{"title":"Reconfiguration of the Union of Arborescences","authors":"Yusuke Kobayashi, Ryoga Mahara, Tamás Schwarcz","doi":"10.1007/s00453-025-01310-2","DOIUrl":null,"url":null,"abstract":"<div><p>An arborescence in a digraph is an acyclic arc subset in which every vertex except a root has exactly one incoming arc. In this paper, we show the reconfigurability of the union of <i>k</i> arborescences for fixed <i>k</i> in the following sense: for any pair of arc subsets that can be partitioned into <i>k</i> arborescences, one can be transformed into the other by exchanging arcs one by one so that every intermediate arc subset can also be partitioned into <i>k</i> arborescences. This generalizes the result by Ito et al. (2023), who showed the case with <span>\\(k=1\\)</span>. Since the union of <i>k</i> arborescences can be represented as a common matroid basis of two matroids, our result gives a new non-trivial example of matroid pairs for which two common bases are always reconfigurable to each other.</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"87 7","pages":"1040 - 1059"},"PeriodicalIF":0.7000,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algorithmica","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s00453-025-01310-2","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0
Abstract
An arborescence in a digraph is an acyclic arc subset in which every vertex except a root has exactly one incoming arc. In this paper, we show the reconfigurability of the union of k arborescences for fixed k in the following sense: for any pair of arc subsets that can be partitioned into k arborescences, one can be transformed into the other by exchanging arcs one by one so that every intermediate arc subset can also be partitioned into k arborescences. This generalizes the result by Ito et al. (2023), who showed the case with \(k=1\). Since the union of k arborescences can be represented as a common matroid basis of two matroids, our result gives a new non-trivial example of matroid pairs for which two common bases are always reconfigurable to each other.
期刊介绍：
Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential.
Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming.
In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.
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