Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization

Design and analysis of sequential and parallel single-source shortest-paths algorithms

We study the performance of algorithms for the Single-Source Shortest-Paths (SSSP) problem on graphs with n nodes and m edges with nonnegative random weights. All previously known SSSP algorithms for directed graphs required superlinear time. Wie give the first SSSP algorithms that provably achieve linear O(n-m)average-case execution time on arbitrary directed graphs with random edge weights. For independent edge weights, the linear-time bound holds with high probability, too. Additionally, our result implies improved average-case bounds for the All-Pairs Shortest-Paths (APSP) problem on sparse graphs, and it yields the first theoretical average-case analysis for the "Approximate Bucket Implementation" of Dijkstra\u27s SSSP algorithm (ABI-Dijkstra). Futhermore, we give constructive proofs for the existence of graph classes with random edge weights on which ABI-Dijkstra and several other well-known SSSP algorithms require superlinear average-case time. Besides the classical sequential (single processor) model of computation we also consider parallel computing: we give the currently fastest average-case linear-work parallel SSSP algorithms for large graph classes with random edge weights, e.g., sparse rondom graphs and graphs modeling the WWW, telephone calls or social networks.In dieser Arbeit untersuchen wir die Laufzeiten von Algorithmen für das Kürzeste-Wege Problem (Single-Source Shortest-Paths, SSSP) auf Graphen mit n Knoten, M Kanten und nichtnegativen zufälligen Kantengewichten. Alle bisherigen SSSP Algorithmen benötigen auf gerichteten Graphen superlineare Zeit. Wir stellen den ersten SSSP Algorithmus vor, der auf beliebigen gerichteten Graphen mit zufälligen Kantengewichten eine beweisbar lineare average-case-Komplexität O(n+m)aufweist. Sind die Kantengewichte unabhängig, so wird die lineare Zeitschranke auch mit hoher Wahrscheinlichkeit eingehalten. Außerdem impliziert unser Ergebnis verbesserte average-case-Schranken für das All-Pairs Shortest-Paths (APSP) Problem auf dünnen Graphen und liefert die erste theoretische average-case-Analyse für die "Approximate Bucket Implementierung" von Dijkstras SSSP Algorithmus (ABI-Dijkstra). Weiterhin führen wir konstruktive Existenzbeweise für Graphklassen mit zufälligen Kantengewichten, auf denen ABI-Dijkstra und mehrere andere bekannte SSSP Algorithmen durchschnittlich superlineare Zeit benötigen. Neben dem klassischen seriellen (Ein-Prozessor) Berechnungsmodell betrachten wir auch Parallelverarbeitung; für umfangreiche Graphklassen mit zufälligen Kantengewichten wie z.B. dünne Zufallsgraphen oder Modelle für das WWW, Telefonanrufe oder soziale Netzwerke stellen wir die derzeit schnellsten parallelen SSSP Algorithmen mit durchschnittlich linearer Arbeit vor

Theory and Practice of Time-Space Trade-Offs in Memory Limited Search

. 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.

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We study the performance of algorithms for the Single-Source Shortest-Paths (SSSP) problem on graphs with n nodes and m edges with nonnegative random weights. All previously known SSSP algorithms for directed graphs required superlinear time. Wie give the first SSSP algorithms that provably achieve linear O(n-m)average-case execution time on arbitrary directed graphs with random edge weights. For independent edge weights, the linear-time bound holds with high probability, too. Additionally, our result implies improved average-case bounds for the All-Pairs Shortest-Paths (APSP) problem on sparse graphs, and it yields the first theoretical average-case analysis for the "Approximate Bucket Implementation" of Dijkstra's SSSP algorithm (ABI-Dijkstra). Futhermore, we give constructive proofs for the existence of graph classes with random edge weights on which ABI-Dijkstra and several other well-known SSSP algorithms require superlinear average-case time. Besides the classical sequential (single processor) model of computation we also consider parallel computing: we give the currently fastest average-case linear-work parallel SSSP algorithms for large graph classes with random edge weights, e.g., sparse rondom graphs and graphs modeling the WWW, telephone calls or social networks.In dieser Arbeit untersuchen wir die Laufzeiten von Algorithmen für das Kürzeste-Wege Problem (Single-Source Shortest-Paths, SSSP) auf Graphen mit n Knoten, M Kanten und nichtnegativen zufälligen Kantengewichten. Alle bisherigen SSSP Algorithmen benötigen auf gerichteten Graphen superlineare Zeit. Wir stellen den ersten SSSP Algorithmus vor, der auf beliebigen gerichteten Graphen mit zufälligen Kantengewichten eine beweisbar lineare average-case-Komplexität O(n+m)aufweist. Sind die Kantengewichte unabhängig, so wird die lineare Zeitschranke auch mit hoher Wahrscheinlichkeit eingehalten. Außerdem impliziert unser Ergebnis verbesserte average-case-Schranken für das All-Pairs Shortest-Paths (APSP) Problem auf dünnen Graphen und liefert die erste theoretische average-case-Analyse für die "Approximate Bucket Implementierung" von Dijkstras SSSP Algorithmus (ABI-Dijkstra). Weiterhin führen wir konstruktive Existenzbeweise für Graphklassen mit zufälligen Kantengewichten, auf denen ABI-Dijkstra und mehrere andere bekannte SSSP Algorithmen durchschnittlich superlineare Zeit benötigen. Neben dem klassischen seriellen (Ein-Prozessor) Berechnungsmodell betrachten wir auch Parallelverarbeitung; für umfangreiche Graphklassen mit zufälligen Kantengewichten wie z.B. dünne Zufallsgraphen oder Modelle für das WWW, Telefonanrufe oder soziale Netzwerke stellen wir die derzeit schnellsten parallelen SSSP Algorithmen mit durchschnittlich linearer Arbeit vor