Community Structure in Industrial SAT Instances

Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental process. It is believed that these techniques exploit the underlying structure of industrial instances. However, there are few works trying to exactly characterize the main features of this structure. The research community on complex networks has developed techniques of analysis and algorithms to study real-world graphs that can be used by the SAT community. Recently, there have been some attempts to analyze the structure of industrial SAT instances in terms of complex networks, with the aim of explaining the success of SAT solving techniques, and possibly improving them. In this paper, inspired by the results on complex networks, we study the community structure, or modularity, of industrial SAT instances. In a graph with clear community structure, or high modularity, we can find a partition of its nodes into communities such that most edges connect variables of the same community. In our analysis, we represent SAT instances as graphs, and we show that most application benchmarks are characterized by a high modularity. On the contrary, random SAT instances are closer to the classical Erd\"os-R\'enyi random graph model, where no structure can be observed. We also analyze how this structure evolves by the effects of the execution of a CDCL SAT solver. In particular, we use the community structure to detect that new clauses learned by the solver during the search contribute to destroy the original structure of the formula. This is, learned clauses tend to contain variables of distinct communities

Comparing several heuristics for a packing problem

Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items, into a minimum size rectangular bin, without overlapping. The restriction is that the items cannot be rotated. The current paper is comparing a greedy algorithm with a hybrid genetic algorithm in order to see which technique is better for the given problem. The algorithms are tested on different sizes data.Comment: 5 figures, 2 tables; accepted: International Journal of Advanced Intelligence Paradigm

Architecture of autonomous systems

Automation of Space Station functions and activities, particularly those involving robotic capabilities with interactive or supervisory human control, is a complex, multi-disciplinary systems design problem. A wide variety of applications using autonomous control can be found in the literature, but none of them seem to address the problem in general. All of them are designed with a specific application in mind. In this report, an abstract model is described which unifies the key concepts underlying the design of automated systems such as those studied by the aerospace contractors. The model has been kept as general as possible. The attempt is to capture all the key components of autonomous systems. With a little effort, it should be possible to map the functions of any specific autonomous system application to the model presented here

Strategies for automatic planning: A collection of ideas

The main goal of the Jet Propulsion Laboratory (JPL) is to obtain science return from interplanetary probes. The uplink process is concerned with communicating commands to a spacecraft in order to achieve science objectives. There are two main parts to the development of the command file which is sent to a spacecraft. First, the activity planning process integrates the science requests for utilization of spacecraft time into a feasible sequence. Then the command generation process converts the sequence into a set of commands. The development of a feasible sequence plan is an expensive and labor intensive process requiring many months of effort. In order to save time and manpower in the uplink process, automation of parts of this process is desired. There is an ongoing effort to develop automatic planning systems. This has met with some success, but has also been informative about the nature of this effort. It is now clear that innovative techniques and state-of-the-art technology will be required in order to produce a system which can provide automatic sequence planning. As part of this effort to develop automatic planning systems, a survey of the literature, looking for known techniques which may be applicable to our work was conducted. Descriptions of and references for these methods are given, together with ideas for applying the techniques to automatic planning

Flight Gate Assignment with a Quantum Annealer

Optimal flight gate assignment is a highly relevant optimization problem from airport management. Among others, an important goal is the minimization of the total transit time of the passengers. The corresponding objective function is quadratic in the binary decision variables encoding the flight-to-gate assignment. Hence, it is a quadratic assignment problem being hard to solve in general. In this work we investigate the solvability of this problem with a D-Wave quantum annealer. These machines are optimizers for quadratic unconstrained optimization problems (QUBO). Therefore the flight gate assignment problem seems to be well suited for these machines. We use real world data from a mid-sized German airport as well as simulation based data to extract typical instances small enough to be amenable to the D-Wave machine. In order to mitigate precision problems, we employ bin packing on the passenger numbers to reduce the precision requirements of the extracted instances. We find that, for the instances we investigated, the bin packing has little effect on the solution quality. Hence, we were able to solve small problem instances extracted from real data with the D-Wave 2000Q quantum annealer.Comment: Updated figure

The matching relaxation for a class of generalized set partitioning problems

This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs. Besides providing dual bounds, the relaxations are also used on a variable reduction technique and a matheuristic. We show how that general method can be tailored to sample applications, and also perform a successful computational evaluation with benchmark instances of a problem in maritime logistics.Comment: 33 pages. A preliminary (4-page) version of this paper was presented at CTW 2016 (Cologne-Twente Workshop on Graphs and Combinatorial Optimization), with proceedings on Electronic Notes in Discrete Mathematic

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn