{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T18:10:17Z","timestamp":1788891017624,"version":"build-2803163510"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T00:00:00Z","timestamp":1752105600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T00:00:00Z","timestamp":1752105600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1007\/s10107-025-02252-x","type":"journal-article","created":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T10:12:14Z","timestamp":1752142334000},"page":"29-59","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On covering Euclidean space with Q-arrangements of cones"],"prefix":"10.1007","volume":"219","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4941-6632","authenticated-orcid":false,"given":"Khalil","family":"Ghorbal","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christelle","family":"Kozaily","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,7,10]]},"reference":[{"key":"2252_CR1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719000","volume-title":"The Linear Complementarity Problem","author":"RW Cottle","year":"2009","unstructured":"Cottle, R.W., Pang, J.S., Stone, R.E.: The Linear Complementarity Problem. Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, United States (2009)"},{"key":"2252_CR2","doi-asserted-by":"publisher","unstructured":"Cottle, R.W., Randow, R., Stone, R.E.: On spherically convex sets and Q-matrices. Linear Algebra and its Applications 41, 73\u201380 (1981) https:\/\/doi.org\/10.1016\/0024-3795(81)90088-4","DOI":"10.1016\/0024-3795(81)90088-4"},{"issue":"1","key":"2252_CR3","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/BF01588247","volume":"17","author":"J-S Pang","year":"1979","unstructured":"Pang, J.-S.: On Q-matrices. Mathematical Programming 17(1), 243\u2013247 (1979). https:\/\/doi.org\/10.1007\/BF01588247","journal-title":"Mathematical Programming"},{"key":"2252_CR4","doi-asserted-by":"publisher","unstructured":"Garcia, C.B., Gould, F.J., Turnbull, T.R.: In: Curtis\u00a0Eaves, B., Gould, F.J., Peitgen, H.-O., Todd, M.J. (eds.) Relations Between PL Maps, Complementary Cones, and Degree in Linear Complementarity Problems, pp. 91\u2013144. Springer, Boston, MA (1983). https:\/\/doi.org\/10.1007\/978-1-4613-3572-6_7","DOI":"10.1007\/978-1-4613-3572-6_7"},{"issue":"4","key":"2252_CR5","doi-asserted-by":"publisher","first-page":"1645","DOI":"10.1137\/22M1517184","volume":"44","author":"M Radons","year":"2023","unstructured":"Radons, M., Tonelli-Cueto, J.: Generalized perron roots and solvability of the absolute value equation. SIAM Journal on Matrix Analysis and Applications 44(4), 1645\u20131666 (2023). https:\/\/doi.org\/10.1137\/22M1517184","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"issue":"1","key":"2252_CR6","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/0024-3795(72)90019-5","volume":"5","author":"KG Murty","year":"1972","unstructured":"Murty, K.G.: On the number of solutions to the complementarity problem and spanning properties of complementary cones. Linear Algebra and its Applications 5(1), 65\u2013108 (1972). https:\/\/doi.org\/10.1016\/0024-3795(72)90019-5","journal-title":"Linear Algebra and its Applications"},{"key":"2252_CR7","doi-asserted-by":"publisher","unstructured":"Samelson, H., Thrall, R.M., Wesler, O.: A partition theorem for Euclidean n-space. In: Proceedings of the American Mathematical Society (1958). https:\/\/doi.org\/10.2307\/2033091","DOI":"10.2307\/2033091"},{"issue":"1","key":"2252_CR8","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/BF01589438","volume":"35","author":"JT Fredricksen","year":"1986","unstructured":"Fredricksen, J.T., Watson, L.T., Murty, K.G.: A finite characterization of K-matrices in dimensions less than four. Mathematical programming 35(1), 17\u201331 (1986). https:\/\/doi.org\/10.1007\/BF01589438","journal-title":"Mathematical programming"},{"key":"2252_CR9","doi-asserted-by":"publisher","unstructured":"Kelly, L.M., Watson, L.T.: Q-matrices and spherical geometry. Linear Algebra and its Applications 25, 175\u2013189 (1979) https:\/\/doi.org\/10.1016\/0024-3795(79)90017-X","DOI":"10.1016\/0024-3795(79)90017-X"},{"key":"2252_CR10","doi-asserted-by":"publisher","unstructured":"Coxson, G.E.: The P-matrix problem is co-np-complete. Mathematical Programming 64, 173\u2013178 (1994) https:\/\/doi.org\/10.1007\/BF01582570","DOI":"10.1007\/BF01582570"},{"key":"2252_CR11","doi-asserted-by":"publisher","unstructured":"Watson, L.T.: A variational approach to the linear complementarity problem. PhD thesis, Dept. of Mathematics, University of Michigan, Ann Arbor, MI (1974). https:\/\/doi.org\/10.7302\/21411","DOI":"10.7302\/21411"},{"key":"2252_CR12","unstructured":"Morris\u00a0Jr, W.D.: Oriented matroids and the linear complementarity problem. Technical report, Cornell University Operations Research and Industrial Engineering (1986). https:\/\/catalog.library.cornell.edu\/catalog\/1325771"},{"key":"2252_CR13","doi-asserted-by":"publisher","unstructured":"Morris\u00a0Jr, W.D.: Counterexamples