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Problem solving techniques for the design of algorithms

Classics

"By studying the problem-solving techniques that people use to design algorithms we can learn something about building systems that automatically derive algorithms or assist human designers. In this paper we present a model of algorithm design based on our analysis of the protocols of two subjects designing three convex hull algorithms. The subjects work mainly in a data-flow problem space in which the objects are representations of partially specified algorithms. A small number of general-purpose operators construct and modify the representations; these operators are adapted to the current problem state by means-ends analysis. The problem space also includes knowledge-rich schemas such as divide and conquer that subjects incorporate into their algorithms. A particularly versatile problem-solving method in this problem space is symbolic execution, which can be used to refine, verify, or explain components of an algorithm. The subjects also work in a task-domain space about geometry. The interplay between problem solving in the two spaces makes possible the process of discovery. We have observed that the time a subject takes to design an algorithm is proportional to the number of components in the algorithm's data-flow representation. Finally, the details of the problem spaces provide a model for building a robust automated system." Information Processing and Management 20(l-2):97-118.


General branch and bound, and its relation to A* and AO*

Classics

Branch and Bound (B&B) is a problem-solving technique which is widely used for various problems encountered in operations research and combinatorial mathematics. Various heuristic search procedures used in artificial intelligence (AI) are considered to be related to B&B procedures. However, in the absence of any generally accepted terminology for B&B procedures, there have been widely differing opinions regarding the relationships between these procedures and B&B. This paper presents a formulation of B&B general enough to include previous formulations as special cases, and shows how two well-known AI search procedures (A∗ and AO∗) are special cases of this general formulation.


RULEMASTER: A second-generation knowledge-engineering facility

Classics

Simulation and expert systems are remarkably similar. Both employ various representations to model some aspect of an uncertain world, with the model being formed as a piece of com puter software. This is then employed to aid decision making. Ideas about combining simulation and expert systems are presented, and a taxonomy is developed. It is concluded that the most fruitful areas of cross-fertilization are advice-giving ex pert systems that assist the simulation scientist and simulation user, new simulation tools built from knowledge-based tools, and intelligent front ends for simulation packages. Advice-giving systems will increasingly be part of simulation environments, rather than stand alone.



Universal coding, information, prediction, and estimation

Classics

A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity.


Towards Chunking as a General Learning Mechanism

Classics

"Chunks have long been proposed as a basic organizational unit for human memory. More recently chunks have been used to model human learning on simple perceptual-motor skills. In this paper we describe recent progress in extending chunking to be a general learning mechanism by implementing it within a general problem solver. Using the Soar problem-solving architecture, we take significant steps toward a general problem solver that can learn about all aspects of its behavior. We demonstrate chunking in Soar on three tasks: the Eight Puzzle, Tic-Tat-Toe, and a part of the RI computer-configuration task. Not only is there improvement with practice, but chunking also produces significant transfer of learned behavior, and strategy acquisition."Proceedings of the AAAi-84 National Conference. AAAI, University of Texas at Austin, TX, August, 1984.



Heuristics: Intelligent Search Strategies for Computer Problem Solving

Classics

Optical transport networks based on wavelength division multiplexing (WDM) are considered to be the most appropriate choice for future Internet backbone. On the other hand, future DOE networks are expected to have the ability to dynamically provision on-demand survivable services to suit the needs of various high performance scientific applications and remote collaboration. Since a failure in aWDMnetwork such as a cable cut may result in a tremendous amount of data loss, efficient protection of data transport in WDM networks is therefore essential. As the backbone network is moving towards GMPLS/WDM optical networks, the unique requirement to support DOE's sciencemore » mission results in challenging issues that are not directly addressed by existing networking techniques and methodologies. The objectives of this project were to develop cost effective protection and restoration mechanisms based on dedicated path, shared path, preconfigured cycle (p-cycle), and so on, to deal with single failure, dual failure, and shared risk link group (SRLG) failure, under different traffic and resource requirement models; to devise efficient service provisioning algorithms that deal with application specific network resource requirements for both unicast and multicast; to study various aspects of traffic grooming in WDM ring and mesh networks to derive cost effective solutions while meeting application resource and QoS requirements; to design various diverse routing and multi-constrained routing algorithms, considering different traffic models and failure models, for protection and restoration, as well as for service provisioning; to propose and study new optical burst switched architectures and mechanisms for effectively supporting dynamic services; and to integrate research with graduate and undergraduate education.


A new polynomial-time algorithm for linear programming

Classics

We present a new polynomial-time algorithm for linear programming. The running-time of this algorithm is O(n3-5L2), as compared to O(n6L2) for the ellipsoid algorithm. We prove that given a polytope P and a strictly interior point a ε P, there is a projective transformation of the space that maps P, a to P', a' having the following property. The ratio of the radius of the smallest sphere with center a', containing P' to the radius of the largest sphere with center a' contained in P' is O (n). The algorithm consists of repeated application of such projective transformations each followed by optimization over an inscribed sphere to create a sequence of points which converges to the optimal solution in polynomial-time.