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Intell.</a> <a href="/?q=in%3A524806" title="Articles in this Issue">340, Article ID 104277, 39 p. (2025)</a>. </div> <div class="abstract">Summary: Local search is a common method for solving combinatorial optimisation problems. We focus on general-purpose local search solvers that accept as input a constraint model &ndash; a declarative description of a problem consisting of a set of decision variables under a set of constraints. Existing approaches typically take as input models written in solver-independent constraint modelling languages like MiniZinc. The <span class="zbmathjax-textsc">Athanor</span> solver we describe herein differs in that it begins from a specification of a problem in the abstract constraint specification language <span class="zbmathjax-textsc">Essence</span>, which allows problems to be described without commitment to low-level modelling decisions through its support for a rich set of abstract types. The advantage of proceeding from <span class="zbmathjax-textsc">Essence</span> is that the structure apparent in a concise, abstract specification of a problem can be exploited to generate high quality neighbourhoods automatically, avoiding the difficult task of identifying that structure in an equivalent constraint model. Based on the twin benefits of neighbourhoods derived from high level types and the scalability derived by searching directly over those types, our empirical results demonstrate strong performance in practice relative to existing solution methods.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68T20" title="MSC2020">68T20</a> </td> <td class="space"> Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C27" title="MSC2020">90C27</a> </td> <td class="space"> Combinatorial optimization </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Alocal+search">local search</a>; <a href="/?q=ut%3Acombinatorial+optimization">combinatorial optimization</a></div> <div class="software"> <h3>Software:</h3><a href="/software/27491">Essence</a>; <a href="/software/24724">CHUFFED</a>; <a href="/software/23883">BPPLIB</a>; <a href="/software/6261">MiniZinc</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">&times;</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07996673" data-ciurl="/ci/07996673" data-biburl="/bibtex/07996673.bib" data-amsurl="/amsrefs/07996673.bib" data-xmlurl="/xml/07996673.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07996673.pdf" title="Zbl 07996673 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.artint.2024.104277" aria-label="DOI for “\textsc{Athanor}: local search over abstract constraint specifications”" title="10.1016/j.artint.2024.104277">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2410.05937"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Hoos, H.; Stützle, T., Stochastic Local Search: Foundations &amp; Applications, 2004, Elsevier</td> </tr><tr> <td>[2]</td> <td class="space">Fernandes, G. A.; de Souza, S. R., A matheuristic approach to the multi-mode resource constrained project scheduling problem, Comput. Ind. Eng., 162, Article 107592 pp., 2021</td> </tr><tr> <td>[3]</td> <td class="space">Arnold, F.; Sörensen, K., Knowledge-guided local search for the vehicle routing problem, Comput. Oper. Res., 105, 32-46, 2019 &middot; <a href="/1458.90056" class="nowrap">Zbl 1458.90056</a></td> </tr><tr> <td>[4]</td> <td class="space">Ceschia, S.; Guido, R.; Schaerf, A., Solving the static INRC-II nurse rostering problem by simulated annealing based on large neighborhoods, Ann. Oper. Res., 288, 1, 95-113, 2020</td> </tr><tr> <td>[5]</td> <td class="space">Nethercote, N.; Stuckey, P. J.; Becket, R.; Brand, S.; Duck, G. J.; Tack, G., MiniZinc: towards a standard CP modelling language, (Proceedings of the International Conference on the Principles and Practice of Constraint Programming. Proceedings of the International Conference on the Principles and Practice of Constraint Programming, LNCS, vol. 4741, 2007, Springer), 529-543</td> </tr><tr> <td>[6]</td> <td class="space">Akgün, O.; Gent, I. P.; Jefferson, C.; Miguel, I.; Nightingale, P.; Salamon, A.; Spracklen, P., A