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  • 1.
    Nilsson, Mikael
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Intergrated Computer systems. Linköping University, Faculty of Science & Engineering.
    Efficient Temporal Reasoning with Uncertainty2015Licentiate thesis, monograph (Other academic)
    Abstract [en]

    Automated Planning is an active area within Artificial Intelligence. With the help of computers we can quickly find good plans in complicated problem domains, such as planning for search and rescue after a natural disaster. When planning in realistic domains the exact duration of an action generally cannot be predicted in advance. Temporal planning therefore tends to use upper bounds on durations, with the explicit or implicit assumption that if an action happens to be executed more quickly, the plan will still succeed. However, this assumption is often false. If we finish cooking too early, the dinner will be cold before everyone is at home and can eat. Simple Temporal Networks with Uncertainty (STNUs) allow us to model such situations. An STNU-based planner must verify that the temporal problems it generates are executable, which is captured by the property of dynamic controllability (DC). If a plan is not dynamically controllable, adding actions cannot restore controllability. Therefore a planner should verify after each action addition whether the plan remains DC, and if not, backtrack. Verifying dynamic controllability of a full STNU is computationally intensive. Therefore, incremental DC verification algorithms are needed.

    We start by discussing two existing algorithms relevant to the thesis. These are the very first DC verification algorithm called MMV (by Morris, Muscettola and Vidal) and the incremental DC verification algorithm called FastIDC, which is based on MMV.

    We then show that FastIDC is not sound, sometimes labeling networks as dynamically controllable when they are not.  We analyze the algorithm to pinpoint the cause and show how the algorithm can be modified to correctly and efficiently detect uncontrollable networks.

    In the next part we use insights from this work to re-analyze the MMV algorithm. This algorithm is pseudo-polynomial and was later subsumed by first an n5 algorithm and then an n4 algorithm. We show that the basic techniques used by MMV can in fact be used to create an n4 algorithm for verifying dynamic controllability, with a new termination criterion based on a deeper analysis of MMV. This means that there is now a comparatively easy way of implementing a highly efficient dynamic controllability verification algorithm. From a theoretical viewpoint, understanding MMV is important since it acts as a building block for all subsequent algorithms that verify dynamic controllability. In our analysis we also discuss a change in MMV which reduces the amount of regression needed in the network substantially.

    In the final part of the thesis we show that the FastIDC method can result in traversing part of a temporal network multiple times, with constraints slowly tightening towards their final values.  As a result of our analysis we then present a new algorithm with an improved traversal strategy that avoids this behavior.  The new algorithm, EfficientIDC, has a time complexity which is lower than that of FastIDC. We prove that it is sound and complete.

     

  • 2.
    Nilsson, Mikael
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Intergrated Computer systems. Linköping University, The Institute of Technology.
    On the Complexity of Finding Spanner Paths2013In: Booklet of Abstracts, The European Workshop on Computational Geometry (EuroCG) / [ed] Sandor P. Fekete, 2013, 77-80 p.Conference paper (Refereed)
    Abstract [en]

    We study the complexity of finding so called spanner paths between arbitrary nodes in Euclidean graphs. We study both general Euclidean graphs and a special type of graphs called Integer Graphs. The problem is proven NP-complete for general Euclidean graphs with non-constant stretches (e.g. (2n)^(3/2) where n denotes the number of nodes in the graph). An algorithm solving the problem in O(2^(0.822n)) is presented. Integer graphs are simpler and for these special cases a better algorithm is presented. By using a partial order of so called Images the algorithm solves the spanner path problem using O(2^(c(\log n)^2)) time, where c is a constant depending only on the stretch.

  • 3.
    Nilsson, Mikael
    Institutionen för datavetenskap, Naturvetenskapliga fakulteten, Lunds universitet.
    Spanneröar och spannervägar2009Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this Master Thesis the possibility to efficiently divide a graph into spanner islands is examined. Spanner islands are islands of the graph that fulfill the spanner condition, that the distance between two nodes via the edges in the graph cannot be too far, regulated by the stretch constant, compared to the Euclidian distance between them. In the resulting division the least number of nodes connecting to other islands is sought-after. Different heuristics are evaluated with the conclusion that for dense graphs a heuristic using MAX-FLOW to divide problematic nodes gives the best result whereas for sparse graphs a heuristic using the single-link clustering method performs best. The problem of finding a spanner path, a path fulfilling the spanner condition, between two nodes is also investigated. The problem is proven to be NP-complete for a graph of size n if the spanner constant is greater than n^(1+1/k)*k^0.5 for some integer k. An algorithm with complexity O(2^(0.822n)) is given. A special type of graph where all the nodes are located on integer locations along the real line is investigated. An algorithm to solve this problem is presented with a complexity of O(2^((c*log n)^2))), where c is a constant depending only on the spanner constant. For instance, the complexity O(2^((5.32*log n)^2))) can be reached for stretch 1.5.

