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Bichromatic coloring game on triangulations 关于三角形的双色着色游戏
4区 管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-09-01 DOI: 10.1051/ro/2023162
Naoki Matsumoto
In this paper, we study bichromatic coloring game on a disk triangulation, which is introduced by Aichholzer et al. in 2005. They proved that if a disk triangulation has at most two inner vertices, then the second player can force a tie in the bichromatic coloring game on the disk triangulation. We prove that the same statement holds for any disk triangulation with at most four inner vertices, and that the bound of the number of inner vertices is the best possible. Furthermore, we consider the game on topological triangulations.
本文研究了由Aichholzer等人于2005年提出的圆盘三角剖分上的双色着色游戏。他们证明,如果一个圆盘三角形最多有两个内部顶点,那么第二个玩家可以在圆盘三角形的双色着色游戏中强行打平。我们证明了相同的命题适用于任何至多有四个内顶点的圆盘三角剖分,并且内顶点的数目界是可能的最佳界。进一步,我们考虑了拓扑三角剖分上的博弈。
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引用次数: 0
Reducible 3-critical graphs 可约3临界图
4区 管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-09-01 DOI: 10.1051/ro/2023143
Imran Allie
In this paper, we provide further insights into the reducibility of 3-critical graphs. A graph is 3-critical if it is class two, that is, has chromatic index 4, and the removal of any one edge renders a graph with chromatic index 3. We consider two types of reductions: the suppression of a 2-connected subgraph into a single edge; and the suppression of a 3-connected subgraph into a single vertex. That is, in cases where the 2- or 3-connected subgraph is cubic or strictly subcubic. We show that every cyclically 2-connected 3-critical graph can be reduced to a smaller 3-critical graph using this method. We also prove that every 3-critical graph which is cyclically k -connected with k = 2 or k = 3, contains a 3-critical minor which is cyclically k -connected with k ≥ 4.
在本文中,我们对3临界图的可约性提供了进一步的见解。如果图是第二类,即具有色指数4,则图是3临界的,并且删除任何一条边都会使图具有色指数3。我们考虑两种类型的约简:将2连通子图抑制成一条边;以及将3连通子图压制成单个顶点。也就是说,在2连通或3连通子图是三次或严格次三次的情况下。我们证明了每个循环2连通3临界图都可以用这种方法简化成一个更小的3临界图。我们还证明了每一个与k = 2或k = 3循环k连通的3临界图都包含一个与k≥4循环k连通的3临界次图。
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引用次数: 0
Maximum weight t-sparse set problem on vector-weighted graphs 向量加权图上的最大权t稀疏集问题
4区 管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-09-01 DOI: 10.1051/ro/2023145
Yuquan Lin, Wensong Lin
Let t be a nonnegative integer and G = ( V ( G ), E ( G )) be a graph. For v ∈ V ( G ), let N G ( v ) = { u ∈ V ( G ) { v } : uv ∈ E ( G )}. And for S ⊆ V ( G ), we define d S ( G ; v ) = | N G (v) ∩ S | for v ∈ S and d S ( G ; v ) = −1 for v ∈ V ( G ) S . A subset S ⊆ V ( G ) is called a t -sparse set of G if the maximum degree of the induced subgraph G [ S ] does not exceed t . In particular, a 0-sparse set is precisely an independent set. A vector-weighted graph $ (G,vec{w},t)$ is a graph G with a vector weight function $ vec{w}:V(G)to {mathbb{R}}^{t+2}$, where $ vec{w}(v)=(w(v;-1),w(v;0),dots,w(v;t))$ for each v ∈ V ( G ). The weight of a t -sparse set S in $ (G,vec{w},t)$ is defined as $ vec{w}(S,G)={sum }_v w(v;{d}_S(G;v))$. And a t -sparse set S is a maximum weight t -sparse set of $ (G,vec{w},t)$ if there is no t -sparse set of larger weight in $ (G,vec{w},t)$. In this paper, we propose the maximum weight t -sparse set problem on vector-weighted graphs, which is to find a maximum weight t -sparse set of $ (G,vec{w},t)$. We design a dynamic programming algorithm to find a maximum weight t -sparse set of an outerplane graph $ (G,vec{w},t)$ which takes O (( t + 2) 4 n ) time, where n = | V ( G )|. Moreover, we give a polynomial-time algorithm for this problem on graphs with bounded treewidth.
