scholarly journals On Factors of Independent Transversals in $k$-Partite Graphs

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Raphael Yuster
Keyword(s):  
Bipartite Graph ◽  
Greedy Algorithm ◽  
Pairwise Disjoint ◽  
Independent Set ◽  
Single Vertex ◽  
Hall's Theorem ◽  
Hall’S Theorem ◽  
The Greedy Algorithm

A $[k,n,1]$-graph is a $k$-partite graph with parts of order $n$ such that the bipartite graph induced by any pair of parts is a matching. An independent transversal in such a graph is an independent set that intersects each part in a single vertex. A factor of independent transversals is a set of $n$ pairwise-disjoint independent transversals. Let $f(k)$ be the smallest integer $n_0$ such that every $[k,n,1]$-graph has a factor of independent transversals assuming $n \geqslant n_0$. Several known conjectures imply that for $k \geqslant 2$, $f(k)=k$ if $k$ is even and $f(k)=k+1$ if $k$ is odd. While a simple greedy algorithm based on iterating Hall's Theorem shows that $f(k) \leqslant 2k-2$, no better bound is known and in fact, there are instances showing that the bound $2k-2$ is tight for the greedy algorithm. Here we significantly improve upon the greedy algorithm bound and prove that $f(k) \leqslant 1.78k$ for all $k$ sufficiently large, answering a question of MacKeigan.

scholarly journals Matroids And Greedy Algorithms. A Deeper Justification of Using Greedy Approach To Find A Maximal set of a Matroid

2017 ◽  
Vol 16 (2) ◽  
pp. 48
Author(s):  
Syed Aqib Haider
Keyword(s):  
Greedy Algorithm ◽  
Local Level ◽  
Greedy Algorithms ◽  
Optimal Solution ◽  
Independent Set ◽  
Computation Time ◽  
Optimal Choice ◽  
Greedy Approach ◽  
The Greedy Algorithm ◽  
Selection Of

<p>Greedy algorithms are used in solving a diverse set of problems in small computation time. However, for solving problems using greedy approach, it must be proved that the greedy strategy applies. The greedy approach relies on selection of optimal choice at a local level reducing the problem to a single sub problem, which actually leads to a globally optimal solution. Finding a maximal set from the independent set of a matroid M(S, I) also uses greedy approach and justification is also provided in standard literature (e.g. Introduction to Algorithms by Cormen et .al.). However, the justification does not clearly explain the equivalence of using greedy algorithm and contraction of M by the selected element. This paper thus attempts to give a lucid explanation of the fact that the greedy algorithm is equivalent to reducing the Matroid into its contraction by selected element. This approach also provides motivation for research on the selection of the test used in algorithm which might lead to smaller computation time of the algorithm.</p>

scholarly journals Randomized Greedy Algorithms for Independent Sets and Matchings in Regular Graphs: Exact Results and Finite Girth Corrections

2009 ◽  
Vol 19 (1) ◽  
pp. 61-85 ◽  
Author(s):  
DAVID GAMARNIK ◽  
DAVID A. GOLDBERG
Keyword(s):  
Greedy Algorithm ◽  
Greedy Algorithms ◽  
Independent Set ◽  
Independent Sets ◽  
Simple Expression ◽  
Regular Graphs ◽  
Bounded Degree ◽  
Constant Degree ◽  
Image Position ◽  
The Greedy Algorithm

We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant-degree regular graphs. We show that forr-regular graphs withnnodes and girth at leastg, the algorithm finds an independent set of expected cardinalitywheref(r) is a function which we explicitly compute. A similar result is established for matchings. Our results imply improved bounds for the size of the largest independent set in these graphs, and provide the first results of this type for matchings. As an implication we show that the greedy algorithm returns a nearly perfect matching when both the degreerand girthgare large. Furthermore, we show that the cardinality of independent sets and matchings produced by the greedy algorithm inarbitrarybounded-degree graphs is concentrated around the mean. Finally, we analyse the performance of the greedy algorithm for the case of random i.i.d. weighted independent sets and matchings, and obtain a remarkably simple expression for the limiting expected values produced by the algorithm. In fact, all the other results are obtained as straightforward corollaries from the results for the weighted case.