  • 4.
    Nilsson, Mikael
    et al.
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, The Institute of Technology.
    Kvarnström, Jonas
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, The Institute of Technology.
    Doherty, Patrick
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, The Institute of Technology.
    Classical Dynamic Controllability Revisited: A Tighter Bound on the Classical Algorithm2014In: Proceedings of the 6th International Conference on Agents and Artificial Intelligence (ICAART), 2014, 130-141 p.Conference paper (Refereed)
    Abstract [en]

    Simple Temporal Networks with Uncertainty (STNUs) allow the representation of temporal problems wheresome durations are uncontrollable (determined by nature), as is often the case for actions in planning. It is essentialto verify that such networks are dynamically controllable (DC) – executable regardless of the outcomesof uncontrollable durations – and to convert them to an executable form. We use insights from incrementalDC verification algorithms to re-analyze the original verification algorithm. This algorithm, thought to bepseudo-polynomial and subsumed by an O(n5) algorithm and later an O(n4) algorithm, is in fact O(n4) givena small modification. This makes the algorithm attractive once again, given its basis in a less complex andmore intuitive theory. Finally, we discuss a change reducing the amount of work performed by the algorithm.

  • 5.
    Nilsson, Mikael
    et al.
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, Faculty of Science & Engineering.
    Kvarnström, Jonas
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, Faculty of Science & Engineering.
    Doherty, Patrick
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, Faculty of Science & Engineering.
    Efficient Processing of Simple Temporal Networks with Uncertainty: Algorithms for Dynamic Controllability Verification2016In: Acta Informatica, ISSN 0001-5903, E-ISSN 1432-0525, Vol. 53, no 6-8, 723-752 p.Article in journal (Refereed)
    Abstract [en]

    Temporal formalisms are essential for reasoning about actions that are carried out over time. The exact durations of such actions are generally hard to predict. In temporal planning, the resulting uncertainty is often worked around by only considering upper bounds on durations, with the assumption that when an action happens to be executed more quickly, the plan will still succeed. However, this  assumption is often false: If we finish cooking too early, the dinner will be cold before everyone is ready to eat. 

    Using Simple Temporal Networks with Uncertainty (STNU), a planner can correctly take both lower and upper duration bounds into  account. It must then verify that the plans it generates are executable regardless of the actual outcomes of the uncertain durations. This is captured by the property of dynamic controllability (DC), which should be verified incrementally during plan generation. 

    Recently a new incremental algorithm for verifying dynamic controllability was proposed: EfficiantIDC, which can verify if an STNU that is DC remains DC after the addition or tightening of a constraint (corresponding to a new action being added to a plan). The algorithm was shown to have a worst case complexity of O(n4) for each addition or tightening. This can be amortized over the construction of a whole STNU for an amortized complexity in O(n3). In this paper we improve the EfficientIDC algorithm in a way that prevents it from having to reprocess nodes. This improvement leads to a lower worst case complexity in O(n3).

  • 6.
    Nilsson, Mikael
    et al.
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Intergrated Computer systems. Linköping University, The Institute of Technology.
    Kvarnström, Jonas
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Intergrated Computer systems. Linköping University, The Institute of Technology.
    Doherty, Patrick
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Intergrated Computer systems. Linköping University, The Institute of Technology.
    EfficientIDC: A Faster Incremental Dynamic Controllability Algorithm2014In: Proceedings of the 24th International Conference on Automated Planning and Scheduling (ICAPS), AAAI Press, 2014, 199-207 p.Conference paper (Refereed)
    Abstract [en]

    Simple Temporal Networks with Uncertainty (STNUs) allow the representation of temporal problems where some durations are uncontrollable (determined by nature), as is often the case for actions in planning. It is essential to verify that such networks are dynamically controllable (DC) – executable regardless of the outcomes of uncontrollable durations – and to convert them to an executable form. We use insights from incremental DC verification algorithms to re-analyze the original verification algorithm. This algorithm, thought to be pseudo-polynomial and subsumed by an O(n5) algorithm and later an O(n4) algorithm, is in fact O(n4) given a small modification. This makes the algorithm attractive once again, given its basis in a less complex and more intuitive theory. Finally, we discuss a change reducing the amount of work performed by the algorithm.

