## Theory and Practice of Time-Space Trade-Offs in Memory Limited Search (2001)

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Venue: | In Proceedings of KI-01, Lecture Notes in Computer Science |

Citations: | 6 - 3 self |

### BibTeX

@INPROCEEDINGS{Edelkamp01theoryand,

author = {Stefan Edelkamp and Ulrich Meyer},

title = {Theory and Practice of Time-Space Trade-Offs in Memory Limited Search},

booktitle = {In Proceedings of KI-01, Lecture Notes in Computer Science},

year = {2001},

pages = {169--184},

publisher = {Springer}

}

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### Abstract

. Having to cope with memory limitations is an ubiquitous issue in heuristic search. We present theoretical and practical results on new variants for exploring state-space with respect to memory limitations. We establish ##### ## minimum-space algorithms that omit both the open and the closed list to determine the shortest path between every two nodes and study the gap in between full memorization in a hash table and the information-theoretic lower bound. The proposed structure of suffix-lists elaborates on a concise binary representation of states by applying bit-state hashing techniques. Significantly more states can be stored while searching and inserting # items into suffix lists is still available in ### ### ## time. Bit-state hashing leads to the new paradigm of partial iterative-deepening heuristic search, in which full exploration is sacrificed for a better detection of duplicates in large search depth. We give first promising results in the application area of communication protocols. 1

### Citations

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- 1999
(Show Context)
Citation Context ...nimal counterexamples in the protocol space according to a given implementation corresponds to the search for an optimal solution with the goal as the failure state. From a model checking perspective =-=[3]-=- the approach allows to implement various heuristics to direct the search into the direction of the failure. From an AI-perspective partial search, maybe assisted with sequential hashing, condenses du... |

767 |
Design and Validation of Computer Protocols
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(Show Context)
Citation Context ...n the following we study algorithms and data structures to certify the correctness of a such a protocol. 4.2 Supertrace The idea of bit-state hashing is adopted from Holzman’s protocol validator Spi=-=n [12]-=-, that parses the expressive concurrent Promela protocol specification language. It compresses the state description of several hundred bits down to only a few bits to build a hash table with up to en... |

412 | Depth-first iterative-deepening: An optimal admissible tree search
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- 1985
(Show Context)
Citation Context ...h distance value smaller than the optimal solution path length is larger than this memory bound, storing the entire list of visited nodes is no longer possible. Iterative deepening A*, IDA* for short =-=[16]-=-, has proven effective to successively search the problem graph with bounded DFS traversals according to an increasing threshold for the tentative values. IDA* consumes space linear in the solution le... |

317 |
Relationships between nondeterministic and deterministic tape complexities
- Savitch
- 1970
(Show Context)
Citation Context ...paths. In the following we will devise an Ç ÐÓ� Ò space algorithm for BFS and shortest paths with small integer weights. The principle is similar to the simulation of nondeterministic Turing mac=-=hines [20]. 2.1 -=-Divide-And-Conquer BFS To compute the breadth-first-level for each node, with very limited space, we may use a DAC strategy Path that reports if there is a path from � to � with Ð edges. If Ð eq... |

114 | Planning with pattern databases
- Edelkamp
- 2001
(Show Context)
Citation Context ... the application of this pre-compilation technique is limited to suitable domain abstractions that yield better results than on-line computations as findings in protocol verification [8], AI-planning =-=[6]-=-, and selected single-agent problems [14] indicate. Therefore, to lessen memory consumption according to a large number of states is still a problem. Transposition tables are used to store and improve... |

82 | An analysis of bitstate hashing
- HOLZMANN
- 1998
(Show Context)
Citation Context ...verage with Ò�ÑissÈ with the average probability of � collision È � Ò Ñ � Ò� Ñ, since the �-th element collides with one of the �salready inserted elements with a probability of =-=at most �s�Ñ, � � � Ò [13]. For multi-bit hashing and � (indepen-=-dent) hash-functions by assumingÈ �Ò�Ñcoverage is Òsimproved tosÈ� with average probability of collision È� � Ò �� � ¡ � Ñ � ,since � elements occupy at most ���Ñ... |

