Showing papers by "Robert E. Tarjan published in 2010"
TL;DR: Hewlett-Packard's breadth of product offering has helped the company achieve unparalleled market reach; however, it has co-ordinated efforts to improve the quality of its products and services.
Abstract: Hewlett-Packard (HP) offers many innovative products to meet diverse customer needs. The breadth of its product offering has helped the company achieve unparalleled market reach; however, it has co...
37 citations
TL;DR: In this article, the authors present an experimental study of algorithms for the shortest path feasibility problem, where given a directed weighted graph, find a negative cycle or present a short proof that none exists.
Abstract: This is an experimental study of algorithms for the shortest-path feasibility problem: Given a directed weighted graph, find a negative cycle or present a short proof that none exists. We study previously known and new algorithms. Our testbed is more extensive than those previously used, including both static and incremental problems, as well as worst-case instances. We show that, while no single algorithm dominates, a small subset (including new algorithms) has very robust performance in practice. Our work advances the state of the art in the area.
32 citations
TL;DR: It is observed that a simple, linear-time implementation of dynamic trees is remarkably fast for graphs of small diameter, and that worst-case and randomized data structures are best when queries are very frequent.
Abstract: Dynamic tree data structures maintain forests that change over time through edge insertions and deletions. Besides maintaining connectivity information in logarithmic time, they can support aggregation of information over paths, trees, or both. We perform an experimental comparison of several versions of dynamic trees: ST-trees, ET-trees, RC-trees, and two variants of top trees (self-adjusting and worst-case). We quantify their strengths and weaknesses through tests with various workloads, most stemming from practical applications. We observe that a simple, linear-time implementation is remarkably fast for graphs of small diameter, and that worst-case and randomized data structures are best when queries are very frequent. The best overall performance, however, is achieved by self-adjusting ST-trees.
32 citations
17 Jan 2010
TL;DR: It is shown that rebalancing steps occur with a frequency that is exponentially small in the height of the affected node, and the performance of the structure is theoretically superior to that of many if not all classic balanced tree structures.
Abstract: We address the vexing issue of deletions in balanced trees. Rebalancing after a deletion is generally more complicated than rebalancing after an insertion. Textbooks neglect deletion rebalancing, and many database systems do not do it. We describe a relaxation of AVL trees in which rebalancing is done after insertions but not after deletions, yet access time remains logarithmic in the number of insertions. For many applications of balanced trees, our structure offers performance competitive with that of classical balanced trees. With the addition of periodic rebuilding, the performance of our structure is theoretically superior to that of many if not all classic balanced tree structures. Our structure needs O(log log m) bits of balance information per node, where m is the number of insertions, or O(log log n) with periodic rebuilding, where n is the number of nodes. An insertion takes up to two rotations and O(1) amortized time. Using an analysis that relies on an exponential potential function, we show that rebalancing steps occur with a frequency that is exponentially small in the height of the affected node.
19 citations
01 Jan 2010
TL;DR: In his first lecture, Polya as mentioned in this paper discussed what combinatorics is about: the study of counting various combinations or configurations, and he stated with a problem based on the mystical sign known, appropriately, as an “abracadabra”.
Abstract: January 5. In his first lecture, Polya discussed in general terms what combinatorics is about: The study of counting various combinations or configurations. He stated with a problem based on the mystical sign known, appropriately, as an “abracadabra”.
4 citations
01 Jan 2010
TL;DR: In this paper, Hamiltonian and Eulerian paths and cycles come under the general heading of "de Bruijn sequences" and are named after them rather than de Bruijn, and the specific terms "Hamiltonian" and "Eulerian" are somewhat better known.
Abstract: March 14. Hamiltonian and Eulerian paths and cycles come under the general heading of “de Bruijn sequences”. The specific terms “Hamiltonian” and “Eulerian” are somewhat better known; hence this chapter has been named after them rather than de Bruijn.
1 citations
01 Jan 2010
TL;DR: In this article, the authors consider a set of objects that have various properties, such as α, β, γ, λ, etc., each of the objects may any or none of the properties.
Abstract: Suppose we have a set of N objects that have various properties α, β, γ, … λ. Each of the objects may any or none of the properties. Let Nα be the number of objects that have property α. Some of these objects may have other properties in addition to property α; that doesn’t matter. (In fact, that’s the whole idea!) Similarly, let Nβ be the number of objects that have property β, and so on.