  • 7.
    Nilsson, Mikael
    et al.
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Intergrated Computer systems. Linköping University, The Institute of Technology.
    Kvarnström, Jonas
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Intergrated Computer systems. Linköping University, The Institute of Technology.
    Doherty, Patrick
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Intergrated Computer systems. Linköping University, The Institute of Technology.
    Incremental Dynamic Controllability in Cubic Worst-Case Time2014In: Proceedings of the 21st International Symposium on Temporal Representation and Reasoning (TIME) / [ed] Cesta, A; Combi, C; Laroussinie, F, IEEE Computer Society Digital Library, 2014, 17-26 p.Conference paper (Refereed)
    Abstract [en]

    It is generally hard to predict the exact duration of an action. The uncertainty in the duration is often modeled in temporal planning by the use of upper bounds on durations, with the assumption that if an action happens to be executed more quickly, the plan will still succeed. However, this assumption is often false: If we finish cooking too early, the dinner will be cold before everyone is ready to eat. Simple Temporal Problems with Uncertainty (STPUs) allow us to model such situations. An STPU-based planner must verify that the plans it generates are executable, captured by the property of dynamic controllability. The EfficientIDC (EIDC) algorithm can do this incrementally during planning, with an amortized complexity per step of $O(n^3)$ but a worst-case complexity per step of $O(n^4)$. In this paper we show that the worst-case run-time of EIDC does occur, leading to repeated reprocessing of nodes in the STPU while verifying the dynamic controllability property. We present a new version of the algorithm, called EIDC2, which through optimal ordering of nodes avoids any need for reprocessing. This gives EIDC2 a strictly lower worst-case run-time, making it the fastest known algorithm for incrementally verifying dynamic controllability of STPUs.

  • 8.
    Nilsson, Mikael
    et al.
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, The Institute of Technology.
    Kvarnström, Jonas
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, The Institute of Technology.
    Doherty, Patrick
    Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab. Linköping University, Department of Computer and Information Science, UASTECH - Autonomous Unmanned Aircraft Systems Technologies. Linköping University, The Institute of Technology.
    Incremental Dynamic Controllability Revisited2013In: Proceedings of the 23rd International Conference on Automated Planning and Scheduling (ICAPS), AAAI Press, 2013Conference paper (Refereed)
    Abstract [en]

    Simple Temporal Networks with Uncertainty (STNUs) allow the representation of temporal problems where some durations are determined by nature, as is often the case for actions in planning. As such networks are generated it is essential to verify that they are dynamically controllable – executable regardless of the outcomes of uncontrollable durations – and to convert them to a dispatchable form. The previously published FastIDC algorithm achieves this incrementally and can therefore be used efficiently during plan construction. In this paper we show that FastIDC is not sound when new constraints are added, sometimes labeling networks as dynamically controllable when they are not. We analyze the algorithm, pinpoint the cause, and show how the algorithm can be modified to correctly detect uncontrollable networks.

  • 9.
    Nilsson, Mikael
    et al.
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, Faculty of Science & Engineering.
    Kvarnström, Jonas
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, Faculty of Science & Engineering.
    Doherty, Patrick
    Linköping University, Department of Computer and Information Science, Artificial Intelligence and Integrated Computer Systems. Linköping University, Faculty of Science & Engineering.
    Revisiting Classical Dynamic Controllability: A Tighter Complexity Analysis2015In: Agents and Artificial Intelligence: 6th International Conference, ICAART 2014, Angers, France, March 6–8, 2014, Revised Selected Papers / [ed] Béatrice Duval; Jaap van den Herik; Stephane Loiseau; Joaquim Filipe, Springer, 2015, Vol. 8946, 243-261 p.Conference paper (Refereed)
    Abstract [en]

    Simple Temporal Networks with Uncertainty (STNUs) allow the representation of temporal problems where some durations are uncontrollable (determined by nature), as is often the case for actions in planning.  It is essential to verify that such networks are dynamically controllable (DC) -- executable regardless of the outcomes of uncontrollable durations -- and to convert them to an executable form. We use insights from incremental DC verification algorithms to re-analyze the original, classical, verification algorithm. This algorithm is the entry level algorithm for DC verification, based on a less complex and more intuitive theory than subsequent algorithms. We show that with a small modification the algorithm is transformed from pseudo-polynomial to O(n4) which makes it still useful.  We also discuss a change reducing the amount of work performed by the algorithm.

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