Journal of Combinatorial Optimization最新文献

{"title":"Approximation algorithm for prize-collecting vertex cover with fairness constraints","authors":"Mingchao Zhou, Zhao Zhang, Ding-Zhu Du","doi":"10.1007/s10878-024-01215-w","DOIUrl":"https://doi.org/10.1007/s10878-024-01215-w","url":null,"abstract":"<p>Considering fairness has become increasingly important in recent research. This paper proposes the prize-collecting vertex cover problem with fairness constraints (FPCVC). In a prize-collecting vertex cover problem, those edges that are not covered incur penalties. By adding fairness concerns into the problem, the vertex set is divided into <i>l</i> groups, the goal is to find a vertex set to minimize the cost-plus-penalty value under the constraints that the profit of edges collected by each group exceeds a coverage requirement. In this paper, we propose a hybrid algorithm (combining deterministic rounding and randomized rounding) for the FPCVC problem which, with probability at least <span>(1-1/l^{alpha })</span>, returns a feasible solution with an objective value at most <span>(left( frac{9(alpha +1)}{2}ln l+3right) )</span> times that of an optimal solution, where <span>(alpha )</span> is a constant. We also show a lower bound of <span>(Omega (ln l))</span> for the approximability of FPCVC. Thus, our approximation ratio is asymptotically best possible. Experiments show that our algorithm performs fairly well empirically.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"225 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142384318","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":"Construction of floorplans for plane graphs over polygonal boundaries","authors":"Rohit Lohani, Krishnendra Shekhawat","doi":"10.1007/s10878-024-01217-8","DOIUrl":"https://doi.org/10.1007/s10878-024-01217-8","url":null,"abstract":"<p>A floorplan (<i>F</i>) is a partition of a polygonal boundary (<i>P</i>) into <i>n</i>-regions satisfying the adjacencies given by an <i>n</i>-vertex graph. Here, it is assumed that the sides of the polygonal boundary are either parallel to the <i>x</i>-axis or <i>y</i>-axis or have slopes <span>(-1)</span> or 1. For a given polygonal boundary <i>P</i> (having <i>m</i> line segments) and a plane triangulated graph <i>G</i>, this paper presents a linear-time algorithm for constructing a floorplan with the required polygonal boundary satisfying all given adjacencies. Further, it has been proved that the number of sides of each region in the obtained floorplan (<i>F</i>) is at most <i>m</i> + 1 (except one region, which can have at most <i>m</i> + 5 sides) for the given polygonal boundary <i>P</i> of length <i>m</i>. </p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"55 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142384366","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":"Matroid-rooted packing of arborescences","authors":"Zoltán Szigeti","doi":"10.1007/s10878-024-01219-6","DOIUrl":"https://doi.org/10.1007/s10878-024-01219-6","url":null,"abstract":"<p>The problem of matroid-based packing of arborescences was introduced and solved in Durand de Gevigney et al. (SIAM J Discret Math 27(1):567-574) . Frank (In personal communication) reformulated the problem in an extended framework. We proved in Fortier et al. (J Graph Theory 93(2):230-252) that the problem of matroid-based packing of spanning arborescences is NP-complete in the extended framework. Here we show a characterization of the existence of a matroid-based packing of spanning arborescences in the original framework. This leads us to the introduction of a new problem on packing of arborescences with a new matroid constraint. We characterize mixed graphs having a matroid-rooted, <i>k</i>-regular, (<i>f</i>, <i>g</i>)-bounded packing of mixed arborescences, that is, a packing of mixed arborescences such that their roots form a basis in a given matroid, each vertex belongs to exactly <i>k</i> of them and each vertex <i>v</i> is the root of least <i>f</i>(<i>v</i>) and at most <i>g</i>(<i>v</i>) of them. We also characterize dypergraphs having a matroid-rooted, <i>k</i>-regular, (<i>f</i>, <i>g</i>)-bounded packing of hyperarborescences.