scholarly journals CIRCUITS IN GRAPHS THROUGH A PRESCRIBED SET OF ORDERED VERTICES

2010 ◽  
Vol 11 (03n04) ◽  
pp. 121-141
Author(s):  
DAVID COUDERT ◽  
FREDERIC GIROIRE ◽  
IGNASI SAU
Keyword(s):  
Maximum Degree ◽  
Undirected Graph ◽  
Linear Program ◽  
Integer Linear Program ◽  
Simple Circuit

A circuit in a simple undirected graph G = (V, E) is a sequence of vertices {v1, v2, …, vk+1} such that v1 = vk+1 and {vi, vi+1} ∈ E for i = 1, …, k. A circuit C is said to be edge-simple if no edge of G is used twice in C. In this article we study the following problem: which is the largest integer k such that, given any subset of k ordered vertices of a graph G, there exists an edge-simple circuit visiting the k vertices in the prescribed order? We first study the case when G has maximum degree at most 3, establishing the value of k for several subcases, such as when G is planar or 3-vertex-connected. Our main result is that k = 10 in infinite square grids. To prove this, we introduce a methodology based on the notion of core graph, in order to reduce the number of possible vertex configurations, and then we test each one of the resulting configurations with an Integer Linear Program (ILP) solver.

scholarly journals A cost-aggregating integer linear program for motif finding

2011 ◽  
Vol 9 (4) ◽  
pp. 326-334 ◽  
Author(s):  
Carl Kingsford ◽  
Elena Zaslavsky ◽  
Mona Singh
Keyword(s):  
Linear Program ◽  
Integer Linear Program ◽  
Motif Finding

scholarly journals Association rule hiding using integer linear programming

2021 ◽  
Vol 11 (4) ◽  
pp. 3451
Author(s):  
Suma B. ◽  
Shobha G.
Keyword(s):  
Data Mining ◽  
Linear Programming ◽  
Integer Linear Programming ◽  
Association Rule ◽  
Real Life ◽  
Linear Program ◽  
Integer Linear Program ◽  
Optimization Approach ◽  
Integer Linear Program Formulation ◽  
The Impact

<span>Privacy preserving data mining has become the focus of attention of government statistical agencies and database security research community who are concerned with preventing privacy disclosure during data mining. Repositories of large datasets include sensitive rules that need to be concealed from unauthorized access. Hence, association rule hiding emerged as one of the powerful techniques for hiding sensitive knowledge that exists in data before it is published. In this paper, we present a constraint-based optimization approach for hiding a set of sensitive association rules, using a well-structured integer linear program formulation. The proposed approach reduces the database sanitization problem to an instance of the integer linear programming problem. The solution of the integer linear program determines the transactions that need to be sanitized in order to conceal the sensitive rules while minimizing the impact of sanitization on the non-sensitive rules. We also present a heuristic sanitization algorithm that performs hiding by reducing the support or the confidence of the sensitive rules. The results of the experimental evaluation of the proposed approach on real-life datasets indicate the promising performance of the approach in terms of side effects on the original database.</span>

Pitchfork domination in graphs

2020 ◽  
Vol 12 (02) ◽  
pp. 2050025
Author(s):  
Manal N. Al-Harere ◽  
Mohammed A. Abdlhusein
Keyword(s):  
Maximum Degree ◽  
Undirected Graph ◽  
Minimum Degree ◽  
Dominating Set ◽  
Domination Number ◽  
Dominating Sets ◽  
Minimum Cardinality ◽  
New Model ◽  
Domination In Graphs

In this paper, a new model of domination in graphs called the pitchfork domination is introduced. Let [Formula: see text] be a finite, simple and undirected graph without isolated vertices, a subset [Formula: see text] of [Formula: see text] is a pitchfork dominating set if every vertex [Formula: see text] dominates at least [Formula: see text] and at most [Formula: see text] vertices of [Formula: see text], where [Formula: see text] and [Formula: see text] are non-negative integers. The domination number of [Formula: see text], denotes [Formula: see text] is a minimum cardinality over all pitchfork dominating sets in [Formula: see text]. In this work, pitchfork domination when [Formula: see text] and [Formula: see text] is studied. Some bounds on [Formula: see text] related to the order, size, minimum degree, maximum degree of a graph and some properties are given. Pitchfork domination is determined for some known and new modified graphs. Finally, a question has been answered and discussed that; does every finite, simple and undirected graph [Formula: see text] without isolated vertices have a pitchfork domination or not?

scholarly journals MINIMIZAÇÃO DOS CUSTOS DE TRANSPORTES RODOVIÁRIO FLORESTAL COM O USO DA PROGRAMAÇÃO LINEAR E OTIMIZAÇÃO DO PROCESSO

FLORESTA ◽  
2002 ◽  
Vol 32 (1) ◽  
Author(s):  
Pedro Giovani Lacowicz ◽  
Ricardo Berger ◽  
Romano Timofeiczyk Júnior ◽  
João Carlos Garzel Leodoro Da Silva
Keyword(s):  
Cycle Time ◽  
Cost Minimization ◽  
Road Transport ◽  
Linear Program ◽  
Integer Linear Program ◽  
Fixed Cost ◽  
Forest Road ◽  
Time Optimization ◽  
Transport Cycle ◽  
Loading And Unloading

Este trabalho tratou da minimização dos custos do transporte rodoviário florestal, através da programação linear inteira e otimização dos tempos de ciclo de transporte. Após a obtenção dos dados de uma empresa florestal, foram elaborados três cenários, quais sejam: Cenário I: levantamento do quadro atual da empresa, como subsídio comparativo após a racionalização e otimização das etapas que mais consomem tempo do ciclo; Cenário II: realizada em função do uso da programação linear, juntamente com a racionalização dos tempos de fila de espera para carga e descarga; Cenário III: além da programação linear e racionalização dos tempos de espera em fila, utilizou-se, paralelamente, uma otimização do tempo de carga e uma elevação da velocidade de transporte. Os resultados mostraram-se significativos, onde a racionalização e a otimização contribuíram para a redução no número de caminhões e do custo total, traduzindo-se em aumentos na produção dos veículos, na receita bruta e líquida dos freteiros. Cost Minimization of Forest Road Transport by Using the Integer Linear Program and Transport Cycle Time Optimization Abstract This study was about the decreasent of the costs of forest road transport, using the integer linear program and transport cycle time optimization. After obtaining all of the costs, consumed time and the current company picture, a total of three evaluations were done and are described below in settings. Setting I: The current company picture data was calculated as a comparative subsidy following the racionalization and optimization stages that are more time-consuming in the transport cycle. Setting II: This evaluation was done in terms of linear programation use, together with the loading and unloading waiting in line time racionalization. Setting III: In this evaluation, besides the linear programation use and waiting in line time racionalization, it was simultaneously used a time optimization and a foster transport speed. The acquired results were very meaningful, while the racionalization and optimization happened, the trucks rate and total cost successively decreased, resulting in better vehicles performance, and consequently, an increase in the gross and net drivers’ income. Even though there was a costs decrease and an outsiders’ income increase, wich was not enough to pay their total costs, that is, only the variable ones were totally paid and part of the outsiders’ fixed cost.

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