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.

Ex Input:
In this paper we present an interface between a symbolic planner and a geometric task planner, which is different to a standard trajectory planner in that the former is able to perform geometric reasoning on abstract entitiestasks. We believe that this approach facilitates a more principled interface to symbolic planning, while also leaving more room for the geometric planner to make independent decisions. We show how the two planners could be interfaced, and how their planning and backtracking could be interleaved. We also provide insights for a methodology for using the combined system, and experimental results to use as a benchmark with future extensions to both the combined system, as well as to the geometric task planner.

Ex Output:
Towards Combining HTN Planning and Geometric Task Planning

Ex Input:
We consider the problem of repeatedly solving a variant of the same dynamic programming problem in successive trials. An instance of the type of problems we consider is to find the optimal binary search tree. At the beginning of each trial, the learner probabilistically chooses a tree with the n keys at the internal nodes and the n+ 1 gaps between keys at the leaves. It is then told the frequencies of the keys and gaps and is charged by the average search cost for the chosen tree. The problem is online because the frequencies can change between trials. The goal is to develop algorithms with the property that their total average search cost (loss) in all trials is close to the total loss of the best tree chosen in hind sight for all trials. The challenge, of course, is that the algorithm has to deal with exponential number of trees. We develop a methodology for tackling such problems for a wide class of dynamic programming algorithms. Our framework allows us to extend online learning algorithms like Hedge [9] and Component Hedge [15] to a significantly wider class of combinatorial objects than was possible before.

Ex Output:
Online Dynamic Programming

Ex Input:
We present algorithms for generating alternative solutions for explicit acyclic AND/OR structures in non-decreasing order of cost. The proposed algorithms use a best first search technique and report the solutions using an implicit representation ordered by cost. In this paper, we present two versions of the search algorithm (a) an initial version of the best first search algorithm, ASG, which may present one solution more than once while generating the ordered solutions, and (b) another version, LASG, which avoids the construction of the duplicate solutions. The actual solutions can be reconstructed quickly from the implicit compact representation used. We have applied the methods on a few test domains, some of them are synthetic while the others are based on well known problems including the search space of the 5-peg Tower of Hanoi problem, the matrix-chain multiplication problem and the problem of finding secondary structure of RNA. Experimental results show the efficacy of the proposed algorithms over the existing approach. Our proposed algorithms have potential use in various domains ranging from knowledge based frameworks to service composition, where the AND/OR structure is widely used for representing problems.

Ex Output:
Algorithms for Generating Ordered Solutions for Explicit AND/OR Structures