In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Example Input: In many combinatorial problems one may need to model the diversity or similarity of sets of assignments. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this type we can use soft variants of the well known AllDifferent and AllEqual constraints. We present a taxonomy of six soft global constraints, generated by combining the two latter ones and the two standard cost functions, which are either maximised or minimised. We characterise the complexity of achieving arc and bounds consistency on these constraints, resolving those cases for which NP-hardness was neither proven nor disproven. In particular, we explore in depth the constraint ensuring that at least k pairs of variables have a common value. We show that achieving arc consistency is NP-hard, however bounds consistency can be achieved in polynomial time through dynamic programming. Moreover, we show that the maximum number of pairs of equal variables can be approximated by a factor of 12 with a linear time greedy algorithm. Finally, we provide a fixed parameter tractable algorithm with respect to the number of values appearing in more than two distinct domains. Interestingly, this taxonomy shows that enforcing equality is harder than enforcing difference.
Example Output: Soft Constraints of Difference and Equality

Example Input: In this paper, we describe a system for generating threedimensional visual simulations of natural language motion expressions. We use a rich formal model of events and their participants to generate simulations that satisfy the minimal constraints entailed by the associated utterance, relying on semantic knowledge of physical objects and motion events. This paper outlines technical considerations and discusses implementing the aforementioned semantic models into such a system.
Example Output: Multimodal Semantic Simulations of Linguistically Underspecified Motion Events

Example Input: An Autonomous Underwater Vehicle (AUV) needs to acquire a certain degree of autonomy for any particular underwater mission to fulfil the mission objectives successfully and ensure its safety in all stages of the mission in a large scale operating filed. In this paper, a novel combinatorial conflict-free-task assignment strategy consisting an interactive engagement of a local path planner and an adaptive global route planner, is introduced. The method is established upon the heuristic search potency of the Particle Swarm Optimization (PSO) algorithm to address the discrete nature of routing-task assignment approach and the complexity of NP-hard path planning problem. The proposed hybrid method, is highly efficient for having a reactive guidance framework that guarantees successful completion of missions specifically in cluttered environments. To examine the performance of the method in a context of mission productivity, mission time management and vehicle safety, a series of simulation studies are undertaken. The results of simulations declare that the proposed method is reliable and robust, particularly in dealing with uncertainties, and it can significantly enhance the level of vehicle’s autonomy by relying on its reactive nature and capability of providing fast feasible solutions. Keywords-Autonomous underwater vehicles, Path planning, Route planning, Autonomy, Evolutionary optimization
Example Output:
Toward Efficient Task Assignment and Motion Planning for Large Scale Underwater Mission