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Star-topology decoupled state space search. (English) Zbl 1444.68172
Summary: State space search is a basic method for analyzing reachability in discrete transition systems. To tackle large compactly described transition systems – the state space explosion – a wealth of techniques (e.g., partial-order reduction) have been developed that reduce the search space without affecting the existence of (optimal) solution paths. Focusing on classical AI planning, where the compact description is in terms of a vector of state variables, an initial state, a goal condition, and a set of actions, we add another technique, that we baptize star-topology decoupling, into this arsenal. A star topology partitions the state variables into components so that a single center component directly interacts with several leaf components, but the leaves interact only via the center. Many applications explicitly come with such structure; any classical planning task can be viewed in this way by selecting the center as a subset of state variables separating connected leaf components.
Our key observation is that, given such a star topology, the leaves are conditionally independent given the center, in the sense that, given a fixed path of transitions by the center, the possible center-compliant paths are independent across the leaves. Our decoupled search hence branches over center transitions only, and maintains the center-compliant paths for each leaf separately. As we show, this method has exponential separations to all previous search reduction techniques, i.e., examples where it results in exponentially less effort. One can, in principle, prune duplicates in a way so that the decoupled state space can never be larger than the original one. Standard search algorithms remain applicable using simple transformations. Our experiments exhibit large improvements on standard AI planning benchmarks with a pronounced star topology.

MSC:
68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
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[1] Gnad, D.; Hoffmann, J., Beating LM-cut with \(h^{m a x}\) (sometimes): fork-decoupled state space search, (Brafman, R.; Domshlak, C.; Haslum, P.; Zilberstein, S., Proceedings of the 25th International Conference on Automated Planning and Scheduling, ICAPS’15, (2015), AAAI Press), 88-96
[2] Gnad, D.; Hoffmann, J.; Domshlak, C., From fork decoupling to star-topology decoupling, (Lelis, L.; Stern, R., Proceedings of the 8th Annual Symposium on Combinatorial Search, SOCS’15, (2015), AAAI Press), 53-61
[3] Á. Torralba, D. Gnad, P. Dubbert, J. Hoffmann, On state-dominance criteria in fork-decoupled search, in: [116], 2016.
[4] Ghallab, M.; Nau, D.; Traverso, P., Automated planning: theory and practice, (2004), Morgan Kaufmann · Zbl 1074.68613
[5] Lamperti, G.; Zanella, M., Diagnosis of active systems, (2003), Kluwer Academic Publishers · Zbl 1044.93002
[6] Clarke, E.; Grumberg, O.; Peled, D., Model checking, (2001), MIT Press
[7] Korf, R. E.; Zhang, W., Divide-and-conquer frontier search applied to optimal sequence alignment, (Kautz, H. A.; Porter, B., Proceedings of the 17th National Conference of the American Association for Artificial Intelligence, AAAI’00, (2000), AAAI Press Austin, TX, USA), 910-916
[8] Valmari, A., Stubborn sets for reduced state space generation, (Proceedings of the 10th International Conference on Applications and Theory of Petri Nets, (1989)), 491-515
[9] Godefroid, P.; Wolper, P., Using partial orders for the efficient verification of deadlock freedom and safety properties, (Proceedings of the 3rd International Workshop on Computer Aided Verification, CAV’91, (1991)), 332-342
[10] Valmari, A., A stubborn attack on state explosion, Form. Methods Syst. Des., 1, 297-322, (1992) · Zbl 0783.68083
[11] Peled, D., All from one, one for all: on model checking using representatives, (Proceedings of the 5th International Conference on Computer Aided Verification, CAV’93, (1993)), 409-423
[12] Godefroid, P., Partial-order methods for the verification of concurrent systems - an approach to the state-explosion problem, Lect. Notes Comput. Sci., vol. 1032, (1996), Springer · Zbl 1293.68005
[13] Edelkamp, S.; Leue, S.; Lluch-Lafuente, A., Partial-order reduction and trail improvement in directed model checking, Int. J. Softw. Tools Technol. Transf., 6, 277-301, (2004)
[14] Nissim, R.; Apsel, U.; Brafman, R. I., Tunneling and decomposition-based state reduction for optimal planning, (Raedt, L. D., Proceedings of the 20th European Conference on Artificial Intelligence, ECAI’12, (2012), IOS Press Montpellier, France), 624-629 · Zbl 1327.68228
[15] M. Wehrle, M. Helmert, Y. Alkhazraji, R. Mattmüller, The relative pruning power of strong stubborn sets and expansion core, in: [115], 2013.
