Journal of Combinatorial Optimization最新文献

{"title":"The prize-collecting single machine scheduling with bounds and penalties","authors":"Guojun Hu, Pengxiang Pan, Suding Liu, Ping Yang, Runtao Xie","doi":"10.1007/s10878-024-01203-0","DOIUrl":"https://doi.org/10.1007/s10878-024-01203-0","url":null,"abstract":"<p>This study investigates the prize-collecting single machine scheduling with bounds and penalties (PC-SMS-BP). In this problem, a set of <i>n</i> jobs and a single machine are considered, where each job <span>(J_j)</span> has a processing time <span>(p_{j})</span>, a profit <span>(pi _{j})</span> and a rejection penalty <span>(w_{j})</span>. The upper bound on the processing number is <i>U</i>. The objective of this study is to find a feasible schedule that minimizes the makespan of the accepted jobs and the total rejection penalty of the rejected jobs under the condition that the number of the accepted jobs does not exceed a given threshold <i>U</i> while the total profit of the accepted jobs does not fall below a specified profit bound <span>(varPi )</span>. We first demonstrate that this problem is <i>NP</i>-hard. Then, a pseudo-polynomial time dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS) are proposed. Finally, numerical experiments are conducted to compare the effectiveness of the two proposed algorithms.\u0000</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141994521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the complexity of minimum maximal acyclic matchings","authors":"Juhi Chaudhary, Sounaka Mishra, B. S. Panda","doi":"10.1007/s10878-024-01200-3","DOIUrl":"https://doi.org/10.1007/s10878-024-01200-3","url":null,"abstract":"<p><span>Low-Acy-Matching</span> asks to find a maximal matching <i>M</i> in a given graph <i>G</i> of minimum cardinality such that the set of <i>M</i>-saturated vertices induces an acyclic subgraph in <i>G</i>. The decision version of <span>Low-Acy-Matching</span> is known to be <span>({textsf{NP}})</span>-complete. In this paper, we strengthen this result by proving that the decision version of <span>Low-Acy-Matching</span> remains <span>({textsf{NP}})</span>-complete for bipartite graphs with maximum degree 6 and planar perfect elimination bipartite graphs. We also show the hardness difference between <span>Low-Acy-Matching</span> and <span>Max-Acy-Matching</span>. Furthermore, we prove that, even for bipartite graphs, <span>Low-Acy-Matching</span> cannot be approximated within a ratio of <span>(n^{1-epsilon })</span> for any <span>(epsilon &gt;0)</span> unless <span>({textsf{P}}={textsf{NP}})</span>. Finally, we establish that <span>Low-Acy-Matching</span> exhibits <span>(textsf{APX})</span>-hardness when restricted to 4-regular graphs.\u0000</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"190 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141899467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Polynomial algorithms for sparse spanners on subcubic graphs","authors":"R. Gómez, F. K. Miyazawa, Y. Wakababayashi","doi":"10.1007/s10878-024-01197-9","DOIUrl":"https://doi.org/10.1007/s10878-024-01197-9","url":null,"abstract":"<p>Let <i>G</i> be a connected graph and <span>(t ge 1)</span> a (rational) constant. A <i>t</i>-<i>spanner</i> of <i>G</i> is a spanning subgraph of <i>G</i> in which the distance between any pair of vertices is at most <i>t</i> times its distance in <i>G</i>. We address two problems on spanners. The first one, known as the <i>minimum</i> <i>t</i>-<i>spanner problem</i> (<span>MinS</span> <span>(_t)</span>), seeks in a connected graph a <i>t</i>-spanner with the smallest possible number of edges. In the second one, called <i>minimum cost tree</i> <i>t</i>-<i>spanner problem</i> (<span>MCTS</span> <span>(_t)</span>), the input graph has costs assigned to its edges and seeks a <i>t</i>-spanner that is a tree with minimum cost. It is an optimization version of the <i>tree</i> <i>t</i>-<i>spanner problem</i> (<span>TreeS</span> <span>(_t)</span>), a decision problem concerning the existence of a <i>t</i>-spanner that is a tree. <span>MinS</span> <span>(_t)</span> is known to be <span>({textsc {NP}})</span>-hard for every <span>(t ge 2)</span>. On the other hand, <span>TreeS</span> <span>(_t)</span> admits a polynomial-time algorithm for <span>(t le 2)</span> and is <span>({textsc {NP}})</span>-complete for <span>(t ge 4)</span>; but its complexity for <span>(t=3)</span> remains open. We focus on the class of subcubic