{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:44:24Z","timestamp":1760237064307,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T00:00:00Z","timestamp":1582243200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this contribution, we provide a detailed analysis of the search operation for the Interval Merging Binary Tree (IMBT), an efficient data structure proposed earlier to handle typical anomalies in the transmission of data packets. A framework is provided to decide under which conditions IMBT outperforms other data structures typically used in the field, as a function of the statistical characteristics of the commonly occurring anomalies in the arrival of data packets. We use in the modeling Bernstein theorem, Markov property, Fibonacci sequences, bipartite multi-graphs, and contingency tables.<\/jats:p>","DOI":"10.3390\/e22020245","type":"journal-article","created":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T10:49:16Z","timestamp":1582282156000},"page":"245","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Input Pattern Classification Based on the Markov Property of the IMBT with Related Equations and Contingency Tables"],"prefix":"10.3390","volume":"22","author":[{"given":"Istv\u00e1n","family":"Finta","sequence":"first","affiliation":[{"name":"Nokia, Bell Labs, B\u00f3kay street 36\u201342, H-1083 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S\u00e1ndor","family":"Sz\u00e9n\u00e1si","sequence":"additional","affiliation":[{"name":"Department of Informatics, J. Selye University, Bratislavsk\u00e1 cesta 3322, SK-94501 Kom\u00e1rno, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L\u00f3r\u00e1nt","family":"Farkas","sequence":"additional","affiliation":[{"name":"Nokia, Bell Labs, B\u00f3kay street 36\u201342, H-1083 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,21]]},"reference":[{"key":"ref_1","unstructured":"Cormen, T.H., Leiserson, C.E., Rivest, R.L., and Stein, C. (2009). Introduction to Algorithms, MIT Press and McGraw-Hill. [3rd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/TNET.2002.808407","article-title":"Chord: A Scalable Peer-to-peer Lookup Protocol for Internet Applications","volume":"11","author":"Stoica","year":"2003","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Finta, I., Farkas, L., Sergy\u00e1n, S., and Sz\u00e9n\u00e1si, S. (2017, January 21\u201323). Interval Merging Binary Tree. Proceedings of the ICA3PP 2017, Helsinki, Finland.","DOI":"10.1007\/978-3-319-65482-9_32"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Finta, I., \u00c9lias, G., and Ill\u00e9s, J. (2018, January 21\u201322). Packet Loss and Duplication Handling in Stream Processing Environment. Proceedings of the CINTI 2018, Budapest, Hungary.","DOI":"10.1109\/CINTI.2018.8928195"},{"key":"ref_5","unstructured":"(2019, November 28). STORM\u2014A Distributed Real-Time Computation System. Available online: http:\/\/storm.apache.org\/documentation\/Home.html."},{"key":"ref_6","first-page":"71","article-title":"State-space Analysis of the Interval Merging Binary Tree","volume":"16","author":"Finta","year":"2019","journal-title":"Acta Polytech. Hung."},{"key":"ref_7","unstructured":"Adelson-Velsky, G., and Landis, E. (1962). An algorithm for the organization of information. Doklady Akademii Nauk, Russian Academy of Sciences."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1007\/BF00289509","article-title":"Symmetric binary B-Trees: Data structure and maintenance algorithms","volume":"1","author":"Bayer","year":"1972","journal-title":"Acta Inform."},{"key":"ref_9","unstructured":"Lauritzen, S.L. (2019, November 28). Lectures on Contingency Tables, 2002, Electronic edition, Aalborg University. Available online: http:\/\/www.stats.ox.ac.uk\/~steffen\/papers\/cont.pdf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0963548307008668","article-title":"Enumerating Contingency Tables via Random Permanents","volume":"17","author":"Barvionk","year":"2008","journal-title":"Comb. Probab. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1002\/rsa.20301","article-title":"An approximation algorithm for counting contingency tables","volume":"37","author":"Barvinok","year":"2010","journal-title":"Random Struct. Algorithms"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Chung, K.L. (1960). Markov Chains with Stationary Transition Probabilities, Springer.","DOI":"10.1007\/978-3-642-49686-8"},{"key":"ref_13","unstructured":"Meyn, S.P., and Tweedie, R.L. (2012). Markov Chains and Stochastic Stability, Springer."},{"key":"ref_14","unstructured":"Bernstein, S.N. (1946). Theory of Probabilities."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/S0304-4149(99)00055-1","article-title":"A new weak dependence condition and applications to moment inequalities","volume":"84","author":"Doukhan","year":"1999","journal-title":"Stoch. Process. Their Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1145\/373626.373678","article-title":"Querying Multi-dimensional Data Indexed Using Hilbert Space-Filling Curve","volume":"30","author":"Lawder","year":"2000","journal-title":"ACM Sigmod Rec."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"B\u00f3na, M. (2002). A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory, World Scientific Publishing.","DOI":"10.1142\/4918"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1112\/plms\/s2-17.1.75","article-title":"Asymptotic Equatione in Combinatory Analysis","volume":"2","author":"Hardy","year":"1918","journal-title":"Proc. Lond. Math. Soc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1145\/3828.3835","article-title":"Self-Adjusting Binary Search Trees","volume":"32","author":"Sleator","year":"1985","journal-title":"J. ACM"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/245\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:59:49Z","timestamp":1760173189000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/245"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,21]]},"references-count":19,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["e22020245"],"URL":"https:\/\/doi.org\/10.3390\/e22020245","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,2,21]]}}}