{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:40:27Z","timestamp":1772296827504,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2015,5,12]],"date-time":"2015-05-12T00:00:00Z","timestamp":1431388800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Dyn Games Appl"],"published-print":{"date-parts":[[2016,9]]},"DOI":"10.1007\/s13235-015-0156-0","type":"journal-article","created":{"date-parts":[[2015,5,11]],"date-time":"2015-05-11T12:20:25Z","timestamp":1431346825000},"page":"263-276","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Dijkstra-Type Algorithm for Dynamic Games"],"prefix":"10.1007","volume":"6","author":[{"given":"Martino","family":"Bardi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan Pablo","family":"Maldonado L\u00f3pez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,5,12]]},"reference":[{"key":"156_CR1","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.tcs.2007.07.008","volume":"386","author":"T Alfaro","year":"2007","unstructured":"Alfaro T, Henzinger T, Kupferman O (2007) Concurrent reachability games. Theor Comput Sci 386:188\u2013217","journal-title":"Theor Comput Sci"},{"key":"156_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4171\/IFB\/312","volume":"16","author":"J Andrews","year":"2014","unstructured":"Andrews J, Vladimirsky A (2014) Deterministic control of randomly-terminated processes. Interfaces Free Bound 16:1\u201340","journal-title":"Interfaces Free Bound"},{"key":"156_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-8176-4755-1","volume-title":"Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations","author":"M Bardi","year":"1997","unstructured":"Bardi M, Capuzzo-Dolcetta I (1997) Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkh\u00e4user Boston Inc, Boston"},{"key":"156_CR4","doi-asserted-by":"crossref","unstructured":"Bardi M, Bottacin S, Falcone M (1995) Convergence of discrete schemes for discontinuous value functions of pursuit-evasion games. In: New trends in dynamic games and applications. Ann. Internat. Soc. Dynam. Games, 3, Birkh\u00e4user Boston, pp 273\u2013304","DOI":"10.1007\/978-1-4612-4274-1_14"},{"key":"156_CR5","doi-asserted-by":"crossref","unstructured":"Bardi M, Falcone M and Soravia P (1994) Fully discrete schemes for the value function of pursuit-evasion games. In: Advances in dynamic games and applications. Ann. Internat. Soc. Dynam. Games, 1, Birkh\u00e4user Boston, pp 89\u2013105","DOI":"10.1007\/978-1-4612-0245-5_5"},{"key":"156_CR6","doi-asserted-by":"crossref","unstructured":"Bardi M, Falcone M, Soravia P (1999) Numerical methods for pursuit-evasion games via viscosity solutions. In: Bardi M, Parthasarathy T, Raghavan e TES (eds) Stochastic and differential games: theory and numerical methods. Ann. Internat. Soc. Dynam. Games, 4. Birkh\u00e4user, Boston, pp 105\u2013175","DOI":"10.1007\/978-1-4612-1592-9_3"},{"key":"156_CR7","doi-asserted-by":"crossref","unstructured":"Bardi M, Soravia P (1991) Approximation of differential games of pursuit-evasion by discrete-time games. In: Differential games-developments in modelling and computation, Lecture Notes in Control and Inform. Sci., 156, Springer, pp 131\u2013143","DOI":"10.1007\/BFb0040234"},{"key":"156_CR8","first-page":"19","volume":"37","author":"M Bardi","year":"1994","unstructured":"Bardi M, Soravia P (1994) A comparison result for Hamilton-Jacobi equations and applications to some differential games lacking controllability. Funkcial Ekvac 37:19\u201343","journal-title":"Funkcial Ekvac"},{"key":"156_CR9","doi-asserted-by":"crossref","first-page":"207","DOI":"10.3934\/cpaa.2013.12.207","volume":"12","author":"M Bardi","year":"2013","unstructured":"Bardi M, Terrone G (2013) On the homogenization of some non-coercive Hamilton-Jacobi-Isaacs equations. Commun Pure Appl Anal 12:207\u2013236","journal-title":"Commun Pure Appl Anal"},{"key":"156_CR10","volume-title":"Dynamic programming and optimal control, 2nd edn, vol II","author":"D Bertsekas","year":"2001","unstructured":"Bertsekas D (2001) Dynamic programming and optimal control, 2nd edn, vol II. Athena Scientific, Boston"},{"key":"156_CR11","doi-asserted-by":"crossref","unstructured":"Bertsekas D (2015) Robust shortest path planning and semicontractive dynamic programming, Report LIDS-2915","DOI":"10.1002\/nav.21697"},{"key":"156_CR12","doi-asserted-by":"crossref","first-page":"A570","DOI":"10.1137\/130907707","volume":"36","author":"S