{"ec_funded":1,"oa_version":"Preprint","author":[{"first_name":"Afrouz","full_name":"Jabal Ameli, Afrouz","last_name":"Jabal Ameli"},{"last_name":"Motiei","first_name":"Faezeh","full_name":"Motiei, Faezeh"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"quality_controlled":"1","article_processing_charge":"No","month":"02","external_id":{"arxiv":["2409.11079"]},"title":"On the MST-ratio: Theoretical bounds and complexity of finding the maximum","date_published":"2026-02-14T00:00:00Z","abstract":[{"text":"Given a finite set of red and blue points in R^d, the MST-ratio is defined as the total length of the Euclidean minimum spanning trees of the red points and the blue points, divided by the length of the Euclidean minimum spanning tree of their union. The MST-ratio has recently gained attention due to its direct interpretation in topological models for studying point sets with applications in spatial biology. The maximum MST-ratio of a point set is the maximum MST-ratio over all proper colorings of its points by red and blue. We prove that finding the maximum MST-ratio of a given point set is NP-hard when the dimension is part of the input. Moreover, we present a quadratic-time 3-approximation algorithm for this problem. As part of the proof, we show that in any metric space, the maximum MST-ratio is smaller than 3. Furthermore, we study the average MST-ratio over all colorings of a set of n points. We show that this average is always at least n-2/n-1, and for n random points uniformly distributed in a d-dimensional unit cube, the average tends to (math formular) in expectation as n approaches infinity.","lang":"eng"}],"citation":{"ista":"Jabal Ameli A, Motiei F, Saghafian M. 2026. On the MST-ratio: Theoretical bounds and complexity of finding the maximum. 20th International Conference and Workshops on Algorithms and Computation. WALCOM: International Conference and Workshops on Algorithms and Computation, LNCS, vol. 16444, 386–401.","chicago":"Jabal Ameli, Afrouz, Faezeh Motiei, and Morteza Saghafian. “On the MST-Ratio: Theoretical Bounds and Complexity of Finding the Maximum.” In <i>20th International Conference and Workshops on Algorithms and Computation</i>, 16444:386–401. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/978-981-95-7127-7_26\">https://doi.org/10.1007/978-981-95-7127-7_26</a>.","apa":"Jabal Ameli, A., Motiei, F., &#38; Saghafian, M. (2026). On the MST-ratio: Theoretical bounds and complexity of finding the maximum. In <i>20th International Conference and Workshops on Algorithms and Computation</i> (Vol. 16444, pp. 386–401). Perugia, Italy: Springer Nature. <a href=\"https://doi.org/10.1007/978-981-95-7127-7_26\">https://doi.org/10.1007/978-981-95-7127-7_26</a>","short":"A. Jabal Ameli, F. Motiei, M. Saghafian, in:, 20th International Conference and Workshops on Algorithms and Computation, Springer Nature, 2026, pp. 386–401.","mla":"Jabal Ameli, Afrouz, et al. “On the MST-Ratio: Theoretical Bounds and Complexity of Finding the Maximum.” <i>20th International Conference and Workshops on Algorithms and Computation</i>, vol. 16444, Springer Nature, 2026, pp. 386–401, doi:<a href=\"https://doi.org/10.1007/978-981-95-7127-7_26\">10.1007/978-981-95-7127-7_26</a>.","ama":"Jabal Ameli A, Motiei F, Saghafian M. On the MST-ratio: Theoretical bounds and complexity of finding the maximum. In: <i>20th International Conference and Workshops on Algorithms and Computation</i>. Vol 16444. Springer Nature; 2026:386-401. doi:<a href=\"https://doi.org/10.1007/978-981-95-7127-7_26\">10.1007/978-981-95-7127-7_26</a>","ieee":"A. Jabal Ameli, F. Motiei, and M. Saghafian, “On the MST-ratio: Theoretical bounds and complexity of finding the maximum,” in <i>20th International Conference and Workshops on Algorithms and Computation</i>, Perugia, Italy, 2026, vol. 16444, pp. 386–401."},"OA_type":"green","publication_status":"published","page":"386-401","year":"2026","publication_identifier":{"isbn":["9789819571260"],"eissn":["1611-3349"],"issn":["0302-9743"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"doi":"10.1007/978-981-95-7127-7_26","acknowledgement":"A. J. Ameli—Supported by the project COALESCE (ERC grant no. 853234).\r\nM. Saghafian—Partially supported by the European Research Council (ERC), grant no. 788183, and by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.","publication":"20th International Conference and Workshops on Algorithms and Computation","date_created":"2026-03-08T23:01:45Z","_id":"21410","publisher":"Springer Nature","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2409.11079","open_access":"1"}],"status":"public","volume":16444,"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","call_identifier":"FWF"}],"date_updated":"2026-03-09T10:25:41Z","scopus_import":"1","day":"14","arxiv":1,"OA_place":"repository","conference":{"location":"Perugia, Italy","name":"WALCOM: International Conference and Workshops on Algorithms and Computation","end_date":"2026-03-06","start_date":"2026-03-04"},"oa":1,"alternative_title":["LNCS"],"intvolume":"     16444","type":"conference","department":[{"_id":"HeEd"}]}