graphs. First, we show that for such graphs <span>MinS</span> <span>(_3)</span> can be solved in polynomial time. These results yield a practical polynomial algorithm for <span>TreeS</span> <span>(_3)</span> that is of a combinatorial nature. We also show that <span>MCTS</span> <span>(_2)</span> can be solved in polynomial time. To obtain this last result, we prove a complete linear characterization of the polytope defined by the incidence vectors of the tree 2-spanners of a subcubic graph. A recent result showing that <span>MinS</span> <span>(_3)</span> on graphs with maximum degree at most 5 is NP-hard, together with the current result on subcubic graphs, leaves open only the complexity of <span>MinS</span> <span>(_3)</span> on graphs with maximum degree 4.\u0000</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"299 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141899478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximating the probabilistic p-Center problem under pressure","authors":"Marc Demange, Marcel A. Haddad, Cécile Murat","doi":"10.1007/s10878-024-01194-y","DOIUrl":"https://doi.org/10.1007/s10878-024-01194-y","url":null,"abstract":"<p>The Probabilistic <i>p</i>-Center problem under Pressure (<span>Min P</span> <i>p</i> <span>CP</span>) is a variant of the usual <span>Min</span> <i>p</i><span>-Center</span> problem we recently introduced in the context of wildfire management. The problem is to locate <i>p</i> shelters minimizing the maximum distance people will have to cover in case of fire in order to reach the closest accessible shelter. The landscape is divided into zones and is modeled as an edge-weighted graph with vertices corresponding to zones and edges corresponding to direct connections between two adjacent zones. The risk associated with fire outbreaks is modeled using a finite set of fire scenarios. Each scenario corresponds to a fire outbreak on a single zone (i.e., on a vertex) with the main consequence of modifying evacuation paths in two ways. First, an evacuation path cannot pass through the vertex on fire. Second, the fact that someone close to the fire may not take rational decisions when selecting a direction to escape is modeled using new kinds of evacuation paths. In this paper, we characterize the set of feasible solutions of <span>Min P</span> <i>p</i> <span>CP</span>-instance. Then, we propose some approximation results for <span>Min P</span> <i>p</i> <span>CP</span>. These results require approximation results for two variants of the (deterministic) <span>Min</span> <i>p</i><span>-Center</span> problem called <span>Min MAC</span> <i>p</i><span>-Center</span> and <span>Min Partial</span> <i>p</i><span>-Center</span>.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"35 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141899477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Models for two-dimensional bin packing problems with customer order spread","authors":"Mateus Martin, Horacio Hideki Yanasse, Maristela O. Santos, Reinaldo Morabito","doi":"10.1007/s10878-024-01201-2","DOIUrl":"https://doi.org/10.1007/s10878-024-01201-2","url":null,"abstract":"<p>In this paper, we address an extension of the classical two-dimensional bin packing (2BPP) that considers the spread of customer orders (2BPP-OS). The 2BPP-OS addresses a set of rectangular items, required from different customer orders, to be cut from a set of rectangular bins. All the items of a customer order are dispatched together to the next stage of production or distribution after its completion. The objective is to minimize the number of bins used and the spread of customer orders over the cutting process. The 2BPP-OS gains relevance in manufacturing environments that seek minimum waste solutions with satisfactory levels of customer service. We propose integer linear programming (ILP) models for variants of the 2BPP-OS that consider non-guillotine, 2-stage, restricted 3-stage, and unrestricted 3-stage patterns. We are not aware of integrated approaches for the 2BPP-OS in the literature despite its relevance in practical settings. Using a general-purpose ILP solver, the results show that the 2BPP-OS takes more computational effort to solve than the 2BPP, as it has to consider several symmetries that are often disregarded by the traditional 2BPP approaches. The solutions obtained by the proposed approaches have similar bin usage and significantly better metrics of customer satisfaction concerning the approaches that neglect the customer order spread.