Cacace","year":"2014","unstructured":"Cacace S, Cristiani E, Falcone M (2014) Can local single-pass methods solve any stationary Hamilton-Jacobi equation? SIAM J Sci Comput 36:A570\u2013A587","journal-title":"SIAM J Sci Comput"},{"key":"156_CR13","doi-asserted-by":"crossref","first-page":"A2625","DOI":"10.1137\/110841576","volume":"34","author":"S Cacace","year":"2012","unstructured":"Cacace S, Cristiani E, Falcone M, Picarelli A (2012) A patchy dynamic programming scheme for a class of Hamilton\u2013Jacobi\u2013Bellman equations. SIAM J Sci Comput 34:A2625\u2013A2649","journal-title":"SIAM J Sci Comput"},{"key":"156_CR14","doi-asserted-by":"crossref","unstructured":"Cardaliaguet P, Quincampoix M, Saint-Pierre P (1999) Set-valued numerical analysis for optimal control and differential games. In: Bardi M, Parthasarathy T, Raghavan e TES (eds) Stochastic and differential games: theory and numerical methods. Ann. Internat. Soc. Dynam. Games. Birkh\u00e4user, Boston, pp 177\u2013247","DOI":"10.1007\/978-1-4612-1592-9_4"},{"key":"156_CR15","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s10915-008-9257-x","volume":"39","author":"E Cristiani","year":"2009","unstructured":"Cristiani E (2009) A fast marching method for Hamilton\u2013Jacobi equations modeling monotone front propagations. J Sci Comput 39:189\u2013205","journal-title":"J Sci Comput"},{"key":"156_CR16","doi-asserted-by":"publisher","unstructured":"Cristiani E, Falcone M (2006) A fast marching method for pursuit-evasion games. In: Communications to SIMAI congress 1. doi: 10.1685\/CSC06059","DOI":"10.1685\/CSC06059"},{"key":"156_CR17","doi-asserted-by":"crossref","unstructured":"Cristiani E, Falcone M (2009) Fully-discrete schemes for the value function of pursuit-evasion games with state constraints. In: Advances in dynamic games and their applications, Ann. Internat. Soc. Dynam. Games, 10. Birkh\u00e4user Boston, pp 177\u2013206","DOI":"10.1007\/978-0-8176-4834-3_11"},{"key":"156_CR18","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF01386390","volume":"1","author":"EW Dijkstra","year":"1959","unstructured":"Dijkstra EW (1959) A note on two problems in connection with graphs. Numer Math 1:269\u2013271","journal-title":"Numer Math"},{"key":"156_CR19","volume-title":"Semi-Lagrangian approximations schemes for linear and Hamilton-Jacobi equations","author":"M Falcone","year":"2014","unstructured":"Falcone M, Ferretti R (2014) Semi-Lagrangian approximations schemes for linear and Hamilton-Jacobi equations. SIAM, Philadelphia"},{"key":"156_CR20","first-page":"437","volume":"35","author":"JA Filar","year":"1991","unstructured":"Filar JA, Raghavan TES (1991) Algorithms for stochastic games\u2014A survey. Z Oper Res 35:437\u2013472","journal-title":"Z Oper Res"},{"key":"156_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4054-9","volume-title":"Competitive Markov decision processes","author":"JA Filar","year":"1996","unstructured":"Filar JA, Vrieze OJ (1996) Competitive Markov decision processes. Springer, Berlin"},{"key":"156_CR22","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1145\/28869.28874","volume":"34","author":"ML Fredman","year":"1987","unstructured":"Fredman ML, Tarjan RE (1987) Fibonacci heaps and their uses in improved network optimization algorithms. J Assoc Comput Mach 34:596\u2013615","journal-title":"J Assoc Comput Mach"},{"key":"156_CR23","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/s10957-007-9312-z","volume":"136","author":"L Gr\u00fcne","year":"2008","unstructured":"Gr\u00fcne L, Junge O (2008) Global optimal control of perturbed systems. J Optim Theory Appl 136:411\u2013429","journal-title":"J Optim Theory Appl"},{"key":"156_CR24","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1109\/TAC.2004.835402","volume":"49","author":"HJ Kushner","year":"2004","unstructured":"Kushner HJ (2004) The Gauss-Seidel numerical procedure for Markov stochastic games. IEEE Trans Autom Control 49:1779\u20131784","journal-title":"IEEE Trans Autom Control"},{"key":"156_CR25","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511546877","volume-title":"Planning algorithms","author":"SM LaValle","year":"2006","unstructured":"LaValle SM (2006) Planning algorithms. Cambridge University Press, Cambridge"},{"key":"156_CR26","volume-title":"Max-plus methods for nonlinear control and