Journal of Combinatorial Optimization最新文献

{"title":"A common generalization of budget games and congestion games","authors":"Fuga Kiyosue, Kenjiro Takazawa","doi":"10.1007/s10878-024-01218-7","DOIUrl":"https://doi.org/10.1007/s10878-024-01218-7","url":null,"abstract":"<p>Budget games were introduced by Drees, Riechers, and Skopalik (2014) as a model of noncooperative games arising from resource allocation problems. Budget games have several similarities to congestion games, one of which is that the matroid structure of the strategy space is essential for the existence of a pure Nash equilibrium (PNE). Despite these similarities, however, the theoretical relation between budget games and congestion games has been unclear. In this paper, we provide a common generalization of budget games and congestion games, called generalized budget games (g-budget games, for short), to establish a large class of noncooperative games retaining the nice property of the matroid structure. We show that the model of g-budget games includes weighted congestion games and player-specific congestion games under certain assumptions. We further show that g-budget games also include offset budget games, a generalized model of budget games by Drees, Feldotto, Riechers, and Skopalik (2019). We then prove that every matroid g-budget game has a PNE, which extends the result for budget games. We finally a PNE in a certain class of singleton g-budget games can be computed in a greedy manner.\u0000</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"12 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415784","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":"Algorithmic study on liar’s vertex-edge domination problem","authors":"Debojyoti Bhattacharya, Subhabrata Paul","doi":"10.1007/s10878-024-01208-9","DOIUrl":"https://doi.org/10.1007/s10878-024-01208-9","url":null,"abstract":"<p>Let <span>(G=(V,E))</span> be a graph. For an edge <span>(e=xyin E)</span>, the closed neighbourhood of <i>e</i>, denoted by <span>(N_G[e])</span> or <span>(N_G[xy])</span>, is the set <span>(N_G[x]cup N_G[y])</span>. A vertex set <span>(Lsubseteq V)</span> is liar’s vertex-edge dominating set of a graph <span>(G=(V,E))</span> if for every <span>(e_iin E)</span>, <span>(|N_G[e_i]cap L|ge 2)</span> and for every pair of distinct edges <span>(e_i)</span> and <span>(e_j)</span>, <span>(|(N_G[e_i]cup N_G[e_j])cap L|ge 3)</span>. This paper introduces the notion of liar’s vertex-edge domination which arises naturally from some applications in communication networks. Given a graph <i>G</i>, the <span>Minimum Liar’s Vertex-Edge Domination Problem</span> (<span>MinLVEDP</span>) asks to find a liar’s vertex-edge dominating set of <i>G</i> of minimum cardinality. In this paper, we study this problem from an algorithmic point of view. We show that <span>MinLVEDP</span> can be solved in linear time for trees, whereas the decision version of this problem is NP-complete for general graphs, chordal graphs, and bipartite graphs. We further study approximation algorithms for this problem. We propose two approximation algorithms for <span>MinLVEDP</span> in general graphs and <i>p</i>-claw free graphs. On the negative side, we show that the <span>MinLVEDP</span> cannot be approximated within <span>(frac{1}{2}(frac{1}{8}-epsilon )ln |V|)</span> for any <span>(epsilon &gt;0)</span>, unless <span>(NPsubseteq DTIME(|V|^{O(log (log |V|)}))</span>. Finally, we prove that the <span>MinLVEDP</span> is APX-complete for bounded degree graphs and <i>p</i>-claw-free graphs for <span>(pge 6)</span>.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"60 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415822","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":"W-prize-collecting scheduling problem on parallel machines","authors":"Bo Hou, Tianjiao Guo, Suogang Gao, Guanghua Wang, Weili Wu, Wen Liu","doi":"10.1007/s10878-024-01212-z","DOIUrl":"https://doi.org/10.1007/s10878-024-01212-z","url":null,"abstract":"<p>In this paper, we consider the <i>W</i>-prize-collecting scheduling problem on parallel machines. In this problem, we are given a set of <i>n</i> jobs, a set of <i>m</i> identical parallel machines and a value <i>W</i>. Each job <span>(J_j)</span> has a processing time, a profit and a rejection penalty. Each job is either accepted and processed on one of the machines without preemption, or rejected and paid a rejection penalty. The objective is to minimize the sum of the makespan of accepted jobs and the penalties of rejected jobs, and at the same time the total profit brought by accepted jobs is not less than <i>W</i>. We design a 2-approximation algorithm for the problem based on the greedy method and the list scheduling algorithm.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"9 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415786","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":"Minimizing the maximum lateness for scheduling with release times and job rejection","authors":"Imed Kacem, Hans Kellerer","doi":"10.1007/s10878-024-01205-y","DOIUrl":"https://doi.org/10.1007/s10878-024-01205-y","url":null,"abstract":"<p>We study scheduling problems with release times and rejection costs with the objective function of minimizing the maximum lateness. Our main result is a PTAS for the single machine problem with an upper bound on the rejection costs. This result is extended to parallel, identical machines. The corresponding problem of minimizing the rejection costs with an upper bound on the lateness is also examined. We show how to compute a PTAS for determining an approximation of the Pareto frontier on both objective functions on parallel, identical machines. Moreover, we present an FPTAS with strongly polynomial time for the maximum lateness problem without release times on identical machines when the number of machines is constant. Finally, we extend this FPTAS to the case of unrelated machines.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"17 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415818","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 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}