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"46 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142383951","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":"Approximation algorithms for solving the trip-constrained vehicle routing cover problems","authors":"Jianping Li, Ping Yang, Junran Lichen, Pengxiang Pan","doi":"10.1007/s10878-024-01216-9","DOIUrl":"https://doi.org/10.1007/s10878-024-01216-9","url":null,"abstract":"&lt;p&gt;In this paper, we address the trip-constrained vehicle routing cover problem (the TcVRC problem). Specifically, given a metric complete graph &lt;span&gt;(G=(V,E;w))&lt;/span&gt; with a set &lt;i&gt;D&lt;/i&gt; &lt;span&gt;((subseteq V))&lt;/span&gt; of depots, a set &lt;i&gt;J&lt;/i&gt; &lt;span&gt;((=Vbackslash D))&lt;/span&gt; of customer locations, each customer having unsplittable demand 1, and &lt;i&gt;k&lt;/i&gt; vehicles with capacity &lt;i&gt;Q&lt;/i&gt;, it is asked to find a set &lt;span&gt;({mathcal {C}})&lt;/span&gt; &lt;span&gt;(={C_i~|~i=1,2,ldots ,k})&lt;/span&gt; of &lt;i&gt;k&lt;/i&gt; tours for &lt;i&gt;k&lt;/i&gt; vehicles to service all customers, each tour for a vehicle starts and ends at one depot in &lt;i&gt;D&lt;/i&gt; and permits to be replenished at some other depots in &lt;i&gt;D&lt;/i&gt; before continuously servicing at most &lt;i&gt;Q&lt;/i&gt; customers, i.e., the number of customers continuously serviced in per trip of each tour is at most &lt;i&gt;Q&lt;/i&gt; (except the two end-vertices of that trip), where each trip is a path or cycle, starting at a depot and ending at other depot (maybe the same depot) in &lt;i&gt;D&lt;/i&gt;, such that there are no other depots in the interior of that path or cycle, the objective is to minimize the maximum weight of such &lt;i&gt;k&lt;/i&gt; tours in &lt;span&gt;({mathcal {C}})&lt;/span&gt;, i.e., &lt;span&gt;(min _{{mathcal {C}}}max {w(C_i)~|~i=1,2,ldots ,k })&lt;/span&gt;, where &lt;span&gt;(w(C_i))&lt;/span&gt; is the total weight of edges in that tour &lt;span&gt;(C_i)&lt;/span&gt;. Considering &lt;i&gt;k&lt;/i&gt; vehicles whether to have common depot or suppliers, we consider three variations of the TcVRC problem, i.e., (1) the trip-constrained vehicle routing cover problem with multiple suppliers (the TcVRC-MS problem) is asked to find a set &lt;span&gt;({mathcal {C}}={C_i~|~i=1,2,ldots ,k })&lt;/span&gt; of &lt;i&gt;k&lt;/i&gt; tours mentioned-above, the objective is to minimize the maximum weight of such &lt;i&gt;k&lt;/i&gt; tours in &lt;span&gt;({mathcal {C}})&lt;/span&gt;; (2) the trip-constrained vehicle routing cover problem with common depot and multiple suppliers (the TcVRC-CDMS problem) is asked to find a set &lt;span&gt;({mathcal {C}}={C_i~|~i=1,2,ldots ,k })&lt;/span&gt; of &lt;i&gt;k&lt;/i&gt; tours mentioned-above, where each tour starts and ends at same depot &lt;i&gt;v&lt;/i&gt; in &lt;i&gt;D&lt;/i&gt;, each vehicle having its suppliers at some depots in &lt;i&gt;D&lt;/i&gt; (possibly including &lt;i&gt;v&lt;/i&gt;), the objective is to minimize the maximum weight of such &lt;i&gt;k&lt;/i&gt; tours in &lt;span&gt;({mathcal {C}})&lt;/span&gt;; (3) the trip-constrained &lt;i&gt;k&lt;/i&gt;-traveling salesman problem with non-suppliers (the Tc&lt;i&gt;k&lt;/i&gt;TS-NS problem, simply the Tc&lt;i&gt;k&lt;/i&gt;TSP-NS) is asked to find a set &lt;span&gt;({mathcal {C}}={C_i~|~i=1,2,ldots ,k})&lt;/span&gt; of &lt;i&gt;k&lt;/i&gt; tours mentioned-above, where each tour starts and ends at same depot &lt;i&gt;v&lt;/i&gt; in &lt;i&gt;D&lt;/i&gt;, each vehicle having non-suppliers, the objective is to minimize the maximum weight of such &lt;i&gt;k&lt;/i&gt; tours in &lt;span&gt;({mathcal {C}})&lt;/span&gt;. As for the main contributions, we design some approximation algorithms to solve these three aforementioned problems in polynomial time, whose approximation ratios achieve three constants &lt;span&gt;(8-frac{2}{k})&lt;/span&gt;, &lt;span&gt;(frac{7}{2}-frac{1}{k})&lt;/span&gt; and 5, respec","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"4 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142384373","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":"Faster algorithms for evacuation problems in networks with a single sink of small degree and bounded capacitated edges","authors":"Yuya Higashikawa, Naoki Katoh, Junichi Teruyama, Yuki Tokuni","doi":"10.1007/s10878-024-01213-y","DOIUrl":"https://doi.org/10.1007/s10878-024-01213-y","url":null,"abstract":"<p>In this paper, we propose new algorithms for <i>evacuation problems</i> defined on <i>dynamic flow networks</i>. A dynamic flow network is a directed graph in which <i>source</i> nodes are