\u0000</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"52 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141899468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Customer churn prediction using a novel meta-classifier: an investigation on transaction, Telecommunication and customer churn datasets","authors":"Fatemeh Ehsani, Monireh Hosseini","doi":"10.1007/s10878-024-01196-w","DOIUrl":"https://doi.org/10.1007/s10878-024-01196-w","url":null,"abstract":"<p>With the advancement of electronic service platforms, customers exhibit various purchasing behaviors. Given the extensive array of options and minimal exit barriers, customer migration from one digital service to another has become a common challenge for businesses. Customer churn prediction (CCP) emerges as a crucial marketing strategy aimed at estimating the likelihood of customer abandonment. In this paper, we aim to predict customer churn intentions using a novel robust meta-classifier. We utilized three distinct datasets: transaction, telecommunication, and customer churn datasets. Employing Decision Tree, Random Forest, XGBoost, AdaBoost, and Extra Trees as the five base supervised classifiers on these three datasets, we conducted cross-validation and evaluation setups separately. Additionally, we employed permutation and SelectKBest feature selection to rank the most practical features for achieving the highest accuracy. Furthermore, we utilized BayesSearchCV and GridSearchCV to discover, optimize, and tune the hyperparameters. Subsequently, we applied the refined classifiers in a funnel of a new meta-classifier for each dataset individually. The experimental results indicate that our proposed meta-classifier demonstrates superior accuracy compared to conventional classifiers and even stacking ensemble methods. The predictive outcomes serve as a valuable tool for businesses in identifying potential churners and taking proactive measures to retain customers, thereby enhancing customer retention rates and ensuring business sustainability.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"215 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Algorithms for a two-machine no-wait flow shop scheduling problem with two competing agents","authors":"Qi-Xia Yang, Long-Cheng Liu, Min Huang, Tian-Run Wang","doi":"10.1007/s10878-024-01198-8","DOIUrl":"https://doi.org/10.1007/s10878-024-01198-8","url":null,"abstract":"<p>In this paper, we consider the following two-machine no-wait flow shop scheduling problem with two competing agents <span>(F2~|~M_1rightarrow M_2,~ M_2,~ p_{ij}^{A} = p,~ notext{- }wait~|~C_{max }^A:~ C_{max }^B~le Q )</span>: Given a set of <i>n</i> jobs <span>(mathcal {J} = { J_1, J_2, ldots , J_n})</span> and two competing agents <i>A</i> and <i>B</i>. Agent <i>A</i> is associated with a set of <span>(n_A)</span> jobs <span>(mathcal {J}^A = {J_1^A, J_2^A, ldots , J_{n_A}^A})</span> to be processed on the machine <span>(M_1)</span> first and then on the machine <span>(M_2)</span> with no-wait constraint, and agent <i>B</i> is associated with a set of <span>(n_B)</span> jobs <span>(mathcal {J}^B = {J_1^B, J_2^B, ldots , J_{n_B}^B})</span> to be processed on the machine <span>(M_2)</span> only, where the processing times for the jobs of agent <i>A</i> are all the same (i.e., <span>(p_{ij}^A = p)</span>), <span>(mathcal {J} = mathcal {J}^A cup mathcal {J}^B)</span> and <span>(n = n_A + n_B)</span>. The objective is to build a schedule <span>(pi )</span> of the <i>n</i> jobs that minimizing the makespan of agent <i>A</i> while maintaining the makespan of agent <i>B</i> not greater than a given value <i>Q</i>. We first show that the problem is polynomial time solvable in some special cases. For the non-solvable case, we present an <span>(O(n log n))</span>-time <span>((1 + frac{1}{n_A +1}))</span>-approximation algorithm and show that this ratio of <span>((1 + frac{1}{n_A +1}))</span> is asymptotically tight. Finally, <span>((1+epsilon ))</span>-approximation algorithms are provided.