framework for constraint based local search using Essence, (IJCAI, 2018), 1242-1248</td> </tr><tr> <td>[7]</td> <td class="space">Attieh, S.; Dang, N.; Jefferson, C.; Miguel, I.; Nightingale, P., Athanor: high-level local search over abstract constraint specifications in Essence, (Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence (IJCAI-19), 2019)</td> </tr><tr> <td>[8]</td> <td class="space">Frisch, A. M.; Grum, M.; Jefferson, C.; Hernández, B. M.; Miguel, I., The Essence of Essence, (Modelling and Reformulating Constraint Satisfaction Problems, 2005), 73-88</td> </tr><tr> <td>[9]</td> <td class="space">Frisch, A. M.; Grum, M.; Jefferson, C.; Hernández, B. M.; Miguel, I., The design of Essence: a constraint language for specifying combinatorial problems, (IJCAI, 2007), 80-87</td> </tr><tr> <td>[10]</td> <td class="space">Frisch, A. M.; Harvey, W.; Jefferson, C.; Martínez-Hernández, B.; Miguel, I., Essence: a constraint language for specifying combinatorial problems, Constraints, 13, 3, 268-306, 2008 &middot; <a href="/1147.68424" class="nowrap">Zbl 1147.68424</a></td> </tr><tr> <td>[11]</td> <td class="space">Smith, B. M., Symmetry and search in a network design problem, (International Conference on Integration of Artificial Intelligence. International Conference on Integration of Artificial Intelligence, (AI) and Operations Research (OR) Techniques in Constraint Programming, 2005, Springer), 336-350 &middot; <a href="/1133.68436" class="nowrap">Zbl 1133.68436</a></td> </tr><tr> <td>[12]</td> <td class="space">Sörensen, K.; Sevaux, M.; Schittekat, P., Multiple neighbourhood search in commercial VRP packages: evolving towards self-adaptive methods, (Adaptive and Multilevel Metaheuristics, 2008), 239-253</td> </tr><tr> <td>[13]</td> <td class="space">Akgün, O.; Frisch, A. M.; Gent, I. P.; Jefferson, C.; Miguel, I.; Nightingale, P., Conjure: automatic generation of constraint models from problem specifications, Artif. Intell., 310, Article 103751 pp., 2022 &middot; <a href="/07570882" class="nowrap">Zbl 07570882</a></td> </tr><tr> <td>[14]</td> <td class="space">Michel, L.; Hentenryck, P. V., Localizer, Constraints, 5, 43-84, 2000 &middot; <a href="/0988.90015" class="nowrap">Zbl 0988.90015</a></td> </tr><tr> <td>[15]</td> <td class="space">Voudouris, C.; Dorne, R.; Lesaint, D.; Liret, A., iOpt: a software toolkit for heuristic search methods, (Principles and Practice of Constraint Programming, 2001, Springer), 716-729 &middot; <a href="/1067.68681" class="nowrap">Zbl 1067.68681</a></td> </tr><tr> <td>[16]</td> <td class="space">Hentenryck, P. V.; Michel, L., Constraint-Based Local Search, 2009, The MIT Press</td> </tr><tr> <td>[17]</td> <td class="space">Michel, L.; Van Hentenryck, P., Constraint-Based Local Search, 223-260, 2018</td> </tr><tr> <td>[18]</td> <td class="space">Van Hentenryck, P.; Michel, L., Synthesis of constraint-based local search algorithms from high-level models, (AAAI, 2007, AAAI Press), 273-278</td> </tr><tr> <td>[19]</td> <td class="space">Newton, M. H.; Pham, D. N.; Sattar, A.; Maher, M., Kangaroo: an efficient constraint-based local search system using lazy propagation, (Principles and Practice of Constraint Programming, 2011, Springer), 645-659</td> </tr><tr> <td>[20]</td> <td class="space">De Landtsheer, R.; Ponsard, C., OscaR.cbls: an open source framework for constraint-based local search, (Proceedings of ORBEL 27, 2013)</td> </tr><tr> <td>[21]</td> <td class="space">Björdal, G.; Monette, J.-N.; Flener, P.; Pearson, J., A constraint-based local search backend for MiniZinc, Constraints, 20, 3, 325-345, 2015 &middot; <a href="/1325.90076" class="nowrap">Zbl 1325.90076</a></td> </tr><tr> <td>[22]</td> <td class="space">Björdal, G., From declarative models to local search, 2021, Acta Universitatis Upsaliensis, Ph.D. thesis</td> </tr><tr> <td>[23]</td> <td class="space">Björdal, G.; Flener, P.; Pearson, J.; Stuckey, P. J.; Tack, G., Declarative local-search neighbourhoods in MiniZinc, (Alamaniotis, M.; Lagniez, J.