76 | Searching with pattern databases, in
- Culberson, Schaeffer
- 1996
(Show Context)
Citation Context ...Í the threshold for the next iteration. The value Û Ù� Ú is the weight of the transitition Ù� Ú , � Ù and � Ù is the heuristic estimate and combined merit for node Ù, respectively. Pa=-=ttern data-bases [4]-=- are a general tool to improve the estimate that can cope with complex subproblem interactions. A solution preserving relaxation of the search problem is traversed prior to the search and the goal dis... |

69 | Enhanced iterative-deepening search
- Reinefeld, Marsland
- 1994
(Show Context)
Citation Context ...refore, to lessen memory consumption according to a large number of states is still a problem. Transposition tables are used to store and improve the distances until the memory bound has been reached =-=[18]. -=-However, when the memory is exhausted, IDA*’s time consumption is often stinged by uncaught duplicates. Different node caching strategies have been applied: MREC [21] switches from A* to IDA* if the... |

63 |
Membership in constant time and almostminimum space
- Brodnik, Munro
- 1999
(Show Context)
Citation Context ...r ideas appeared in [2] but the data structure there is static and not theoretically analyzed. Another dynamic variant achieving asympotically equivalent storage bounds as our approach is sketched in =-=[1]-=-. However, constants are only given for two static examples. We provide constants for the dynamic version; comparing with the numbers of [1], our dynamic version could host up to five times more eleme... |

54 | Efficient memory-bounded search methods
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- 1992
(Show Context)
Citation Context ...*’s time consumption is often stinged by uncaught duplicates. Different node caching strategies have been applied: MREC [21] switches from A* to IDA* if the memory limit is reached. In contrast, SMA=-=* [19] r-=-eassigns the space by dynamically deleting a previously expanded node, propagating up computed �-values to the parents in order to save re-computation as far as possible. However, the effect of node... |

36 |
Fast recursive formulation for best-first search that allow controlled use of memory
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- 1989
(Show Context)
Citation Context ...e memory bound has been reached [18]. However, when the memory is exhausted, IDA*’s time consumption is often stinged by uncaught duplicates. Different node caching strategies have been applied: MRE=-=C [21] s-=-witches from A* to IDA* if the memory limit is reached. In contrast, SMA* [19] reassigns the space by dynamically deleting a previously expanded node, propagating up computed �-values to the parents... |

25 |
Divide-and-conquer bidirectional search: First results
- Korf
(Show Context)
Citation Context ...rch efforts for optimally solving Atomix, a PSPACE-complete AI single-agent search problem [14]. Omitting the visited list and exploring the space in a Divide-and-Conquer fashion has been proposed in =-=[17]-=-, and the algorithms we consider study the effect of removing the horizon-list as well. Another model checking approach for state compression as to answer to the representation problem of large sets o... |

21 | Trail-directed model checking
- Edelkamp, Lluch-Lafuente, et al.
(Show Context)
Citation Context ...age with bitstate duplicate elimination is very close to 100 % for moderately sized systems (Ò � Ñ). Moreover, the technique of trail-directed search can effectivly improve non-optimal existing pa=-=ths [9]-=-. The results for searching deadlocks in one large communication protocol are depicted in Table 6, where the number of expansions with respect to different optimal search algorithms for an increasing ... |

21 | Formalization and Validation of the General Inter-ORB Protocol (GIOP) using PROMELA and SPIN
- Kamel, Leue
(Show Context)
Citation Context ...pansion numbers in these two algorithms do not match exactly, but indicate a common trend. The considered protocol instance is the industrial General Inter-ORB Protocol (GIOP, 1 server and 3 clients) =-=[15]-=-, which is a key component of the Common Object Request Broker Architecture (CORBA) specification. The witness for a seeded deadlock in depth 70 has to be established according to the heuristic that c... |

19 | Protocol verification with heuristic search
- Edelkamp, Lafuente, et al.
- 2001
(Show Context)
Citation Context ...h table. However, the application of this pre-compilation technique is limited to suitable domain abstractions that yield better results than on-line computations as findings in protocol verification =-=[8]-=-, AI-planning [6], and selected single-agent problems [14] indicate. Therefore, to lessen memory consumption according to a large number of states is still a problem. Transposition tables are used to ... |