[16] Wehrle, M.; Helmert, M., Efficient stubborn sets: generalized algorithms and selection strategies, (Chien, S.; Do, M.; Fern, A.; Ruml, W., Proceedings of the 24th International Conference on Automated Planning and Scheduling, ICAPS’14, (2014), AAAI Press)
[17] Starke, P., Reachability analysis of Petri nets using symmetries, J. Math. Model. Simul. Syst. Anal., 8, 293-304, (1991) · Zbl 0733.68059
[18] Emerson, E. A.; Sistla, A. P., Symmetry and model-checking, Form. Methods Syst. Des., 9, 105-131, (1996)
[19] M. Fox, D. Long, The detection and exploitation of symmetry in planning problems, in: [124], 1999, pp. 956-961.
[20] N. Pochter, A. Zohar, J.S. Rosenschein, Exploiting problem symmetries in state-based planners, in: [117], 2011.
[21] C. Domshlak, M. Katz, A. Shleyfman, Enhanced symmetry breaking in cost-optimal planning as forward search, in: [121], 2012.
[22] McMillan, K. L., Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits, (von Bochmann, G.; Probst, D. K., Proceedings of the 4th International Workshop on Computer Aided Verification, CAV’92, Lect. Notes Comput. Sci., (1992), Springer), 164-177
[23] Esparza, J.; Römer, S.; Vogler, W., An improvement of Mcmillan’s unfolding algorithm, Form. Methods Syst. Des., 20, 285-310, (2002) · Zbl 1017.68085
[24] S.L. Hickmott, J. Rintanen, S. Thiébaux, L.B. White, Planning via Petri net unfolding, in: [119], 2007, pp. 1904-1911.
[25] Bonet, B.; Haslum, P.; Hickmott, S. L.; Thiébaux, S., Directed unfolding of Petri nets, Trans. Petri Nets Other Models Concur., 1, 172-198, (2008) · Zbl 1171.68562
[26] Esparza, J.; Heljanko, K., Unfoldings - a partial-order approach to model checking, Monogr. Theor. Comput. Sci., (2008), Springer · Zbl 1153.68035
[27] Baldan, P.; Bruni, A.; Corradini, A.; König, B.; Rodríguez, C.; Schwoon, S., Efficient unfolding of contextual Petri nets, Theor. Comput. Sci., 449, 2-22, (2012) · Zbl 1263.68117
[28] Bonet, B.; Haslum, P.; Khomenko, V.; Thiébaux, S.; Vogler, W., Recent advances in unfolding technique, Theor. Comput. Sci., 551, 84-101, (2014) · Zbl 1360.68628
[29] Sacerdoti, E. D., Planning in a hierarchy of abstraction spaces, Artif. Intell., 5, 115-135, (1974) · Zbl 0288.68052
[30] Knoblock, C., Automatically generating abstractions for planning, Artif. Intell., 68, 243-302, (1994) · Zbl 0942.68712
[31] Lansky, A. L.; Getoor, L., Scope and abstraction: two criteria for localized planning, (Mellish, S., Proceedings of the 14th International Joint Conference on Artificial Intelligence, IJCAI’95, (1995), Morgan Kaufmann Montreal, Canada), 1612-1619
[32] Amir, E.; Engelhardt, B., Factored planning, (Gottlob, G., Proceedings of the 18th International Joint Conference on Artificial Intelligence, IJCAI’03, (2003), Morgan Kaufmann Acapulco, Mexico), 929-935
[33] Brafman, R.; Domshlak, C., Factored planning: how, when, and when not, (Gil, Y.; Mooney, R. J., Proceedings of the 21st National Conference of the American Association for Artificial Intelligence, AAAI’06, (2006), AAAI Press Boston, Massachusetts, USA), 809-814
[34] E. Kelareva, O. Buffet, J. Huang, S. Thiébaux, Factored planning using decomposition trees, in: [119], 2007, pp. 1942-1947.
[35] R.I. Brafman, C. Domshlak, From one to many: planning for loosely coupled multi-agent systems, in: [122], 2008, pp. 28-35.
