47 research outputs found

    Parameterized Complexity of Finding a Spanning Tree with Minimum Reload Cost Diameter

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    We study the minimum diameter spanning tree problem under the reload cost model (DIAMETER-TREE for short) introduced by Wirth and Steffan (2001). In this problem, given an undirected edge-colored graph G, reload costs on a path arise at a node where the path uses consecutive edges of different colors. The objective is to find a spanning tree of G of minimum diameter with respect to the reload costs. We initiate a systematic study of the parameterized complexity of the DIAMETER-TREE problem by considering the following parameters: the cost of a solution, and the treewidth and the maximum degree Delta of the input graph. We prove that DIAMETER-TREE is para-np-hard for any combination of two of these three parameters, and that it is FPT parameterized by the three of them. We also prove that the problem can be solved in polynomial time on cactus graphs. This result is somehow surprising since we prove DIAMETER-TREE to be NP-hard on graphs of treewidth two, which is best possible as the problem can be trivially solved on forests. When the reload costs satisfy the triangle inequality, Wirth and Steffan (2001) proved that the problem can be solved in polynomial time on graphs with Delta=3, and Galbiati (2008) proved that it is NP-hard if Delta=4. Our results show, in particular, that without the requirement of the triangle inequality, the problem is NP-hard if Delta=3, which is also best possible. Finally, in the case where the reload costs are polynomially bounded by the size of the input graph, we prove that DIAMETER-TREE is in XP and W[1]-hard parameterized by the treewidth plus Delta

    Parameterized complexity of the MINCCA problem on graphs of bounded decomposability

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    In an edge-colored graph, the cost incurred at a vertex on a path when two incident edges with different colors are traversed is called reload or changeover cost. The "Minimum Changeover Cost Arborescence" (MINCCA) problem consists in finding an arborescence with a given root vertex such that the total changeover cost of the internal vertices is minimized. It has been recently proved by G\"oz\"upek et al. [TCS 2016] that the problem is FPT when parameterized by the treewidth and the maximum degree of the input graph. In this article we present the following results for the MINCCA problem: - the problem is W[1]-hard parameterized by the treedepth of the input graph, even on graphs of average degree at most 8. In particular, it is W[1]-hard parameterized by the treewidth of the input graph, which answers the main open problem of G\"oz\"upek et al. [TCS 2016]; - it is W[1]-hard on multigraphs parameterized by the tree-cutwidth of the input multigraph; - it is FPT parameterized by the star tree-cutwidth of the input graph, which is a slightly restricted version of tree-cutwidth. This result strictly generalizes the FPT result given in G\"oz\"upek et al. [TCS 2016]; - it remains NP-hard on planar graphs even when restricted to instances with at most 6 colors and 0/1 symmetric costs, or when restricted to instances with at most 8 colors, maximum degree bounded by 4, and 0/1 symmetric costs.Comment: 25 pages, 11 figure

    A testbed for embedded systems

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    Testing and Debugging are often the most difficult phase of software development. This is especially true of embedded systems which are usually concurrent, have real-time performance and correctness constraints and which execute in the field in an environment which may not permit internal scrutiny of the software behaviour. Although good software engineering practices help, they will never eliminate the need for testing and debugging. This is because failings in the specification and design are often only discovered through testing and understanding these failings and how to correct them comes from debugging. These observations suggest that embedded software should be designed in a way which makes testing and debugging easier and that tools which support these activities are required. Due to the often hostile environment in which the finished embedded system will function, it is necessary to have a platform which allows the software to be developed and tested "in vitro". The Testbed system achieves these goals by providing dynamic modification and process migration facilities for use during development as well as powerful monitoring and background debugging support. These facilities are built on a basic run-time harness supporting an event-driven programming model with a global communication mechanism. This programming model is well suited to the reactive nature of embedded systems. The main research contributions of this work are in the areas of finding deadlock-free, path-optimal routings for networks and of dynamic modification with automated conversion of data which may include pointers