设t为非负整数,G = (V (G), E (G))为图。对于v∈v (G),设N G (v) = {u∈v (G){ v}: uv∈E (G)}。对于S (G),定义d S (G);v) = | N G (v)∩S | for v∈S and d S (G;对于v∈v (G) S, v) =−1。若引生子图G [S]的最大度不超过t,则称子图S的t -稀疏集G。特别地,0-稀疏集是一个独立集。向量加权图$ (G,vec{w},t)$是具有向量权函数$ vec{w}:V(G)to {mathbb{R}}^{t+2}$的图G,其中$ vec{w}(v)=(w(v;-1),w(v;0),dots,w(v;t))$对于每个v∈v (G)。定义$ (G,vec{w},t)$中t -稀疏集S的权值为$ vec{w}(S,G)={sum }_v w(v;{d}_S(G;v))$。一个t -稀疏集S是一个最大权值t -稀疏集$ (G,vec{w},t)$如果在$ (G,vec{w},t)$中没有更大权值的t -稀疏集。本文提出向量权图上的最大权t -稀疏集问题,即寻找一个最大权t -稀疏集$ (G,vec{w},t)$。我们设计了一种动态规划算法来寻找外平面图$ (G,vec{w},t)$的最大权值t -稀疏集,该算法需要O ((t + 2) 4n)时间,其中n = | V (G)|。此外,我们还给出了树宽有界图的多项式时间算法。
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引用次数: 0
Dislocation hyperbolic augmented Lagrangian algorithm for nonconvex optimization 非凸优化的位错双曲增广拉格朗日算法
4区 管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-09-01 DOI: 10.1051/ro/2023153
Lennin Mallma Ramirez, Nelson Maculan, Adilson Elias Xavier, Vinicius Layter Xavier
The dislocation hyperbolic augmented Lagrangian algorithm (DHALA) solves the nonconvex programming problem considering an update rule for its penalty parameter and considering a condition to ensure the complementarity condition. in this work, we ensure that the sequence generated by DHALA converges to a Karush-Kuhn-Tucker (KKT) point, and we present computational experiments to demonstrate the performance of our proposed algorithm.
位错双曲增广拉格朗日算法(DHALA)考虑了惩罚参数的更新规则和保证互补条件,解决了非凸规划问题。在这项工作中,我们确保由DHALA生成的序列收敛到一个Karush-Kuhn-Tucker (KKT)点,并通过计算实验来证明我们提出的算法的性能。
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引用次数: 0
Sufficient conditions for graphs to have strong parity factors 图具有强宇称因子的充分条件
4区 管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-09-01 DOI: 10.1051/ro/2023147
Sizhong Zhou, Yuli Zhang
A graph G has a strong parity factor F if for every subset X ⊆ V ( G ) with | X | even, G contains a spanning subgraph F such that δ ( F ) ≥ 1, d F ( u ) ≡ 1 (mod 2) for any u ∈ X , and d F ( v ) ≡ 0 (mod 2) for any v ∈ V ( G ) X . In this article, we first provide a size condition for a graph having a strong parity factor. Then we put forward a toughness condition to guarantee that a graph has a strong parity factor.