-M.; Lallouet, A., 2018 IEEE 30th International Conference on Tools with Artificial Intelligence (ICTAI), 2018, IEEE Computer Society), 98-105</td> </tr><tr> <td>[24]</td> <td class="space">Benoist, T.; Estellon, B.; Gardi, F.; Megel, R.; Nouioua, K., Localsolver 1.x: a black-box local-search solver for 0-1 programming, 4OR, 9, 3, 299-316, 2011 &middot; <a href="/1231.90318" class="nowrap">Zbl 1231.90318</a></td> </tr><tr> <td>[25]</td> <td class="space">Nightingale, P.; Akgün, O.; Gent, I. P.; Jefferson, C.; Miguel, I.; Spracklen, P., Automatically improving constraint models in Savile row, Artif. Intell., 251, 35-61, 2017 &middot; <a href="/1419.68099" class="nowrap">Zbl 1419.68099</a></td> </tr><tr> <td>[26]</td> <td class="space">Gent, I. P.; Jefferson, C.; Miguel, I., Minion: a fast scalable constraint solver, (ECAI, vol. 141, 2006), 98-102</td> </tr><tr> <td>[27]</td> <td class="space">Pham, Q. D.; Deville, Y.; Van Hentenryck LS, P., (Graph): a constraint-based local search for constraint optimization on trees and paths, Constraints, 17, 357-408, 2012 &middot; <a href="/1309.90089" class="nowrap">Zbl 1309.90089</a></td> </tr><tr> <td>[28]</td> <td class="space">Ågren, M.; Flener, P.; Pearson, J., Set variables and local search, (Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 2005, Springer), 19-33 &middot; <a href="/1133.68424" class="nowrap">Zbl 1133.68424</a></td> </tr><tr> <td>[29]</td> <td class="space">Björdal, G., String Variables for Constraint-Based Local Search, 2016</td> </tr><tr> <td>[30]</td> <td class="space">Shaw, P., Using constraint programming and local search methods to solve vehicle routing problems, (Proceedings of the International Conference on the Principles and Practice of Constraint Programming. Proceedings of the International Conference on the Principles and Practice of Constraint Programming, LNCS, vol. 1520, 1998, Springer), 417-431</td> </tr><tr> <td>[31]</td> <td class="space">Perron, L.; Shaw, P.; Furnon, V., Propagation guided large neighborhood search, (Proceedings of the International Conference on the Principles and Practice of Constraint Programming. Proceedings of the International Conference on the Principles and Practice of Constraint Programming, LNCS, vol. 3258, 2004, Springer), 468-481 &middot; <a href="/1152.68572" class="nowrap">Zbl 1152.68572</a></td> </tr><tr> <td>[32]</td> <td class="space">Prud&rsquo;homme, C.; Lorca, X.; Jussien, N., Explanation-based large neighborhood search, Constraints, 19, 4, 339-379, 2014 &middot; <a href="/1316.90048" class="nowrap">Zbl 1316.90048</a></td> </tr><tr> <td>[33]</td> <td class="space">Michel, L.; Hentenryck, P. V., Constraint-Based Local Search, 223-260, 2018, Springer International Publishing: Springer International Publishing Cham</td> </tr><tr> <td>[34]</td> <td class="space">Frisch, A. M.; Stuckey, P. J., The proper treatment of undefinedness in constraint languages, (Proceedings of the International Conference on the Principles and Practice of Constraint Programming, 2009), 367-382</td> </tr><tr> <td>[35]</td> <td class="space">Lourenço, H. R.; Martin, O. C.; Stützle, T., Iterated local search: framework and applications, (Handbook of Metaheuristics, 2019, Springer), 129-168</td> </tr><tr> <td>[36]</td> <td class="space">Miguel, I.; Hnich, B.; Gent, I.; Walsh, I.; Jefferson, C.; Akgün, O., CSPLib: a problem library for constraints, available from, 2000</td> </tr><tr> <td>[37]</td> <td class="space">Berry, D. A.; Fristedt, B., Bandit Problems: Sequential Allocation of Experiments, Monographs on Statistics and Applied Probability, vol. 5 (71-87), 7, 1985, Chapman and Hall: Chapman and Hall London &middot; <a href="/0659.62086" class="nowrap">Zbl 0659.62086</a></td> </tr><tr> <td>[38]</td> <td class="space">Agrawal, R., Sample mean based index policies by o (log n) regret for the multi-armed bandit problem, Adv. Appl. Probab., 27, 4, 1054-1078, 1995 &middot; <a href="/0840.90129" class="nowrap">Zbl 0840.90129</a></td> </tr><tr> <td>[39]</td> <td class="space">Prud&rsquo;homme, C.; Fages, J.