given supplies and a single <i>sink</i> node is given a demand. The evacuation problem seeks a dynamic flow that sends all supplies from sources to the sink such that its demand is satisfied in the minimum feasible time horizon. For this problem, the current best algorithms are developed by Schlöter (2018) and Kamiyama (2019), which run in strongly polynomial time but with high-order polynomial time complexity because they use submodular function minimization as a subroutine. In this paper, we propose new algorithms that do not explicitly execute submodular function minimization, and we prove that they are faster than the current best algorithms when an input network is restricted such that the sink has a small in-degree and every edge has the same capacity.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"52 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142383953","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":"The k-th Roman domination problem is polynomial on interval graphs","authors":"Peng Li","doi":"10.1007/s10878-024-01206-x","DOIUrl":"https://doi.org/10.1007/s10878-024-01206-x","url":null,"abstract":"<p>Let <i>G</i> be some simple graph and <i>k</i> be any positive integer. Take <span>(h: V(G)rightarrow {0,1,ldots ,k+1})</span> and <span>(v in V(G))</span>, let <span>(AN_{h}(v))</span> denote the set of vertices <span>(win N_{G}(v))</span> with <span>(h(w)ge 1)</span>. Let <span>(AN_{h}[v] = AN_{h}(v)cup {v})</span>. The function <i>h</i> is a [<i>k</i>]-Roman dominating function of <i>G</i> if <span>(h(AN_{h}[v]) ge |AN_{h}(v)| + k)</span> holds for any <span>(v in V(G))</span>. The minimum weight of such a function is called the <i>k</i>-th Roman Domination number of <i>G</i>, which is denoted by <span>(gamma _{kR}(G))</span>. In 2020, Banerjee et al. presented linear time algorithms to compute the double Roman domination number on proper interval graphs and block graphs. They posed the open question that whether there is some polynomial time algorithm to solve the double Roman domination problem on interval graphs. It is argued that the interval graph is a nontrivial graph class. In this article, we design a simple dynamic polynomial time algorithm to solve the <i>k</i>-th Roman domination problem on interval graphs for each fixed integer <span>(k&gt;1)</span>.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"224 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142379283","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":"Efficient branch-and-bound algorithms for finding triangle-constrained 2-clubs","authors":"Niels Grüttemeier, Philipp Heinrich Keßler, Christian Komusiewicz, Frank Sommer","doi":"10.1007/s10878-024-01204-z","DOIUrl":"https://doi.org/10.1007/s10878-024-01204-z","url":null,"abstract":"<p>In the <span>Vertex Triangle 2-Club</span> problem, we are given an undirected graph <i>G</i> and aim to find a maximum-vertex subgraph of <i>G</i> that has diameter at most 2 and in which every vertex is contained in at least <span>(ell )</span> triangles in the subgraph. So far, the only algorithm for solving <span>Vertex Triangle 2-Club</span> relies on an ILP formulation (Almeida and Brás in Comput Oper Res 111:258–270, 2019). In this work, we develop a combinatorial branch-and-bound algorithm that, coupled with a set of data reduction rules, outperforms the existing implementation and is able to find optimal solutions on sparse real-world graphs with more than 100,000 vertices in a few minutes. We also extend our algorithm to the <span>Edge Triangle 2-Club</span> problem where the triangle constraint is imposed on all edges of the subgraph.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"70 2 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142276008","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":"Minmax regret 1-sink location problems on dynamic flow path networks with parametric weights","authors":"Tetsuya Fujie, Yuya Higashikawa, Naoki Katoh, Junichi Teruyama, Yuki Tokuni","doi":"10.1007/s10878-024-01199-7","DOIUrl":"https://doi.org/10.1007/s10878-024-01199-7","url":null,"abstract":"<p>This paper addresses the minmax regret 1-sink location problem on a dynamic flow path network with parametric weights. A <i>dynamic flow path network</i> consists of an undirected path with positive edge lengths, positive edge capacities, and nonnegative vertex weights. A path can be considered as a road, an