图G有一个强宇称因子F,如果对每一个子集X V (G)有| × |偶,G包含一个生成子图F,使得δ (F)≥1,对于任意u∈X, F (u)≡1 (mod 2),对于任意V∈V (G) X, F (V)≡0 (mod 2)。在本文中,我们首先提供了具有强奇偶因子的图的大小条件。然后给出了保证图具有强宇称因子的一个韧性条件。
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引用次数: 0
Malmquist index evaluation of countries: 2000-2019 各国马尔姆奎斯特指数评估:2000-2019
IF 1.8 4区 管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-08-08 DOI: 10.1051/ro/2023118
H. Farnoudkia
One of the sophisticated mathematical techniques for evaluating the relative efficiency of decision-making units (DMUs) in a multi-inputs-outputs setting is data envelopment analysis (DEA). A non-parametric productivity index called the Malmquist index (MI) tracks changes in a DMU's overall factor output over time. This study seeks to present a broad overview of the changes in the MI for nearly all of the world's nations over 19 years beginning in 2000. This research evaluates a time series data set made up of 16 economic indexes. Each nation's MI, which compares 2000 and 2019, shows how each nation has changed over that period. One of the most important purposes of this study comparing the countries by their MI is that it allows for a fair comparison of productivity across different time periods and regions. It also provides insights into the sources of productivity growth, such as changes in technology or improvements in efficiency. As a result, the countries can allocate resources more wisely and develop more effective investment plans by understanding the elements that lead to productivity increase. By implementing some statistical techniques, nations are further divided into four categories based on their MI. Furthermore, a yearly distribution of the Malmquist Index (MI) has been included to illustrate its trends between the years 2000 to 2019. Finally, the changing flow for some countries of each category is shown in three-year tracks.
数据包络分析(DEA)是评估多投入产出环境下决策单元(dmu)相对效率的复杂数学技术之一。一种称为Malmquist指数(MI)的非参数生产率指数跟踪了DMU整体要素产出随时间的变化。本研究旨在对自2000年以来的19年中几乎所有国家的MI变化进行全面概述。本研究对由16个经济指标组成的时间序列数据集进行了评价。每个国家的MI比较了2000年和2019年,显示了每个国家在这段时间内的变化。本研究通过MI对各国进行比较的最重要目的之一是,它允许对不同时期和地区的生产率进行公平比较。它还提供了对生产率增长来源的见解,例如技术的变化或效率的提高。因此,各国可以通过了解导致生产率提高的因素,更明智地分配资源,制定更有效的投资计划。通过实施一些统计技术,各国根据其MI进一步分为四类。此外,还包括马姆奎斯特指数(MI)的年度分布,以说明其在2000年至2019年之间的趋势。最后,每个类别的一些国家的流动变化以三年为周期。
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引用次数: 0
Hybrid derivative-free methods for solving system of nonlinear equations 求解非线性方程组的混合无导数方法
IF 1.8 4区 管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-08-07 DOI: 10.1051/ro/2023117
Mohammed Yusuf Waziri, Hadiza Usman Muhammad, Abubakar Sani Halilu, K. Ahmed, Salisu Murtala
This work presents a predictor-corrector iterative approach for solving systems of nonlinear equations. The methods are derivative-free with correction and acceleration parameters obtained via approximating the Jacobian matrix. Using an inexact line search procedure and under appropriate conditions, we proved that the proposed method is globally convergent. We, additionally, present some numerical results to show the efficiency and effectiveness of the proposed method.
这项工作提出了一种求解非线性方程组的预测校正迭代方法。该方法不需要微分,只需要通过逼近雅可比矩阵获得加速度参数和校正参数。在适当的条件下,采用不精确的直线搜索方法,证明了该方法是全局收敛的。此外,我们还给出了一些数值结果来证明该方法的效率和有效性。
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引用次数: 0
The effects of green house gas costs on optimal pricing and production lotsize in an imperfect production system 不完全生产系统中温室气体成本对最优定价和生产规模的影响
IF 1.8 4区 管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-08-01 DOI: 10.1051/ro/2023115
Shib Sankar Sana
The present article deals with an imperfect production system considering costs for greenhouse gas (GHG) to determine the optimal reserve selling price, sales teams' efforts and production lotsize. As per government guidelines, the manufacturer used to adopt green practices in supply chain management to meet the customers’ satisfaction regarding fair prices and quality of the products. In this connection, a mathematical model is formulated and analyzed considering various cost factors and interval values of the key parameters. Finally, numerical illustrations are considered to justify the proposed model.