    A comparative analysis of algorithms for satellite operations scheduling

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    Scheduling is employed in everyday life, ranging from meetings to manufacturing and operations among other activities. One instance of scheduling in a complex real-life setting is space mission operations scheduling, i.e. instructing a satellite to perform fitting tasks during predefined time periods with a varied frequency to achieve its mission goals. Mission operations scheduling is pivotal to the success of any space mission, choreographing every task carefully, accounting for technological and environmental limitations and constraints along with mission goals.;It remains standard practice to this day, to generate operations schedules manually ,i.e. to collect requirements from individual stakeholders, collate them into a timeline, compare against feasibility and available satellite resources, and find potential conflicts. Conflict resolution is done by hand, checked by a simulator and uplinked to the satellite weekly. This process is time consuming, bears risks and can be considered sub-optimal.;A pertinent question arises: can we automate the process of satellite mission operations scheduling? And if we can, what method should be used to generate the schedules? In an attempt to address this question, a comparison of algorithms was deemed suitable in order to explore their suitability for this particular application.;The problem of mission operations scheduling was initially studied through literature and numerous interviews with experts. A framework was developed to approximate a generic Low Earth Orbit satellite, its environment and its mission requirements. Optimisation algorithms were chosen from different categories such as single-point stochastic without memory (Simulated Annealing, Random Search), multi-point stochastic with memory (Genetic Algorithm, Ant Colony System, Differential Evolution) and were run both with and without Local Search.;The aforementioned algorithmic set was initially tuned using a single 89-minute Low Earth Orbit of a scientific mission to Mars. It was then applied to scheduling operations during one high altitude Low Earth Orbit (2.4hrs) of an experimental mission.;It was then applied to a realistic test-case inspired by the European Space Agency PROBA-2 mission, comprising a 1 day schedule and subsequently a 7 day schedule - equal to a Short Term Plan as defined by the European Space Agency.;The schedule fitness - corresponding to the Hamming distance between mission requirements and generated schedule - are presented along with the execution time of each run. Algorithmic performance is discussed and put at the disposal of mission operations experts for consideration.Scheduling is employed in everyday life, ranging from meetings to manufacturing and operations among other activities. One instance of scheduling in a complex real-life setting is space mission operations scheduling, i.e. instructing a satellite to perform fitting tasks during predefined time periods with a varied frequency to achieve its mission goals. Mission operations scheduling is pivotal to the success of any space mission, choreographing every task carefully, accounting for technological and environmental limitations and constraints along with mission goals.;It remains standard practice to this day, to generate operations schedules manually ,i.e. to collect requirements from individual stakeholders, collate them into a timeline, compare against feasibility and available satellite resources, and find potential conflicts. Conflict resolution is done by hand, checked by a simulator and uplinked to the satellite weekly. This process is time consuming, bears risks and can be considered sub-optimal.;A pertinent question arises: can we automate the process of satellite mission operations scheduling? And if we can, what method should be used to generate the schedules? In an attempt to address this question, a comparison of algorithms was deemed suitable in order to explore their suitability for this particular application.;The problem of mission operations scheduling was initially studied through literature and numerous interviews with experts. A framework was developed to approximate a generic Low Earth Orbit satellite, its environment and its mission requirements. Optimisation algorithms were chosen from different categories such as single-point stochastic without memory (Simulated Annealing, Random Search), multi-point stochastic with memory (Genetic Algorithm, Ant Colony System, Differential Evolution) and were run both with and without Local Search.;The aforementioned algorithmic set was initially tuned using a single 89-minute Low Earth Orbit of a scientific mission to Mars. It was then applied to scheduling operations during one high altitude Low Earth Orbit (2.4hrs) of an experimental mission.;It was then applied to a realistic test-case inspired by the European Space Agency PROBA-2 mission, comprising a 1 day schedule and subsequently a 7 day schedule - equal to a Short Term Plan as defined by the European Space Agency.;The schedule fitness - corresponding to the Hamming distance between mission requirements and generated schedule - are presented along with the execution time of each run. Algorithmic performance is discussed and put at the disposal of mission operations experts for consideration

    Seventh Biennial Report : June 2003 - March 2005

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