014

The k-vertex disjoint paths problem is one of the most studied problems in algorithmic graph theo... more The k-vertex disjoint paths problem is one of the most studied problems in algorithmic graph theory. In 1994, Schrijver proved that the problem can be solved in polynomial time for every fixed k when restricted to the class of planar digraphs and it was a long standing open question whether it is fixed-parameter tractable (with respect to parameter k) on this restricted class. Only recently, [13]. achieved a major breakthrough and answered the question positively. Despite the importance of this result (and the brilliance of their proof), it is of rather theoretical importance. Their proof technique is both technically extremely involved and also has at least double exponential parameter dependence. Thus, it seems unrealistic that the algorithm could actually be implemented. In this paper, therefore, we study a smaller class of planar digraphs, the class of upward planar digraphs, a well studied class of planar graphs which can be drawn in a plane such that all edges are drawn upwards. We show that on the class of upward planar digraphs the problem (i) remains NP-complete and (ii) the problem is fixed-parameter tractable. While membership in FPT follows immediately from [13]'s general result, our algorithm has only single exponential parameter dependency compared to the double exponential parameter dependence for general planar digraphs. Furthermore, our algorithm can easily be implemented, in contrast to the algorithm in [13].

International Journal of Biosciences (IJB), 2014

The pollen grains of two genera (Allium and Calochortus) of Liliaceae (sensulato) family were inv... more The pollen grains of two genera (Allium and Calochortus) of Liliaceae (sensulato) family were investigated. Pollens were obtained from the Herbarium at Komarov Botanical Institute of the Russian Academy of Science (RAN) and different parts of Kermanshah region and compared with herbarium of Razi University of Kermanshah, Iran. Both genera were investigated using LM (Light Microscopy) and SEM (Scanning Electron Microscopy). According to LM and SEM, the pollen grains of genera were monad, monosulcate percolate, heteropolar with bilateral symmetry, which the sulcus extends from distal to proximal. Also sulcus membrane ornamentations in both genera were regulate-perforate or perforate-regulate but wall thickness and diameter of the perforations in the mesh networks in Calochortus were upper than Allium genus. According to this study the species of Calochortus can be divided into five subsections (elegant, nitidus, puchelli, gunnisoniani andvenusti). Although are Allium and Calochortus genera were belonging to Alliaceae and Liliaceae family respectively, but in morphology of the pollen grains were very similar and their differences were minimum. In comparison with the other genera of Liliaceae (sensulato) family, these genera (Allium and Calochortus) in term of morphology of pollen grains were similar to some species of Tulipa and Fritillaria (Liliaceae family)

Information Processing Letters, 2019

We study the version of the k-disjoint paths problem where k demand pairs (s 1 , t 1),. .. , (s k... more We study the version of the k-disjoint paths problem where k demand pairs (s 1 , t 1),. .. , (s k , t k) are specified in the input and the paths in the solution are allowed to intersect, but such that no vertex is on more than c paths. We show that on directed acyclic graphs the problem is solvable in time n O(d) if we allow congestion k − d for k paths. Furthermore, we show that, under a suitable complexity theoretic assumption, the problem cannot be solved in time f (k)n o(d/ log d) for any computable function f. Digital Object Identifier 10.4230/LIPIcs...

Theoretical Computer Science, 2016

Berwanger et al. show in Berwanger et al. (2012) that for every graph G of size n and DAG-width k... more Berwanger et al. show in Berwanger et al. (2012) that for every graph G of size n and DAG-width k there is a DAG decomposition of width k and size n O(k). This gives a polynomial time algorithm for determining the DAG-width of a graph for any fixed k. However, if the DAG-width of the graphs from a class is not bounded, such algorithms become exponential. This raises the question whether we can always find a DAG decomposition of size polynomial in n as it is the case for tree width and all generalisations of tree width similar to DAG-width. We show that there is an infinite class of graphs such that every DAG decomposition of optimal width has size super-polynomial in n and, moreover, there is no polynomial size DAG decomposition which would approximate an optimal decomposition up to an additive constant. In the second part we use our construction to prove that deciding whether the DAG-width of a given graph is at most a given constant is PSpace-complete.

Lecture Notes in Computer Science, 2014

The k-vertex disjoint paths problem is one of the most studied problems in algorithmic graph theo... more The k-vertex disjoint paths problem is one of the most studied problems in algorithmic graph theory. In 1994, Schrijver proved that the problem can be solved in polynomial time for every fixed k when restricted to the class of planar digraphs and it was a long standing open question whether it is fixed-parameter tractable (with respect to parameter k) on this restricted class. Only recently, [13]. achieved a major breakthrough and answered the question positively. Despite the importance of this result (and the brilliance of their proof), it is of rather theoretical importance. Their proof technique is both technically extremely involved and also has at least double exponential parameter dependence. Thus, it seems unrealistic that the algorithm could actually be implemented. In this paper, therefore, we study a smaller class of planar digraphs, the class of upward planar digraphs, a well studied class of planar graphs which can be drawn in a plane such that all edges are drawn upwards. We show that on the class of upward planar digraphs the problem (i) remains NP-complete and (ii) the problem is fixed-parameter tractable. While membership in FPT follows immediately from [13]'s general result, our algorithm has only single exponential parameter dependency compared to the double exponential parameter dependence for general planar digraphs. Furthermore, our algorithm can easily be implemented, in contrast to the algorithm in [13].

International Journal of Biosciences (IJB), 2014

The pollen grains of two genera (Allium and Calochortus) of Liliaceae (sensulato) family were inv... more The pollen grains of two genera (Allium and Calochortus) of Liliaceae (sensulato) family were investigated. Pollens were obtained from the Herbarium at Komarov Botanical Institute of the Russian Academy of Science (RAN) and different parts of Kermanshah region and compared with herbarium of Razi University of Kermanshah, Iran. Both genera were investigated using LM (Light Microscopy) and SEM (Scanning Electron Microscopy). According to LM and SEM, the pollen grains of genera were monad, monosulcate percolate, heteropolar with bilateral symmetry, which the sulcus extends from distal to proximal. Also sulcus membrane ornamentations in both genera were regulate-perforate or perforate-regulate but wall thickness and diameter of the perforations in the mesh networks in Calochortus were upper than Allium genus. According to this study the species of Calochortus can be divided into five subsections (elegant, nitidus, puchelli, gunnisoniani andvenusti). Although are Allium and Calochortus genera were belonging to Alliaceae and Liliaceae family respectively, but in morphology of the pollen grains were very similar and their differences were minimum. In comparison with the other genera of Liliaceae (sensulato) family, these genera (Allium and Calochortus) in term of morphology of pollen grains were similar to some species of Tulipa and Fritillaria (Liliaceae family)