[36] Fabre, E.; Jezequel, L.; Haslum, P.; Thiébaux, S., Cost-optimal factored planning: promises and pitfalls, (Brafman, R. I.; Geffner, H.; Hoffmann, J.; Kautz, H. A., Proceedings of the 20th International Conference on Automated Planning and Scheduling, ICAPS’10, (2010), AAAI Press), 65-72
[37] Nissim, R.; Brafman, R. I.; Domshlak, C., A general, fully distributed multi-agent planning algorithm, (van der Hoek, W.; Kaminka, G. A.; Lespérance, Y.; Luck, M.; Sen, S., Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, AAMAS’10, (2010), IFAAMAS), 1323-1330
[38] M. Crosby, M. Rovatsos, R.P.A. Petrick, Automated agent decomposition for classical planning, in: [115], 2013.
[39] Brafman, R.; Domshlak, C., On the complexity of planning for agent teams and its implications for single agent planning, Artif. Intell., 198, 52-71, (2013) · Zbl 1284.68564
[40] Nissim, R.; Brafman, R., Distributed heuristic forward search for multi-agent planning, J. Artif. Intell. Res., 51, 293-332, (2014) · Zbl 1367.68325
[41] D. Wang, B.C. Williams, tburton: a divide and conquer temporal planner, in: [120], 2015, pp. 3409-3417.
[42] Hoffmann, J.; Kissmann, P.; Torralba, Á., “distance”? who cares? tailoring merge-and-shrink heuristics to detect unsolvability, (Schaub, T., Proceedings of the 21st European Conference on Artificial Intelligence, ECAI’14, (2014), IOS Press Prague, Czech Republic) · Zbl 1366.68264
[43] Khomenko, V.; Koutny, M., Towards an efficient algorithm for unfolding Petri nets, (Proceedings of the 12th International Conference on Concurrency Theory, CONCUR’01, (2001)), 366-380 · Zbl 1006.68098
[44] Rodríguez, C.; Schwoon, S., Cunf: a tool for unfolding and verifying Petri nets with Read arcs, (Proceedings of the 11th International Symposium on Automated Technology for Verification and Analysis, ATVA’13, (2013)), 492-495 · Zbl 1410.68237
[45] Xu, L.; Hutter, F.; Hoos, H. H.; Leyton-Brown, K., Satzilla: portfolio-based algorithm selection for sat, J. Artif. Intell. Res., 32, 565-606, (2008) · Zbl 1182.68272
[46] Cenamor, I.; de la Rosa, T.; Fernández, F., IBACOP and IBACOP2 planner, (IPC 2014 Planner Abstracts, (2014)), 35-38
[47] Pearl, J., Heuristics, (1984), Morgan Kaufmann
[48] McDermott, D. V., Using regression-match graphs to control search in planning, Artif. Intell., 109, 111-159, (1999) · Zbl 0916.68145
[49] Bonet, B.; Geffner, H., Planning as heuristic search, Artif. Intell., 129, 5-33, (2001) · Zbl 0971.68146
[50] Hoffmann, J.; Nebel, B., The FF planning system: fast plan generation through heuristic search, J. Artif. Intell. Res., 14, 253-302, (2001) · Zbl 0970.68044
[51] Gerevini, A.; Saetti, A.; Serina, I., Planning through stochastic local search and temporal action graphs, J. Artif. Intell. Res., 20, 239-290, (2003) · Zbl 1058.68103
[52] Helmert, M., The fast downward planning system, J. Artif. Intell. Res., 26, 191-246, (2006) · Zbl 1182.68245
[53] Helmert, M.; Domshlak, C., Landmarks, critical paths and abstractions: What’s the difference anyway?, (Gerevini, A.; Howe, A.; Cesta, A.; Refanidis, I., Proceedings of the 19th International Conference on Automated Planning and Scheduling, ICAPS’09, (2009), AAAI Press), 162-169
[54] Richter, S.; Westphal, M., The LAMA planner: guiding cost-based anytime planning with landmarks, J. Artif. Intell. Res., 39, 127-177, (2010) · Zbl 1205.68383
[55] Domshlak, C.; Hoffmann, J.; Katz, M., Red-black planning: a new systematic approach to partial delete relaxation, Artif. Intell., 221, 73-114, (2015) · Zbl 1328.68194
[56] Bäckström, C.; Nebel, B., Complexity results for SAS^+ planning, Comput. Intell., 11, 625-655, (1995)
[57] Bylander, T., The computational complexity of propositional STRIPS planning, Artif. Intell., 69, 165-204, (1994) · Zbl 0821.68065
[58] Jonsson, P.; Bäckström, C., Incremental planning, (European Workshop on Planning, (1995)) · Zbl 0939.68828
[59] Brafman, R.; Domshlak, C., Structure and complexity in planning with unary operators, J. Artif. Intell. Res., 18, 315-349, (2003) · Zbl 1056.68129
[60] M. Katz, C. Domshlak, Structural patterns heuristics via fork decomposition, in: [122], 2008, pp. 182-189.