-G., Choco-solver: a java library for constraint programming, J. Open Sour. Softw., 7, 78, 4708, 2022</td> </tr><tr> <td>[40]</td> <td class="space">Chu, G.; Stuckey, P.; Schutt, A.; Ehlers, T.; Gange, G.; Francis, K., Chuffed: a lazy clause generation solver</td> </tr><tr> <td>[41]</td> <td class="space">Trick, M. A., A dynamic programming approach for consistency and propagation for knapsack constraints, Ann. Oper. Res., 118, 1, 73-84, 2003 &middot; <a href="/1027.90075" class="nowrap">Zbl 1027.90075</a></td> </tr><tr> <td>[42]</td> <td class="space">Shaw, P., A constraint for bin packing, (Proceedings of the International Conference on the Principles and Practice of Constraint Programming, 2004, Springer), 648-662 &middot; <a href="/1152.68586" class="nowrap">Zbl 1152.68586</a></td> </tr><tr> <td>[43]</td> <td class="space">Régin, J.-C.; Rezgui, M., Discussion about constraint programming bin packing models, (Workshops at the Twenty-Fifth AAAI Conference on Artificial Intelligence, 2011)</td> </tr><tr> <td>[44]</td> <td class="space">Falkenauer, E., A hybrid grouping genetic algorithm for bin packing, J. Heuristics, 2, 5-30, 1996</td> </tr><tr> <td>[45]</td> <td class="space">Beasley, J. E., OR-Library: distributing test problems by electronic mail, J. Oper. Res. Soc., 41, 1069-1072, 1990</td> </tr><tr> <td>[46]</td> <td class="space">Flood, M. M., The traveling-salesman problem, Oper. Res., 4, 1, 61-75, 1956 &middot; <a href="/1414.90304" class="nowrap">Zbl 1414.90304</a></td> </tr><tr> <td>[47]</td> <td class="space">Reinelt, G., TSPLIB95, 1995, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR): Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR) Heidelberg, 338</td> </tr><tr> <td>[48]</td> <td class="space">Toth, P.; Vigo, D., The Vehicle Routing Problem, 2002, SIAM &middot; <a href="/0979.00026" class="nowrap">Zbl 0979.00026</a></td> </tr><tr> <td>[49]</td> <td class="space">Mendoza, J. E.; Guéret, C.; Hoskins, M.; Lobit, H.; Pillac, V.; Vidal, T.; Vigo, D., VRP-REP: the vehicle routing community repository, (Third Meeting of the EURO Working Group on Vehicle Routing and Logistics Optimization (VeRoLog). Third Meeting of the EURO Working Group on Vehicle Routing and Logistics Optimization (VeRoLog), Oslo, Norway, 2014)</td> </tr><tr> <td>[50]</td> <td class="space">Pisinger, D., Where are the hard knapsack problems?, Comput. Oper. Res., 32, 9, 2271-2284, 2005 &middot; <a href="/1116.90089" class="nowrap">Zbl 1116.90089</a></td> </tr><tr> <td>[51]</td> <td class="space">Papadimitriou, I.; Georgiadis, L., Minimum-energy broadcasting in multi-hop wireless networks using a single broadcast tree, Mob. Netw. Appl., 11, 361-375, 2006</td> </tr><tr> <td>[52]</td> <td class="space">Burke, D. A.; Brown, K. N., CSPLib problem 048: minimum energy broadcast (MEB)</td> </tr><tr> <td>[53]</td> <td class="space">López-Ibáñez, M.; Dubois-Lacoste, J.; Cáceres, L. P.; Birattari, M.; Stützle, T., The irace package: iterated racing for automatic algorithm configuration, Oper. Res. Perspect., 3, 43-58, 2016</td> </tr><tr> <td>[54]</td> <td class="space">Smith, B. M.; Brailsford, S. C.; Hubbard, P. M.; Williams, H. P., The progressive party problem: integer linear programming and constraint programming compared, Constraints, 1, 1, 119-138, 1996</td> </tr><tr> <td>[55]</td> <td class="space">Walsh, T., CSPLib problem 013: progressive party problem</td> </tr><tr> <td>[56]</td> <td class="space">Leo, K.; Mears, C.; Tack, G.; de la Banda, M. Garcia, Globalizing constraint models, Artif. Intell., 302, Article 103599 pp., 2022</td> </tr><tr> <td>[57]</td> <td class="space">Nightingale, P., CSPLib problem 056: synchronous optical networking (SONET) problem</td> </tr><tr> <td>[58]</td> <td class="space">Sherali, H. D.; Smith, J. C.; Lee, Y., Enhanced model representations for an intra-ring synchronous optical network design problem allowing demand splitting, INFORMS J. Comput., 12, 284-298, 2000 &middot; <a href="/1238.90107" class="nowrap">Zbl 1238.90107</a></td> </tr><tr> <td>[59]</td> <td class="space">Roussel, O., Controlling a solver execution with the runsolver tool, J. Satisf. Boolean Model. Comput., 7, 4, 139-144, 2011 &middot; <a href="/1331.68210" class="nowrap">Zbl 1331.68210</a></td> </tr><tr> <td>[60]</td> <td class="space">Croes, G. A., A method for solving traveling-salesman problems, Oper. Res., 6, 6, 791-812, 1958 &middot; <a href="/1414.90303" class="nowrap">Zbl 1414.90303</a></td> </tr><tr> <td>[61]</td> <td class="space">De Landtsheer, R.; Guyot, Y.; Ospina, G.; Germeau, F.; Ponsard, C., Reasoning on sequences in constraint-based local search frameworks, (Proceedings of the 15th International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2018), 2018), 117-134 &middot; <a href="/1508.68325" class="nowrap">Zbl 1508.68325</a></td> </tr><tr> <td>[62]</td> <td class="space">Schwerin, P.; Wäscher, G., The bin-packing problem: a problem generator and some numerical experiments with FFD packing and MTP, Int. Trans. Oper. Res., 4, 5-6, 377-389, 1997 &middot; <a href="/0906.90151" class="nowrap">Zbl 0906.90151</a></td> </tr><tr> <td>[63]</td> <td class="space">Delorme, M.; Iori, M.; Martello, S., BPPLIB: a library for bin packing and cutting stock problems, Optim. Lett., 12, 235-250, 2018 &middot; <a href="/1401.90183" class="nowrap">Zbl 1401.90183</a></td> </tr><tr> <td>[64]</td> <td class="space">Katriel, I.; Sellmann, M.; Upfal, E.; Van Hentenryck, P., Propagating knapsack constraints in sublinear time, (Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence (AAAI-07), 2007)</td> </tr><tr> <td>[65]</td> <td class="space">Caseau, Y.; Laburthe, F., Solving small TSPs with constraints, (Logic Programming. Logic Programming, Leuven, Belgium. Logic Programming. Logic Programming, Leuven, Belgium, Proceedings of the Fourteenth International Conference on Logic Programming, July 8-11, 1997, 1997), 316-330</td> </tr><tr> <td>[66]</td> <td class="space">Mısır, M.; Verbeeck, K.; De Causmaecker, P.; Vanden Berghe, G., An intelligent hyper-heuristic framework for chesc 2011, (International Conference on Learning and Intelligent Optimization, 2012, Springer), 461-466</td> </tr><tr> <td>[67]</td> <td class="space">Kheiri, A.; Keedwell, E., A sequence-based selection hyper-heuristic utilising a hidden Markov model, (Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, 2015), 417-424</td> </tr><tr> <td>[68]</td> <td class="space">Yi, W.; Qu, R.; Jiao, L.; Niu, B., Automated design of metaheuristics using reinforcement learning within a novel general search framework, IEEE Trans. Evol. Comput., 2022</td> </tr><tr> <td>[69]</td> <td class="space">Speck, D.; Biedenkapp, A.; Hutter, F.; Mattmüller, R.; Lindauer, M., Learning heuristic selection with dynamic algorithm configuration, (Proceedings of the International Conference on Automated Planning and Scheduling, vol. 31, 2021), 597-605</td> </tr><tr> <td>[70]</td> <td class="space">Stützle, T.; López-Ibáñez, M., Automated design of metaheuristic algorithms, (Handbook of Metaheuristics, 2019), 541-579</td> </tr><tr> <td>[71]</td> <td class="space">Biedenkapp, A.; Bozkurt, H. F.; Eimer, T.; Hutter, F.; Lindauer, M., Dynamic algorithm configuration: foundation of a new meta-algorithmic framework, (ECAI 2020, 2020, IOS Press), 427-434</td> </tr><tr> <td>[72]</td> <td class="space">Adriaensen, S.; Biedenkapp, A.; Shala, G.; Awad, N.; Eimer, T.; Lindauer, M.; Hutter, F., Automated dynamic algorithm configuration, J. Artif. Intell. Res., 75, 1633-1699, 2022 &middot; <a href="/1543.68428" class="nowrap">Zbl 1543.68428</a></td> </tr><tr> <td>[73]</td> <td class="space">Preneel, B., Hash Functions, 543-553, 2011, Springer US: Springer US Boston, MA</td> </tr><tr> <td>[74]</td> <td class="space">Appleby, A., Murmurhash3, 2016, available from</td> </tr><tr> <td>[75]</td> <td class="space">Clarke, D.; Devadas, S.; van Dijk, M.; Gassend, B.; Suh, G. E., Incremental multiset hash functions and their application to memory integrity checking, (Laih, C.-S., Advances in Cryptology - ASIACRYPT 2003, 2003, Springer: Springer Berlin Heidelberg, Berlin, Heidelberg), 188-207 &middot; <a href="/1205.94079" class="nowrap">Zbl 1205.94079</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH&nbsp;Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> &copy; 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms &amp; Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none">&nbsp;<span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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