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.

Space-Efficient Implementations of Graph Search Methods

Abstract: Several space-efficmnt implementations of the two most common and useful kinds of graph search, namely, breadth-first search and depth-first search, are discussed. A straightforward implementation of each method requires n bits and n + O(1) pointers of auxiliary storage, where n is the number of vertices in the graph. We devise methods that need only 2n + m bits, of which m are read-only, where rn is the number of edges in the graph. We save space by folding the queue or stack required by the search into the graph representation; two of our methods for depth-first search are variants of the Deutsch-Schorr-Waite list-marking algorithm. Our algorithms are expressed in a version of Dijkstra's guarded command language.

Minimum cost flows in graphs with unit capacities

Abstract: We consider the minimum cost flow problem on graphs with unit capacities and its special cases. In previous studies, special purpose algorithms exploiting the fact that capacities are one have been developed. In contrast, for maximum flow with unit capacities, the best bounds are proven for slight modifications of classical blocking flow and push-relabel algorithms. In this paper we show that the classical cost scaling algorithms of Goldberg and Tarjan (for general integer capacities) applied to a problem with unit capacities achieve or improve the best known bounds. For weighted bipartite matching we establish a bound of O(\sqrt{rm}\log C) on a slight variation of this algorithm. Here r is the size of the smaller side of the bipartite graph, m is the number of edges, and C is the largest absolute value of an arc-cost. This simplifies a result of [Duan et al. 2011] and improves the bound, answering an open question of [Tarjan and Ramshaw 2012]. For graphs with unit vertex capacities we establish a novel O(\sqrt{n}m\log(nC)) bound. We also give the first cycle canceling algorithm for minimum cost flow with unit capacities. The algorithm naturally generalizes the single source shortest path algorithm of [Goldberg 1995].

Dominator Certification and Independent Spanning Trees: An Experimental Study

Abstract: We present the first implementations of certified algorithms for computing dominators, and exhibit their efficiency experimentally on graphs taken from a variety of applications areas. The certified algorithms are obtained by augmenting dominator-finding algorithms to compute a certificate of correctness that is easy to verify. A suitable certificate for dominators is obtained from the concepts of low-high orders and independent spanning trees. Therefore, our implementations provide efficient constructions of these concepts as well, which are interesting in their own right. Furthermore, we present an experimental study of efficient algorithms for computing dominators on large graphs.

Deletion without rebalancing in multiway search trees

Abstract: Some database systems that use a form of B-tree for the underlying data structure do not do rebalancing on deletion. This means that a bad sequence of deletions can create a very unbalanced tree. Yet such databases perform well in practice. Avoidance of rebalancing on deletion has been justified empirically and by average-case analysis, but to our knowledge, no worst-case analysis has been done. We do such an analysis. We show that the tree height remains logarithmic in the number of insertions, independent of the number of deletions. Furthermore, the amortized time for an insertion or deletion, excluding the search time, is O(1), and nodes are modified by insertions and deletions with a frequency that is exponentially small in their height. The latter results do not hold for standard B-trees. By adding periodic rebuilding of the tree, we obtain a data structure that is theoretically superior to standard B-trees in many ways. Our results suggest that rebalancing on deletion not only is unnecessary but may be harmful.

Linear expected-time algorithms for connectivity problems (Extended Abstract)

Abstract: Researchers in recent years have developed many graph algorithms that are fast in the worst case, but little work has been done on graph algorithms that are fast on the average. (Exceptions include the work of Angluin and Valiant [1], Karp [7], and Schnorr [9].) In this paper we analyze the expected running time of four algorithms for solving graph connectivity problems. Our goal is to exhibit algorithms whose expected time is within a constant factor of optimum and to shed light on the properties of random graphs. In Section 2 we develop and analyze a simple algorithm that finds the connected components of an undirected graph with n vertices in O(n) expected time. In Sections 3 and 4 we describe algorithms for finding the strong components of a directed graph and the blocks of an undirected graph in O(n) expected time. The time required for these three problems is Ω(m) in the worst case, where m is the number of edges in the graph, since all edges must be examined; but our results show that only O(n) edges must be examined on the average.*

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.