Implementasi Algoritma Dijkstra Pada Game Pacman

CCIT Journal ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 170-176
Author(s):  
Anggit Dwi Hartanto ◽  
Aji Surya Mandala ◽  
Dimas Rio P.L. ◽  
Sidiq Aminudin ◽  
Andika Yudirianto
Keyword(s):  
Artificial Intelligence ◽  
Greedy Algorithm ◽  
Dijkstra Algorithm ◽  
Testing Phase ◽  
A Value ◽  
Route Problem ◽  
Starting Point ◽  
The Greedy Algorithm

Pacman is one of the labyrinth-shaped games where this game has used artificial intelligence, artificial intelligence is composed of several algorithms that are inserted in the program and Implementation of the dijkstra algorithm as a method of solving problems that is a minimum route problem on ghost pacman, where ghost plays a role chase player. The dijkstra algorithm uses a principle similar to the greedy algorithm where it starts from the first point and the next point is connected to get to the destination, how to compare numbers starting from the starting point and then see the next node if connected then matches one path with the path). From the results of the testing phase, it was found that the dijkstra algorithm is quite good at solving the minimum route solution to pursue the player, namely by getting a value of 13 according to manual calculations

scholarly journals An Optimized Algorithm and Test Bed for Improvement of Efficiency of ESS and Energy Use

Electronics ◽  
2018 ◽  
Vol 7 (12) ◽  
pp. 388 ◽  
Author(s):  
Seung-Mo Je ◽  
Jun-Ho Huh
Keyword(s):  
Greedy Algorithm ◽  
Energy Use ◽  
Storage System ◽  
Lithium Ion ◽  
Energy Storage System ◽  
Test Bed ◽  
C Language ◽  
Improvement Plan ◽  
The Republic ◽  
The Greedy Algorithm

The Republic of Korea (ROK) has four distinct seasons. Such an environment provides many benefits, but also brings some major problems when using new and renewable energies. The rainy season or typhoons in summer become the main causes of inconsistent production rates of these energies, and this would become a fatal weakness in supplying stable power to the industries running continuously, such as the aquaculture industry. This study proposed an improvement plan for the efficiency of Energy Storage System (ESS) and energy use. Use of sodium-ion batteries is suggested to overcome the disadvantages of lithium-ion batteries, which are dominant in the current market; a greedy algorithm and the Floyd–Warshall algorithm were also proposed as a method of scheduling energy use considering the elements that could affect communication output and energy use. Some significant correlations between communication output and energy efficiency have been identified through the OPNET-based simulations. The simulation results showed that the greedy algorithm was more efficient. This algorithm was then implemented with C-language to apply it to the Test Bed developed in the previous study. The results of the Test Bed experiment supported the proposals.

scholarly journals Enhanced Particle Swarm Optimization for Effective Relay Nodes Deployment in Wireless Sensor Networks

2021 ◽  
Vol 13 (1) ◽  
pp. 53-73
Author(s):  
Bader Alshaqqawi ◽  
Sardar Anisul Haque ◽  
Mohammed Alreshoodi ◽  
Ibrahim Alsukayti
Keyword(s):  
Wireless Sensor Networks ◽  
Particle Swarm Optimization ◽  
Sensor Networks ◽  
Greedy Algorithm ◽  
Pso Algorithm ◽  
Optimization Process ◽  
Wireless Sensor ◽  
Optimization Approach ◽  
Swarm Optimization ◽  
The Greedy Algorithm

One of the critical design problems in Wireless Sensor Networks (WSNs) is the Relay Node Placement (RNP) problem. Inefficient deployment of RNs would have adverse effects on the overall performance and energy efficiency of WSNs. The RNP problem is a typical example of an NP-hard optimization problem which can be addressed using metaheuristics with multi-objective formulation. In this paper, we aimed to provide an efficient optimization approach considering the unconstrained deployment of energy-harvesting RNs into a pre-established stationary WSN. The optimization was carried out for three different objectives: energy consumption, network coverage, and deployment cost. This was approached using a novel optimization approach based on the integration of the Particle Swarm Optimization (PSO) algorithm and a greedy technique. In the optimization process, the greedy algorithm is an essential component to provide effective guidance during PSO convergence. It supports the PSO algorithm with the required information to efficiently alleviate the complexity of the PSO search space and locate RNs in the spots of critical significance. The evaluation of the proposed greedy-based PSO algorithm was carried out with different WSN scenarios of varying complexity levels. A comparison was established with two PSO variants: the classical PSO and a PSO hybridized with the pattern search optimizer. The experimental results demonstrated the significance of the greedy algorithm in enhancing the optimization process for all the considered PSO variants. The results also showed how the solution quality and time efficiency were considerably improved by the proposed optimization approach. Such improvements were achieved using a simple integration technique without adding to the complexity of the system and introducing additional optimization stages. This was more evident in the RNP scenarios of considerably large search spaces, even with highly complex and challenging setups.

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