[61] Garey, M. R.; Johnson, D. S., Computers and intractability—a guide to the theory of NP-completeness, (1979), Freeman San Francisco, CA · Zbl 0411.68039
[62] Henzinger, M. R.; Henzinger, T. A.; Kopke, P. W., Computing simulations on finite and infinite graphs, (Proceedings of the 36th Annual Symposium on Foundations of Computer Science, FOCS’95, (1995), IEEE Computer Society), 453-462 · Zbl 0938.68538
[63] D. Hall, A. Cohen, D. Burkett, D. Klein, Faster optimal planning with partial-order pruning, in: [115], 2013.
[64] Á. Torralba, J. Hoffmann, Simulation-based admissible dominance pruning, in: [118], 2015, pp. 1689-1695.
[65] Hoffmann, J.; Kupferschmid, S., A covering problem for hypercubes, (Kaelbling, L. P., Proceedings of the 19th International Joint Conference on Artificial Intelligence, IJCAI’05, (2005), Morgan Kaufmann Edinburgh, UK), 1523-1524
[66] Moura, L. D.; Bjørner, N., Z3: an efficient SMT solver, (Proceedings of the 14th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS’08, (2008)), 337-340
[67] Trüg, S.; Hoffmann, J.; Nebel, B., Applying automatic planning systems to airport ground-traffic control—a feasibility study, (Biundo, S.; Frühwirth, T.; Palm, G., KI-04: Advances in Artificial Intelligence, (2004), Springer-Verlag Ulm, Germany), 183-197
[68] Rintanen, J., Symmetry reduction for SAT representations of transition systems, (Giunchiglia, E.; Muscettola, N.; Nau, D., Proceedings of the 13th International Conference on Automated Planning and Scheduling, ICAPS’03, (2003), Morgan Kaufmann Trento, Italy), 32-41
[69] Bryant, R. E., Graph-based algorithms for Boolean function manipulation, IEEE Trans. Comput., 35, 677-691, (1986) · Zbl 0593.94022
[70] McMillan, K. L., Symbolic model checking, (1993), Kluwer Academic Publishers · Zbl 1132.68474
[71] Edelkamp, S., Taming numbers and durations in the model checking integrated planning system, J. Artif. Intell. Res., 20, 195-238, (2003) · Zbl 1036.68092
[72] S. Edelkamp, P. Kissmann, On the complexity of BDDs for state space search: a case study in connect four, in: [117], 2011.
[73] Culberson, J. C.; Schaeffer, J., Pattern databases, Comput. Intell., 14, 318-334, (1998)
[74] S. Edelkamp, Planning with pattern databases, in: [123], 2001, pp. 13-24.
[75] Felner, A.; Korf, R.; Hanan, S., Additive pattern database heuristics, J. Artif. Intell. Res., 22, 279-318, (2004) · Zbl 1080.68662
[76] Haslum, P.; Botea, A.; Helmert, M.; Bonet, B.; Koenig, S., Domain-independent construction of pattern database heuristics for cost-optimal planning, (Howe, A.; Holte, R. C., Proceedings of the 22nd National Conference of the American Association for Artificial Intelligence, AAAI’07, (2007), AAAI Press Vancouver, BC, Canada), 1007-1012
[77] J. Seipp, M. Helmert, Counterexample-guided Cartesian abstraction refinement, in: [115], 2013, pp. 347-351. · Zbl 1448.68392
[78] Helmert, M.; Haslum, P.; Hoffmann, J.; Nissim, R., Merge & shrink abstraction: a method for generating lower bounds in factored state spaces, J. ACM, 61, (2014) · Zbl 1295.68189
[79] Bacchus, F.; Yang, Q., Downward refinement and the efficiency of hierarchical problem solving, Artif. Intell., 71, 43-100, (1994) · Zbl 0938.68829
[80] Helmert, M., Fast (diagonally) downward, (IPC 2006 Planner Abstracts, (2006)) · Zbl 1182.68245
[81] P. Haslum, Reducing accidental complexity in planning problems, in: [119], 2007, pp. 1898-1903.
