{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T20:01:18Z","timestamp":1773086478160,"version":"3.50.1"},"publisher-location":"Cham","reference-count":24,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031931116","type":"print"},{"value":"9783031931123","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"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":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-93112-3_27","type":"book-chapter","created":{"date-parts":[[2025,6,10]],"date-time":"2025-06-10T04:56:26Z","timestamp":1749531386000},"page":"371-384","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sparse Approximation in\u00a0Lattices and\u00a0Semigroups"],"prefix":"10.1007","author":[{"given":"Stefan","family":"Kuhlmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Timm","family":"Oertel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Weismantel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,4]]},"reference":[{"issue":"3","key":"27_CR1","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1007\/s11590-022-01927-0","volume":"17","author":"A Alasmari","year":"2023","unstructured":"Alasmari, A., Aliev, I.: On unique recovery of finite-valued integer signals and admissible lattices of sparse hypercubes. Optim. Lett. 17(3), 739\u2013751 (2023)","journal-title":"Optim. Lett."},{"key":"27_CR2","first-page":"05","volume":"192","author":"I Aliev","year":"2021","unstructured":"Aliev, I., Averkov, G., de Loera, J.A., Oertel, T.: Sparse representation of vectors in lattices and semigroups. Math. Program. Seri. B 192, 05 (2021)","journal-title":"Math. Program. Seri. B"},{"key":"27_CR3","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1137\/16M1083876","volume":"1","author":"I Aliev","year":"2017","unstructured":"Aliev, I., De Loera, J.A., Oertel, T., O\u2019Neill, C.: Sparse solutions of linear diophantine equations. SIAM J. Appl. Algebra Geom. 1, 239\u2013253 (2017)","journal-title":"SIAM J. Appl. Algebra Geom."},{"key":"27_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-2969-6","volume-title":"Computing the continuous discretely: Integer-point enumeration in polyhedra","author":"M Beck","year":"2015","unstructured":"Beck, M., Robins, S.: Computing the continuous discretely: Integer-point enumeration in polyhedra, 2nd edn. Undergraduate Texts in Mathematics. Springer, New York, NY (2015)","edition":"2"},{"issue":"2","key":"27_CR5","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1109\/TIT.2005.862083","volume":"52","author":"EJ Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E.J., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theor. 52(2), 489\u2013509 (2006)","journal-title":"IEEE Trans. Inf. Theor."},{"issue":"8","key":"27_CR6","doi-asserted-by":"publisher","first-page":"1207","DOI":"10.1002\/cpa.20124","volume":"59","author":"EJ Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E.J., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207\u20131223 (2006)","journal-title":"Commun. Pure Appl. Math."},{"issue":"12","key":"27_CR7","doi-asserted-by":"publisher","first-page":"4203","DOI":"10.1109\/TIT.2005.858979","volume":"51","author":"EJ Cand\u00e8s","year":"2005","unstructured":"Cand\u00e8s, E.J., Tao, T.: Decoding by linear programming. IEEE Trans. Inf. Theor. 51(12), 4203\u20134215 (2005)","journal-title":"IEEE Trans. Inf. Theor."},{"issue":"6","key":"27_CR8","first-page":"2313","volume":"35","author":"EJ Cand\u00e8s","year":"2007","unstructured":"Cand\u00e8s, E.J., Tao, T.: The Dantzig selector: statistical estimation when p is much larger than n. Ann. Stat. 35(6), 2313\u20132351 (2007)","journal-title":"Ann. Stat."},{"issue":"10","key":"27_CR9","doi-asserted-by":"publisher","first-page":"380","DOI":"10.1080\/00029890.1922.11986179","volume":"29","author":"DR Curtiss","year":"1922","unstructured":"Curtiss, D.R.: On Kellogg\u2019s diophantine problem. Am. Math. Mon. 29(10), 380\u2013387 (1922)","journal-title":"Am. Math. Mon."},{"issue":"1","key":"27_CR10","doi-asserted-by":"publisher","first-page":"161","DOI":"10.2307\/1969503","volume":"51","author":"RP Dilworth","year":"1950","unstructured":"Dilworth, R.P.: A decomposition theorem for partially ordered sets. Ann. Math. 51(1), 161\u2013166 (1950)","journal-title":"Ann. Math."},{"issue":"4","key":"27_CR11","doi-asserted-by":"publisher","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"DL Donoho","year":"2006","unstructured":"Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theor. 52(4), 1289\u20131306 (2006)","journal-title":"IEEE Trans. Inf. Theor."