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"74 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141857939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"First zagreb spectral radius of unicyclic graphs and trees","authors":"Parikshit Das, Kinkar Chandra Das, Sourav Mondal, Anita Pal","doi":"10.1007/s10878-024-01195-x","DOIUrl":"https://doi.org/10.1007/s10878-024-01195-x","url":null,"abstract":"<p>In light of the successful investigation of the adjacency matrix, a significant amount of its modification is observed employing numerous topological indices. The matrix corresponding to the well-known first Zagreb index is one of them. The entries of the first Zagreb matrix are <span>(d_{u_i}+d_{u_j})</span>, if <span>(u_i)</span> is connected to <span>(u_j)</span>; 0, otherwise, where <span>(d_{u_i})</span> is degree of <i>i</i>-th vertex. The current work is concerned with the mathematical properties and chemical significance of the spectral radius (<span>(rho _1)</span>) associated with this matrix. The lower and upper bounds of <span>(rho _1)</span> are computed with characterizing extremal graphs for the class of unicyclic graphs and trees. The chemical connection of the first Zagreb spectral radius is established by exploring its role as a structural descriptor of molecules. The isomer discrimination ability of <span>(rho _1)</span> is also explained.\u0000</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"45 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141857938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An improved upper bound for the online graph exploration problem on unicyclic graphs","authors":"Koji M. Kobayashi, Ying Li","doi":"10.1007/s10878-024-01192-0","DOIUrl":"https://doi.org/10.1007/s10878-024-01192-0","url":null,"abstract":"<p>The <i>online graph exploration problem</i>, which was proposed by Kalyanasundaram and Pruhs (Theor Comput Sci 130(1):125–138, 1994), is defined as follows: Given an edge-weighted undirected connected graph and a specified vertex (called the <i>origin</i>), the task of an algorithm is to compute a path from the origin to the origin which contains all the vertices of the given graph. The goal of the problem is to find such a path of minimum weight. At each time, an online algorithm knows only the weights of edges each of which consists of visited vertices or vertices adjacent to visited vertices. Fritsch (Inform Process Lett 168:1006096, 2021) showed that the competitive ratio of an online algorithm is at most three for any unicyclic graph. On the other hand, Brandt et al. (Theor Comput Sci 839:176–185, 2020) showed a lower bound of two on the competitive ratio for any unicyclic graph. In this paper, we showed the competitive ratio of an online algorithm is at most 5/2 for any unicyclic graph.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"49 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141836766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Risk-adjusted exponential gradient strategies for online portfolio selection","authors":"Jin’an He, Fangping Peng, Xiuying Xie","doi":"10.1007/s10878-024-01187-x","DOIUrl":"https://doi.org/10.1007/s10878-024-01187-x","url":null,"abstract":"<p>This paper concerns online portfolio selection problem whose main feature is with no any statistical assumption on future asset prices. Since online portfolio selection aims to maximize the cumulative wealth, most existing online portfolio strategies do not consider risk factors into the model. To enrich the research on online portfolio selection, we introduce the risk factors into the model and propose two novel risk-adjusted online portfolio strategies. More specifically, we first choose several <i>exponential</i> <i>gradient</i> (<span>(text {EG}(eta ))</span>) with different values of parameter <span>(eta )</span> to build an expert pool. Later, we construct two risk methods to measure performance of each expert. Finally, we calculate the portfolio by the weighted average over all expert advice. We present theoretical and experimental results respectively to analyze the performance of the proposed strategies. Theoretical results show that the proposed strategies not only track the expert with the lowest risk, but also are universal, i.e., they exhibit the same asymptotic average logarithmic growth rate as <i>best</i> <i>constant</i> <i>rebalanced</i> <i>portfolio</i> (BCRP) determined in hindsight. We conduct extensive experiments by using daily stock data collected from the American and Chinese stock markets. Experimental results show the proposed strategies outperform existing online portfolio in terms of the return and risk metrics in most cases.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"43 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141769094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}