to Q-matrix conjectures. Linear Algebra and its Applications 111, 135\u2013145 (1988) https:\/\/doi.org\/10.1016\/0024-3795(88)90055-9","DOI":"10.1016\/0024-3795(88)90055-9"},{"key":"2252_CR14","unstructured":"Aganagi\u0107, W., Cottle, R.W.: On Q-matrices. Technical report, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California (1978). SOL 78-9"},{"issue":"2","key":"2252_CR15","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1287\/moor.23.2.463","volume":"23","author":"DQ Naiman","year":"1998","unstructured":"Naiman, D.Q., Stone, R.E.: A homological characterization of Q-matrices. Mathematics of Operations Research 23(2), 463\u2013478 (1998). https:\/\/doi.org\/10.1287\/moor.23.2.463","journal-title":"Mathematics of Operations Research"},{"key":"2252_CR16","doi-asserted-by":"publisher","unstructured":"De\u00a0Loera, J.A., Morris\u00a0Jr., W.D.: Q-matrix recognition via secondary and universal polytopes. Mathematical Programming 85, 259\u2013276 (1999) https:\/\/doi.org\/10.1007\/s101070050057","DOI":"10.1007\/s101070050057"},{"issue":"3","key":"2252_CR17","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/BF00940344","volume":"60","author":"SJ Chung","year":"1989","unstructured":"Chung, S.J.: Np-completeness of the linear complementarity problem. J. Optim. Theory Appl. 60(3), 393\u2013399 (1989). https:\/\/doi.org\/10.1007\/BF00940344","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"2252_CR18","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1137\/070681867","volume":"30","author":"L Brugnano","year":"2008","unstructured":"Brugnano, L., Casulli, V.: Iterative solution of piecewise linear systems. SIAM Journal on Scientific Computing 30(1), 463\u2013472 (2008). https:\/\/doi.org\/10.1137\/070681867","journal-title":"SIAM Journal on Scientific Computing"},{"key":"2252_CR19","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1997","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton Landmarks in Mathematics and Physics. Princeton University Press, NJ, USA (1997)"},{"key":"2252_CR20","doi-asserted-by":"publisher","unstructured":"Cottle, R.W., Randow, R., Stone, R.E.: On spherically convex sets and q-matrices. Linear Algebra and its Applications 41, 73\u201380 (1981) https:\/\/doi.org\/10.1016\/0024-3795(81)90088-4","DOI":"10.1016\/0024-3795(81)90088-4"},{"key":"2252_CR21","doi-asserted-by":"publisher","unstructured":"Goerss, P.G., Jardine, J.F.: Simplicial Homotopy Theory. Progress in Mathematics. Birkh\u00e4user Basel, Basel, Switzerland (2012). https:\/\/doi.org\/10.1007\/978-3-0348-8707-6","DOI":"10.1007\/978-3-0348-8707-6"},{"key":"2252_CR22","volume-title":"Foundations of Convex Geometry","author":"WA Coppel","year":"1998","unstructured":"Coppel, W.A.: Foundations of Convex Geometry. Cambridge University Press, Cambridge, UK (1998)"},{"issue":"1","key":"2252_CR23","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1007\/BF01581653","volume":"19","author":"RW Cottle","year":"1980","unstructured":"Cottle, R.W.: Completely-Q matrices. Mathematical Programming: Series A and B 19(1), 347\u2013351 (1980). https:\/\/doi.org\/10.1007\/BF01581653","journal-title":"Mathematical Programming: Series A and B"},{"key":"2252_CR24","unstructured":"Kozaily, C.: On the existence of solutions for linear complementarity pro- blems. PhD thesis, Dept. of Mathematics, University of Rennes, France (2024). https:\/\/theses.fr\/s216241"},{"key":"2252_CR25","volume-title":"Invitation \u00e0 la Topologie Alg\u00e9brique Tome II: Cohomologie - Vari\u00e9t\u00e9s","author":"A Jeanneret","year":"2014","unstructured":"Jeanneret, A., Lines, D.: Invitation \u00e0 la Topologie Alg\u00e9brique Tome II: Cohomologie - Vari\u00e9t\u00e9s. \u00c9ditions C\u00e9padu\u00e8s, France (2014)"},{"key":"2252_CR26","doi-asserted-by":"publisher","unstructured":"Karamardian, S.: The complementarity problem. Mathematical programming 2, 107\u2013129 (1972) https:\/\/doi.org\/10.1007\/BF01584538","DOI":"10.1007\/BF01584538"},{"issue":"1","key":"2252_CR27","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1007\/BF01582122","volume":"16","author":"M Aganagic","year":"1979","unstructured":"Aganagic, M., Cottle, R.W.: A note on Q-matrices. Mathematical Programming 16(1), 374\u2013377 (1979). https:\/\/doi.org\/10.1007\/BF01582122","journal-title":"Mathematical Programming"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-025-02252-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10107-025-02252-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-025-02252-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T17:50:15Z","timestamp":1788889815000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10107-025-02252-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,10]]},"references-count":27,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2026,9]]}},"alternative-id":["2252"],"URL":"https:\/\/doi.org\/10.1007\/s10107-025-02252-x","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,10]]},"assertion":[{"value":"23 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}