[82] Tozicka, J.; Jakubuv, J.; Svatos, M.; Komenda, A., Recursive polynomial reductions for classical planning, (Coles, A.; Coles, A.; Edelkamp, S.; Magazzeni, D.; Sanner, S., Proceedings of the 26th International Conference on Automated Planning and Scheduling, ICAPS’16, (2016), AAAI Press), 317-325
[83] C. Domshlak, Y. Dinitz, Multi-agent offline coordination: structure and complexity, in: [123], 2001, pp. 34-43.
[84] Helmert, M., A planning heuristic based on causal graph analysis, (Koenig, S.; Zilberstein, S.; Koehler, J., Proceedings of the 14th International Conference on Automated Planning and Scheduling, ICAPS’04, (2004), Morgan Kaufmann Whistler, Canada), 161-170
[85] Katz, M.; Domshlak, C., New islands of tractability of cost-optimal planning, J. Artif. Intell. Res., 32, 203-288, (2008) · Zbl 1182.68251
[86] Giménez, O.; Jonsson, A., The complexity of planning problems with simple causal graphs, J. Artif. Intell. Res., 31, 319-351, (2008) · Zbl 1182.68242
[87] Giménez, O.; Jonsson, A., Planning over chain causal graphs for variables with domains of size 5 is NP-hard, J. Artif. Intell. Res., 34, 675-706, (2009) · Zbl 1182.68243
[88] Giménez, O.; Jonsson, A., The influence of k-dependence on the complexity of planning, Artif. Intell., 177-179, 25-45, (2012) · Zbl 1238.68151
[89] Katz, M.; Keyder, E., Structural patterns beyond forks: extending the complexity boundaries of classical planning, (Hoffmann, J.; Selman, B., Proceedings of the 26th AAAI Conference on Artificial Intelligence, AAAI’12, (2012), AAAI Press Toronto, ON, Canada), 1779-1785
[90] M. Aghighi, P. Jonsson, S. Ståhlberg, Tractable cost-optimal planning over restricted polytree causal graphs, in: [120], 2015, pp. 3225-3231.
[91] Kronegger, M.; Ordyniak, S.; Pfandler, A., Backdoors to planning, (Brodley, C. E.; Stone, P., Proceedings of the 28th AAAI Conference on Artificial Intelligence, AAAI’14, (2014), AAAI Press Austin, Texas, USA), 2300-2307
[92] M. Kronegger, S. Ordyniak, A. Pfandler, Variable-deletion backdoors to planning, in: [120], 2015, pp. 3305-3312.
[93] Hart, P. E.; Nilsson, N. J.; Raphael, B., A formal basis for the heuristic determination of minimum cost paths, IEEE Trans. Syst. Sci. Cybern., 4, 100-107, (1968)
[94] Haslum, P.; Geffner, H., Admissible heuristics for optimal planning, (Chien, S.; Kambhampati, R.; Knoblock, C., Proceedings of the 5th International Conference on Artificial Intelligence Planning Systems, AIPS’00, (2000), AAAI Press Menlo Park, Breckenridge, CO), 140-149
[95] Hoffmann, J.; Porteous, J.; Sebastia, L., Ordered landmarks in planning, J. Artif. Intell. Res., 22, 215-278, (2004) · Zbl 1080.68670
[96] H. Nakhost, J. Hoffmann, M. Müller, Resource-constrained planning: a Monte Carlo random walk approach, in: [121], 2012, pp. 181-189.
[97] Helmert, M., Concise finite-domain representations for PDDL planning tasks, Artif. Intell., 173, 503-535, (2009) · Zbl 1191.68635
[98] Blum, A. L.; Furst, M. L., Fast planning through planning graph analysis, Artif. Intell., 90, 279-298, (1997) · Zbl 1017.68533
[99] H. Kautz, B. Selman, Unifying SAT-based and graph-based planning, in: [124], 1999, pp. 318-325.
[100] Long, D.; Fox, M., The 3rd international planning competition: results and analysis, J. Artif. Intell. Res., 20, 1-59, (2003) · Zbl 1036.68097
[101] Á. Torralba, C. Linares López, D. Borrajo, Abstraction heuristics for symbolic bidirectional search, in: [116], 2016, pp. 3272-3278.
[102] M. Wehrle, M. Helmert, A. Shleyfman, M. Katz, Integrating partial order reduction and symmetry elimination for cost-optimal classical planning, in: [118], 2015.
[103] D. Gnad, M. Wehrle, J. Hoffmann, Decoupled strong stubborn sets, in: [116], 2016, pp. 3110-3116.