15 |
Improved hierarchical bit-vector compression in document retrieval systems
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- 1986
(Show Context)
Citation Context .... Using hashing with open addressing, Ö is limited to Ç Ò� ÐÓ� Ò . In the following we describe a simple but very space efficient approach with small update and query times. Similar ideas ap=-=peared in [2]-=- but the data structure there is static and not theoretically analyzed. Another dynamic variant achieving asympotically equivalent storage bounds as our approach is sketched in [1]. However, constants... |

15 |
Directed model-checking in HSF-SPIN
- Edelkamp, Lluch-Lafuente, et al.
- 2001
(Show Context)
Citation Context ...,249 407,310 69 - - 442,863 442,941 70 - - 67 67 Table 6. Number of Expanded nodes of Search Algorithms in the GIOP Protocol. plementation. For the experiments we chose a non-trivial protocol example =-=[7]-=-, but recent progress shows that the algorithm has also reduced the search efforts for optimally solving Atomix, a PSPACE-complete AI single-agent search problem [14]. Omitting the visited list and ex... |

13 | Combining state space caching and hash compaction
- Stern, Dill
- 1996
(Show Context)
Citation Context ... generalization of the bit-state hashing idea, Figure 4 depicts the range of possible hash structures: Usual hashing with chaining of synonyms, single-bit hashing, double-bit hashing and hash compact =-=[22]. Let Ò be t-=-he number of reachable states and Ñ be the maximal number of bits available. A coarse approximation for È Òs�� single bit-state hashing coverage with Ò�ÑissÈ with the average probability o... |

9 | A Spectrum of TimeSpace Trade-offs for Undirected s-t Connectivity
- Feige
- 1997
(Show Context)
Citation Context ...of node reachability (i.e., determine whether there any path between two nodes) and graph connectivity have been efficiently solved for the same restricted memory setting using random walk strategies =-=[10, 11]. Howe-=-ver, we are not aware of any equivalent results for BFS and shortest paths. In the following we will devise an Ç ÐÓ� Ò space algorithm for BFS and shortest paths with small integer weights. The ... |

8 | A Fast Randomized LOGSPACE Algorithm for Graph Connectivity
- Feige
- 1996
(Show Context)
Citation Context ...of node reachability (i.e., determine whether there any path between two nodes) and graph connectivity have been efficiently solved for the same restricted memory setting using random walk strategies =-=[10, 11]. Howe-=-ver, we are not aware of any equivalent results for BFS and shortest paths. In the following we will devise an Ç ÐÓ� Ò space algorithm for BFS and shortest paths with small integer weights. The ... |

2 |
Limits and possibilities of sequential hashing with supertrace
- Eckerle, Lais
- 1998
(Show Context)
Citation Context ...rst hash first function covers Ñ�Ò of the search space, the probability that a state Ü is not generated in � independent runs issÑ�Ò � such that Ü is reached with probabilitysÑ�Ò �=-= . Eckerle and Lais [5] have shown tha-=-t this ideal circumstances are not given in practice and refine the model for coverage prediction.sHash Table State × � × State × Bit-Address State × � × Bit-Address � × � × Hash Table ... |

2 |
Finding optimal solutions to Atomix. This volume
- Huner, Edelkamp, et al.
(Show Context)
Citation Context ... technique is limited to suitable domain abstractions that yield better results than on-line computations as findings in protocol verification [8], AI-planning [6], and selected single-agent problems =-=[14]-=- indicate. Therefore, to lessen memory consumption according to a large number of states is still a problem. Transposition tables are used to store and improve the distances until the memory bound has... |

1 |
Finding optimal solutions toAtomix. This volume
- Hüffner, Edelkamp, et al.
(Show Context)
Citation Context ... technique is limited to suitable domain abstractions that yield better results than on-line computations as findings in protocol verification [8], AI-planning [6], and selected single-agent problems =-=[14]-=- indicate. Therefore, to lessen memory consumption according to a large number of states is still a problem. Transposition tables are used to store and improve the distances until the memory bound has... |