estimation","author":"WM McEneaney","year":"2006","unstructured":"McEneaney WM (2006) Max-plus methods for nonlinear control and estimation. Birkh\u00e4user Boston Inc, Boston"},{"key":"156_CR27","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/BF00935250","volume":"33","author":"T Parthasarathy","year":"1981","unstructured":"Parthasarathy T, Raghavan TES (1981) An orderfield property for stochastic games when one player controls transition probabilities. J Optim Theory Appl 33:375\u2013392","journal-title":"J Optim Theory Appl"},{"key":"156_CR28","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1007\/s10107-002-0312-3","volume":"95","author":"TES Raghavan","year":"2003","unstructured":"Raghavan TES, Syed Z (2003) A policy-improvement type algorithm for solving zero-sum two-person stochastic games of perfect information. Math Program Ser A 95:513\u2013532","journal-title":"Math Program Ser A"},{"key":"156_CR29","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1073\/pnas.93.4.1591","volume":"93","author":"JA Sethian","year":"1996","unstructured":"Sethian JA (1996) A fast marching level set method for monotonically advancing fronts. Proc Nat Acad Sci USA 93:1591\u20131595","journal-title":"Proc Nat Acad Sci USA"},{"key":"156_CR30","volume-title":"Level set methods and fast marching methods. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science","author":"JA Sethian","year":"1999","unstructured":"Sethian JA (1999) Level set methods and fast marching methods. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, Second edn. Cambridge University Press, Cambridge","edition":"Second"},{"key":"156_CR31","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1137\/S0036142901392742","volume":"41","author":"JA Sethian","year":"2003","unstructured":"Sethian JA, Vladimirsky A (2003) Ordered upwind methods for static Hamilton\u2013Jacobi equations: theory and algorithms. SIAM J Numer Anal 41:325\u2013363","journal-title":"SIAM J Numer Anal"},{"key":"156_CR32","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1073\/pnas.39.10.1095","volume":"39","author":"LS Shapley","year":"1953","unstructured":"Shapley LS (1953) Stochastic games. Proc Nat Acad Sci USA 39:1095\u20131100","journal-title":"Proc Nat Acad Sci USA"},{"key":"156_CR33","volume-title":"A first course on zero-sum repeated games, Math\u00e9matiques & Applications, vol 37","author":"S Sorin","year":"2002","unstructured":"Sorin S (2002) A first course on zero-sum repeated games, Math\u00e9matiques & Applications, vol 37. Springer, Berlin"},{"key":"156_CR34","doi-asserted-by":"crossref","first-page":"1528","DOI":"10.1109\/9.412624","volume":"40","author":"JN Tsitsiklis","year":"1995","unstructured":"Tsitsiklis JN (1995) Efficient algorithms for globally optimal trajectories. IEEE Trans Autom Control 40:1528\u20131538","journal-title":"IEEE Trans Autom Control"},{"key":"156_CR35","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1287\/moor.1080.0321","volume":"33","author":"A Vladimirsky","year":"2008","unstructured":"Vladimirsky A (2008) Label-setting methods for multimode stochastic shortest path problems on graphs. Math Oper Res 33:821\u2013838","journal-title":"Math Oper Res"},{"key":"156_CR36","doi-asserted-by":"crossref","unstructured":"von Lossow M (2007) A min-max version of Dijkstra\u2019s algorithm with application to perturbed optimal control problems. In: Proceedings of the 6th international congress on industrial and applied mathematics (ICIAM07), Proceedings of the applied mathematics and mechanics, vol 7, pp 4130027\u20134130028","DOI":"10.1002\/pamm.200700646"}],"container-title":["Dynamic Games and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-015-0156-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13235-015-0156-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-015-0156-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,7]],"date-time":"2022-05-07T20:21:05Z","timestamp":1651954865000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13235-015-0156-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,12]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,9]]}},"alternative-id":["156"],"URL":"https:\/\/doi.org\/10.1007\/s13235-015-0156-0","relation":{},"ISSN":["2153-0785","2153-0793"],"issn-type":[{"value":"2153-0785","type":"print"},{"value":"2153-0793","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,12]]}}}