edge length as the distance along the road, and a vertex weight as the number of people at the site. An edge capacity limits the number of people that can enter the edge per unit time. We consider the problem of locating a <i>sink</i> where all the people evacuate quickly. In our model, each weight is represented by a linear function of a common parameter <i>t</i>, and the decision maker who determines the sink location does not know the value of <i>t</i>. We formulate the problem under such uncertainty as the <i>minmax regret problem</i>. Given <i>t</i> and sink location <i>x</i>, the cost is the sum of arrival times at <i>x</i> for all the people determined by <i>t</i>. The regret for <i>x</i> under <i>t</i> is the gap between this cost and the optimal cost under <i>t</i>. The problem is to find the sink location minimizing the maximum regret over all <i>t</i>. For the problem, we propose an <span>(O(n^4 2^{alpha (n)} alpha (n)^2 log n))</span> time algorithm, where <i>n</i> is the number of vertices in the network and <span>(alpha (cdot ))</span> is the inverse Ackermann function. Also, for the special case in which every edge has the same capacity, we show that the complexity can be reduced to <span>(O(n^3 2^{alpha (n)} alpha (n) log n))</span>.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"12 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142084848","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":"Efficient estimation of the modified Gromov–Hausdorff distance between unweighted graphs","authors":"Vladyslav Oles, Nathan Lemons, Alexander Panchenko","doi":"10.1007/s10878-024-01202-1","DOIUrl":"https://doi.org/10.1007/s10878-024-01202-1","url":null,"abstract":"<p>Gromov–Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov–Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov–Hausdorff (mGH) distance, a relaxation of the standard Gromov–Hausdorff (GH) distance with similar topological properties. We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library <span>scikit-tda</span>, and demonstrate its performance on real-world and synthetic networks. The algorithm finds the mGH distances exactly on most graphs with the scale-free property. We use the computed mGH distances to successfully detect outliers in real-world social and computer networks.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"50 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142045389","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":"Meta-heuristic-based hybrid deep learning model for vulnerability detection and prevention in software system","authors":"Lijin Shaji, R. Suji Pramila","doi":"10.1007/s10878-024-01185-z","DOIUrl":"https://doi.org/10.1007/s10878-024-01185-z","url":null,"abstract":"<p>Software vulnerabilities are flaws that may be exploited to cause loss or harm. Various automated machine-learning techniques have been developed in preceding studies to detect software vulnerabilities. This work tries to develop a technique for securing the software on the basis of their vulnerabilities that are already known, by developing a hybrid deep learning model to detect those vulnerabilities. Moreover, certain countermeasures are suggested based on the types of vulnerability to prevent the attack further. For different software projects taken as the dataset, feature fusion is done by utilizing canonical correlation analysis together with Deep Residual Network (DRN). A hybrid deep learning technique trained using AdamW-Rat Swarm Optimizer (AdamW-RSO) is designed to detect software vulnerability. Hybrid deep learning makes use of the Deep Belief Network (DBN) and Generative Adversarial Network (GAN). For every vulnerability, its location of occurrence within the software development procedures and techniques of alleviation via implementation level or design level activities are described. Thus, it helps in understanding the appearance of vulnerabilities, suggesting the use of various countermeasures during the initial phases of software design, and therefore, assures software security. Evaluating the performance of vulnerability detection by the proposed technique regarding recall, precision, and f-measure, it is found to be more effective than the existing methods.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"10 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142013797","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}