本文研究了一个考虑温室气体(GHG)成本的不完全生产系统,以确定最优保留销售价格、销售团队的努力和生产批量。根据政府的指导方针,制造商过去在供应链管理中采用绿色实践,以满足客户对公平价格和产品质量的满意。在此基础上,建立了考虑各种成本因素和关键参数区间值的数学模型并进行了分析。最后,通过数值算例验证了所提模型的正确性。
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引用次数: 0
Degree conditions for the existence of a {P2 ,P5}-factor in a graph 图中{P2,P5}因子存在的度条件
IF 1.8 4区 管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-07-31 DOI: 10.1051/ro/2023111
Su Wang, Wei Zhang
A subgraph of a graph $G$ is spanning if the subgraph covers all vertices of $G$. A path-factor of a graph $G$ is a spanning subgraph $H$ of $G$ such that every component of $H$ is a path. In this article, we prove that (romannumeral1) a connected graph $G$ with $delta(G)geq5$ admits a ${P_2,P_5}$-factor if $G$ satisfies $delta(G)>frac{3alpha(G)-1}{4}$; (romannumeral2) a connected graph $G$ of order $n$ with $ngeq7$ has a ${P_2,P_5}$-factor if $G$ satisfies $max{d_G(x),d_G(y)}geqfrac{3n}{7}$ for any two nonadjacent vertices $x$ and $y$ of $G$.
图的子图 $G$ 子图覆盖的所有顶点是生成的吗 $G$. 图的路径因子 $G$ 是生成子图吗$H$ 的 $G$ 这样每一个分量 $H$ 是一条路径。在本文中,我们证明了(romannumeral1)连通图 $G$ 有$delta(G)geq5$ 承认。 ${P_2,P_5}$-因子if $G$ 满足 $delta(G)>frac{3alpha(G)-1}{4}$;(romannumeral2)连通图 $G$有序的 $n$ 有 $ngeq7$ 有一个 ${P_2,P_5}$-因子if $G$ 满足 $max{d_G(x),d_G(y)}geqfrac{3n}{7}$ 对于任意两个不相邻的顶点$x$ 和 $y$ 的 $G$.
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引用次数: 1
The investment and reinsurance game of insurers and reinsurers with default risk under CEV model CEV模型下具有违约风险的保险人与再保险人的投资与再保险博弈
IF 1.8 4区 管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-07-31 DOI: 10.1051/ro/2023112
Wenjing Hao, Zhijian Qiu, Lu Li
On the premise of considering the interests of insurance companies and reinsurance companies at the same time, this paper studies the investment and reinsurance game between them. Suppose that the compensation process faced by an insurance company is described by Brownian motion with drift. Insurance companies can purchase proportional reinsurance from reinsurance companies, and both companies can invest in a risk-free asset, a risky asset whose price process follows the constant elasticity of variance (CEV) model, and a defaultable bond. With the goal of maximizing the expected utility of weighted terminal wealth, the corresponding Hamilton-Jacobi-Bellman (HJB) equations are established and solved by using the principle of dynamic programming, and the analytical expressions of the equilibrium investment-reinsurance strategies of insurers and reinsurers are derived respectively. Finally, the influence of each model parameter on the equilibrium strategy is analyzed by numerical examples.
本文在同时考虑保险公司和再保险公司利益的前提下,对保险公司和再保险公司之间的投资和再保险博弈进行了研究。假设保险公司面临的赔偿过程用带漂移的布朗运动来描述。保险公司可以从再保险公司购买比例再保险,两家公司可以投资无风险资产、价格过程遵循恒定弹性方差(CEV)模型的风险资产和违约债券。以加权终端财富期望效用最大化为目标,利用动态规划原理建立并求解了相应的Hamilton-Jacobi-Bellman (HJB)方程,分别导出了保险公司和再保险公司均衡投资-再保险策略的解析表达式。最后,通过数值算例分析了各模型参数对平衡策略的影响。
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引用次数: 0
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Rairo-Operations Research
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