arXiv subjects

V. A. Melent'ev

Publications and source records attributed to V. A. Melent'ev.

5 recordsLinked to original sources

arXiv2024

Search for shortest paths based on a projective description of unweighted graphs

The search is based on the preliminary transformation of matrices or adjacency lists traditionally used in the study of graphs into projections cleared of redundant information (refined) followed by the selection of the desired shortest paths. Each projection contains complete information about all the shortest paths from its base (angle vertex) and is based on an enumeration of reachability relations, more complex than the traditionally used binary adjacency relations. The class of graphs considered was expanded to mixed graphs containing both undirected and oriented edges (arcs). A method for representing graph projections in computer memory and finding shortest paths using them is proposed. The reduction in algorithmic complexity achieved, at the same time, will allow the proposed method to be used in information network applications, scientific and technical, transport and logistics, and economic fields.

cs.DC↗

arXiv2024

Shortest paths search method based on the projective description of unweighted mixed graphs

The method is based on the preliminary transformation of the traditionally used matrices or adjacency lists in the graph theory into refined projections free from redundant information, and their subsequent use in constructing shortest paths. Unlike adjacency matrices and lists based on enumerating binary adjacency relations, the refined projection is based on enumerating more complex relations: simple paths from a given graph vertex that are shortest. The preliminary acquisition of such projections reduces the algorithmic complexity of applications using them and improves their volumetric and real-time characteristics to linear ones for a pair of vertices. The class of graphs considered is extended to mixed graphs.

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arXiv2022

On the quick search for the shortest paths in an unweighted dynamic graph by its projections in brief

For the first time proposed: a method for representing the projections of a graph in computer memory and a description based on it of a quick search for shortest paths in unweighted dynamic graphs. The spatial complexity of the projection description does not exceed $(d + 1)\times n$ words, where $d$ is the diameter and $n$ is the number of vertices of the graph. The temporal difficulty of finding one shortest path between two vertices does not exceed d steps with the duration of elementary time of sampling a machine word. The solution can be applied in time delay-critical routing protocols of computer networks and supercomputers.

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arXiv2021

Formal method of synthesis of optimal topologies of computing systems based on projective description of graphs

A deterministic method for synthesizing the interconnect topologies optimized for the required properties is proposed. The method is based on the original description of graphs by projections, on establishing the bijective correspondence of the required properties and the projection properties of the initial graph, on postulating the corresponding restrictions of modified projections and on iteratively applying these restrictions to them either until the projection system is solved and the projections of the desired graph are obtained, or until its incompatibility with the given initial conditions is revealed.

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arXiv2020

On the compatibility of the topologies of parallel tasks and computing systems

Aspects of compatibility of topologies of parallel computing systems and tasks are investigated. The introduction of appropriate indexes based on the original topological model of parallel computations and on the nontraditional description of a graph by its projections is proposed and elucidated. On the example of hypercubic computing system (CS) and tasks with ring and star information topologies, we demonstrate determining the indexes and their use in a comparative analysis of the applicability of interconnect with a given topology for solving tasks with the same and different types of information topologies.

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