[104] Hutter, F.; Hoos, H. H.; Leyton-Brown, K.; Stützle, T., Paramils: an automatic algorithm configuration framework, J. Artif. Intell. Res., 36, 267-306, (2009) · Zbl 1192.68831
[105] Fawcett, C.; Helmert, M.; Hoos, H.; Karpas, E.; Röger, G.; Seipp, J., FD-autotune: automated configuration of fast downward, (IPC 2011 Planner Abstracts, (2011)), 31-37
[106] Seipp, J.; Pommerening, F.; Sievers, S.; Wehrle, M., Fast downward aidos, (UIPC 2016 Planner Abstracts, (2016)), 28-38
[107] Torralba, Á., Sympa: symbolic perimeter abstractions for proving unsolvability, (UIPC 2016 Planner Abstracts, (2016)), 8-11
[108] Jonsson, B., State-space exploration for concurrent algorithms under weak memory orderings, SIGARCH Comput. Archit. News, 36, 65-71, (2008)
[109] Linden, A.; Wolper, P., A verification-based approach to memory fence insertion in PSO memory systems, (Piterman, N.; Smolka, S. A., Proceedings of the 19th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS’13, (2013), Springer-Verlag), 339-353 · Zbl 1381.68173
[110] Travkin, O.; Mütze, A.; Wehrheim, H., SPIN as a linearizability checker under weak memory models, (Proceedings of the 9th International Haifa Verification Conference, HVC’13, (2013)), 311-326
[111] Alrahman, Y. A.; Andric, M.; Beggiato, A.; Lluch-Lafuente, A., Can we efficiently check concurrent programs under relaxed memory models in maude?, (Revised Selected Papers of the 10th International Workshop on Rewriting Logic and Its Applications, WRLA’14, (2014)), 21-41 · Zbl 1367.68057
[112] Gnad, D.; Poser, V.; Hoffmann, J., Beyond forks: finding and ranking star factorings for decoupled search, (Sierra, C., Proceedings of the 26th International Joint Conference on Artificial Intelligence, IJCAI’17, (2017), AAAI Press/IJCAI)
[113] Gnad, D.; Torralba, Á.; Shleyfman, A.; Hoffmann, J., Symmetry breaking in star-topology decoupled search, (Proceedings of the 27th International Conference on Automated Planning and Scheduling, ICAPS’17, (2017), AAAI Press)
[114] Gnad, D.; Torralba, Á.; Hoffmann, J., Symbolic leaf representation in decoupled search, (Fukunaga, A.; Kishimoto, A., Proceedings of the 10th Annual Symposium on Combinatorial Search, SOCS’17, (2017), AAAI Press)
[115] (Borrajo, D.; Fratini, S.; Kambhampati, S.; Oddi, A., Proceedings of the 23rd International Conference on Automated Planning and Scheduling, ICAPS’13, (2013), AAAI Press Rome, Italy)
[116] (Kambhampati, S., Proceedings of the 25th International Joint Conference on Artificial Intelligence, IJCAI’16, (2016), AAAI Press/IJCAI)
[117] (Burgard, W.; Roth, D., Proceedings of the 25th National Conference of the American Association for Artificial Intelligence, AAAI’11, (2011), AAAI Press San Francisco, CA, USA)
[118] (Yang, Q., Proceedings of the 24th International Joint Conference on Artificial Intelligence, IJCAI’15, (2015), AAAI Press/IJCAI)
[119] (Veloso, M., Proceedings of the 20th International Joint Conference on Artificial Intelligence, IJCAI’07, (2007), Morgan Kaufmann Hyderabad, India)
[120] (Bonet, B.; Koenig, S., Proceedings of the 29th AAAI Conference on Artificial Intelligence, AAAI’15, (2015), AAAI Press)
[121] (Bonet, B.; McCluskey, L.; Silva, J. R.; Williams, B., Proceedings of the 22nd International Conference on Automated Planning and Scheduling, ICAPS’12, (2012), AAAI Press)
[122] (Rintanen, J.; Nebel, B.; Beck, J. C.; Hansen, E., Proceedings of the 18th International Conference on Automated Planning and Scheduling, ICAPS’08, (2008), AAAI Press)
[123] (Cesta, A.; Borrajo, D., Proceedings of the 6th European Conference on Planning, ECP’01, (2001), Springer-Verlag)
[124] (Pollack, M., Proceedings of the 16th International Joint Conference on Artificial Intelligence, IJCAI’99, (1999), Morgan Kaufmann Stockholm, Sweden)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.