{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:25:31Z","timestamp":1777645531170,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["FI"],"published-print":{"date-parts":[[2021,6,30]]},"abstract":"<jats:p>A set of nonnegative matrices is called primitive if there exists a product of these matrices that is entrywise positive. Motivated by recent results relating synchronizing automata and primitive sets, we study the length of the shortest product of a primitive set having a column or a row with k positive entries, called its k-rendezvous time (k-RT), in the case of sets of matrices having no zero rows and no zero columns. We prove that the k-RT is at most linear w.r.t. the matrix size n for small k, while the problem is still open for synchronizing automata. We provide two upper bounds on the k-RT: the second is an improvement of the first one, although the latter can be written in closed form. We then report numerical results comparing our upper bounds on the k-RT with heuristic approximation methods.<\/jats:p>","DOI":"10.3233\/fi-2021-2043","type":"journal-article","created":{"date-parts":[[2021,7,3]],"date-time":"2021-07-03T04:40:36Z","timestamp":1625287236000},"page":"289-314","source":"Crossref","is-referenced-by-count":0,"title":["A Linear Bound on the k-rendezvous Time for Primitive Sets of NZ Matrices"],"prefix":"10.1177","volume":"180","author":[{"given":"Costanza","family":"Catalano","sequence":"first","affiliation":[{"name":"Department of Economics, Statistics and Research, Banca d\u2019Italia (Central Bank of Italy), Largo Guido Carli 1, 00044 Frascati, Roma, Italy. costanzacatalano@gmail.com"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Umer","family":"Azfar","sequence":"additional","affiliation":[{"name":"ICTEAM, Universit\u00e9 Catholique de Louvain, Avenue Georges Lema\u00eetres 4-6, Louvain-la-Neuve, Belgium. umer.azfar@student.uclouvain.be"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ludovic","family":"Charlier","sequence":"additional","affiliation":[{"name":"ICTEAM, Universit\u00e9 Catholique de Louvain, Avenue Georges Lema\u00eetres 4-6, Louvain-la-Neuve, Belgium. ludovic.charlier@student.uclouvain.be"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rapha\u00ebl M.","family":"Jungers","sequence":"additional","affiliation":[{"name":"ICTEAM, Universit\u00e9 Catholique de Louvain, Avenue Georges Lema\u00eetres 4-6, Louvain-la-Neuve, Belgium. raphael.jungers@uclouvain.be"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","container-title":["Fundamenta Informaticae"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/FI-2021-2043","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:32:29Z","timestamp":1777444349000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/FI-2021-2043"}},"subtitle":[],"editor":[{"given":"Micha\u0142","family":"Skrzypczak","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Piotr","family":"Hofman","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2021,6,30]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.3233\/fi-2021-2043","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,30]]}}}