Robert E. Tarjan

Bio: Robert E. Tarjan is an academic researcher from Princeton University. The author has contributed to research in topics: Time complexity & Spanning tree. The author has an hindex of 114, co-authored 400 publications receiving 67305 citations. Previous affiliations of Robert E. Tarjan include AT&T & Massachusetts Institute of Technology.

Software self-checking systems and methods

Abstract: Software self-checking mechanisms are described for improving software tamper resistance and/or reliability. Redundant tests are performed to detect modifications to a program while it is running. Modifications are recorded or reported. Embodiments of the software self-checking mechanisms can be implemented such that they are relatively stealthy and robust, and so that it they are compatible with copy-specific static watermarking and other tamper-resistance techniques.

Maintenance of a minimum spanning forest in a dynamic planar graph

Abstract: : We give efficient algorithms for maintaining a minimum spanning forest of a planar graph subject to on-line modifications. The modifications supported include changes in the edge weights, and insertion and deletion of edges and vertices. To implement the algorithms, we develop a data structure called an edge-ordered dynamic tree, which is a variant of the dynamic tree data structure of Sleator and Tarjan. Using this data structure, our algorithms run in O(log n) time per operation and O(n) space. The algorithms can be used to maintain the connected components of a dynamic planar graph in O(log n) time per operation.

A Note on Finding Minimum-Cost Edge-Disjoint Spanning Trees

Abstract: Let G be an undirected graph with n vertices and m edges, such that each edge has a real-valued cost. We consider the problem of finding a set of k edge-disjoint spanning trees in G of minimum total edge cost. This problem can be solved in polynomial time by the matroid greedy algorithm. We present an implementation of this algorithm that runs in O(m log m + k2n2) time. If all edge costs are the same, the algorithm runs in O(k2n2) time. The algorithm can also be extended to find the largest k such that k edge-disjoint spanning trees exist in O(m2) time. We mention several applications of the algorithm.

Finding minimum-cost flows by double scaling

Abstract: Several researchers have recently developed new techniques that give fast algorithms for the minimum-cost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm log log Ulog(nC)) time on networks with n vertices, m edges, maximum arc capacity U, and maximum arc cost magnitude C. The major techniques used are the capacity-scaling approach of Edmonds and Karp, the excess-scaling approach of Ahuja and Orlin, the cost-scaling approach Goldberg and Tarjan, and the dynamic tree data structure of Sleator and Tarjan. For nonsparse graphs with large maximum arc capacity, we obtain a similar but slightly better bound. We also obtain a slightly better bound for the (noncapacitated) transportation problem. In addition, we discuss a capacity-bounding approach to the minimum-cost flow problem.

Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference

Abstract: From the Publisher: Probabilistic Reasoning in Intelligent Systems is a complete andaccessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertainty—and offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognition—in short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information. Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

Nonlinear dimensionality reduction by locally linear embedding.

Abstract: Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text.

The Design and Analysis of Computer Algorithms

Abstract: From the Publisher: With this text, you gain an understanding of the fundamental concepts of algorithms, the very heart of computer science. It introduces the basic data structures and programming techniques often used in efficient algorithms. Covers use of lists, push-down stacks, queues, trees, and graphs. Later chapters go into sorting, searching and graphing algorithms, the string-matching algorithms, and the Schonhage-Strassen integer-multiplication algorithm. Provides numerous graded exercises at the end of each chapter. 0201000296B04062001

Community detection in graphs

Abstract: The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.