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.

Finding Dominators in Directed Graphs

Abstract: This paper describes an algorithm for finding dominators in an arbitrary directed graph. The algorithm uses depth-first search and efficient algorithms for computing disjoint set unions and manipulating priority queues to achieve a time bound of $O(V\log V + E)$ if V is the number of vertices and E is the number of edges in the graph. This bound compares favorably with the $O(V(V + E))$ time bound of previously known algorithms for finding dominators in arbitrary directed graphs, and with the $O(V + E\log E)$ time bound of a known algorithm for finding dominators in reducible graphs. If $E \geqq V\log V$, the new algorithm requires $O(E)$ time and is optimal to within a constant factor.

Fast exact and heuristic methods for role minimization problems

Abstract: We describe several new bottom-up approaches to problems in role engineering for Role-Based Access Control (RBAC). The salient problems are all NP-complete, even to approximate, yet we find that in instances that arise in practice these problems can be solved in minutes. We first consider role minimization, the process of finding a smallest collection of roles that can be used to implement a pre-existing user-to-permission relation. We introduce fast graph reductions that allow recovery of the solution from the solution to a problem on a smaller input graph. For our test cases, these reductions either solve the problem, or reduce the problem enough that we find the optimum solution with a (worst-case) exponential method. We introduce lower bounds that are sharp for seven of nine test cases and are within 3.4% on the other two. We introduce and test a new polynomial-time approximation that on average yields 2% more roles than the optimum. We next consider the related problem of minimizing the number of connections between roles and users or permissions, and we develop effective heuristic methods for this problem as well. Finally, we propose methods for several related problems.

Sorting Using Networks of Queues and Stacks

Abstract: Inspired by Knuth [2, p. 234], we wish to consider the following problem: Suppose we are presented with the layout of a railroad switchyard (Figure 1 ). I f a train is driven into one end of the yard, what rearrangements of the cars may be made before the train comes out the other end? In order to get a handle on the problem, we must introduce some formalization. A switchyard is an acyclic directed graph, with a unique source and a unique sink (Figure 2). Each vertex represents a siding. The vertex/siding is assumed to have indefinite storage space and may be a stack, a queue, or a deque of some sort (see Knuth [2, p. 234]). A stack is a siding which has the property tha t the last element inserted is the first to be removed. A queue has the proper ty tha t the first element inserted is the first to be removed. In the switchyard, the sidings associated with the source and sink are assumed to be queues. Suppose a finite sequence of numbers s = (sl, s2, • • • , sn) is placed in the source queue of a switchyard (Figure 3). We may rearrange s by moving the elements of s through the switchyard. At each step, an element is moved from some siding to another siding along an arc of the switchyard. After a suitable number of such moves, all elements will be in the sink queue. I f they are in order, smallest to largest, we have sorted the sequence s using the switchyard. We wish to analyze the sequences s which may be sorted in a switchyard Y. We lose nothing in our formalism by allowing storage only on the vertices, and not on the arcs of the switchyard. We ignore questions concerning the finite size of the sidings; assuming small sidings complicates the problem considerably. A circuit in the switchyard will allow us to sort any sequence; thus we do not allow circuits. Having established our model, we proceed to discover its properties.

Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation

Abstract: The relaxed heap is a priority queue data structure that achieves the same amortized time bounds as the Fibonacci heap—a sequence of m decrease_key and n delete_min operations takes time O(m + n log n). A variant of relaxed heaps achieves similar bounds in the worst case—O(1) time for decrease_key and O(log n) for delete_min. Relaxed heaps give a processor-efficient parallel implementation of Dijkstra's shortest path algorithm, and hence other algorithms in network optimization. A relaxed heap is a type of binomial queue that allows heap order to be violated.

Scheduling Unit–Time Tasks with Arbitrary Release Times and Deadlines

Abstract: The basic problem considered is that of scheduling n unit-time tasks, with arbitrary release times and deadlines, so as to minimize the maximum task completion time. Previous work has shown that this problem can be solved rather easily when all release times are integers. We are concerned with the general case in which noninteger release times are allowed, a generalization that considerably increases the difficulty of the problem even for only a single processor. Our results are for the one-processor case, where we provide an $O(n\log n)$ algorithm based on the concept of “forbidden regions”.

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.