},{"key":"27_CR12","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1016\/j.orl.2005.09.008","volume":"34","author":"F Eisenbrand","year":"2006","unstructured":"Eisenbrand, F., Shmonin, G.: Carath\u00e9odory bounds for integer cones. Oper. Res. Lett. 34, 564\u2013548 (2006)","journal-title":"Oper. Res. Lett."},{"issue":"3","key":"27_CR13","doi-asserted-by":"publisher","first-page":"668","DOI":"10.1016\/j.acha.2016.12.004","volume":"45","author":"A Flinth","year":"2018","unstructured":"Flinth, A., Kutyniok, G.: Promp: a sparse recovery approach to lattice-valued signals. Appl. Comput. Harmon. Anal. 45(3), 668\u2013708 (2018)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"27_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4948-7","volume-title":"A Mathematical Introduction to Compressive Sensing","author":"S Foucart","year":"2013","unstructured":"Foucart, S., Rauhut, H.: A Mathematical Introduction to Compressive Sensing. Springer, Applied and Numerical Harmonic Analysis (2013)"},{"key":"27_CR15","first-page":"31","volume":"340","author":"L Fukshansky","year":"2019","unstructured":"Fukshansky, L., Needell, D., Sudakov, B.: An algebraic perspective on integer sparse recovery. Appl. Math. Comput. 340, 31\u201342 (2019)","journal-title":"Appl. Math. Comput."},{"key":"27_CR16","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/BF01415672","volume":"42","author":"G Galambos","year":"1995","unstructured":"Galambos, G., Woeginger, G.J.: On-line bin packing \u2013 a restricted survey. Math. Methods Oper. Res. 42, 25\u201342 (1995)","journal-title":"Math. Methods Oper. Res."},{"key":"27_CR17","unstructured":"Gruber, P.M., Lekkerkerker, C.G.: Geometry of numbers, North-holland mathematical library. North-Holland Publishing Co., vol. 37 (1987)"},{"issue":"2","key":"27_CR18","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/0167-6377(92)90065-B","volume":"12","author":"R Kohli","year":"1992","unstructured":"Kohli, R., Krishnamurti, R.: A total-value greedy heuristic for the integer knapsack problem. Oper. Res. Lett. 12(2), 65\u201371 (1992)","journal-title":"Oper. Res. Lett."},{"issue":"5","key":"27_CR19","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1134\/S0001434618110305","volume":"104","author":"SV Konyagin","year":"2018","unstructured":"Konyagin, S.V.: On the recovery of an integer vector from linear measurements. Math. Notes 104(5), 859\u2013865 (2018)","journal-title":"Math. Notes"},{"key":"27_CR20","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.jnt.2022.07.005","volume":"242","author":"MB Nathanson","year":"2023","unstructured":"Nathanson, M.B.: Underapproximation by egyptian fractions. J. Number Theor. 242, 208\u2013234 (2023)","journal-title":"J. Number Theor."},{"key":"27_CR21","unstructured":"OEIS Foundation Inc. The On-Line Encyclopedia of Integer Sequences (2024). https:\/\/oeis.org\/A000058"},{"key":"27_CR22","unstructured":"Schrijver, A.: Theory of Linear and Integer Programming. Wiley (1986)"},{"key":"27_CR23","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1007\/s10107-004-0548-1","volume":"102","author":"SS Seiden","year":"2005","unstructured":"Seiden, S.S., Woeginger, G.J.: The two-dimensional cutting stock problem revisited. Math. Program. Seri. A 102, 519\u2013530 (2005)","journal-title":"Math. Program. Seri. A"},{"key":"27_CR24","unstructured":"Soundararajan, K.: Approximating 1 from below using n egyptian fractions. arxiv.org\/abs\/math\/0502247"}],"container-title":["Lecture Notes in Computer Science","Integer Programming and Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-93112-3_27","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T10:53:52Z","timestamp":1760007232000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-93112-3_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031931116","9783031931123"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-93112-3_27","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"4 June 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"IPCO","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Integer Programming and Combinatorial Optimization","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Baltimore, MD","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 June 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13 June 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ipco2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ipco25.cs.jhu.edu\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}