Robert Tarjan
Princeton University
H-index: 119
North America-United States
Description
Robert Tarjan, With an exceptional h-index of 119 and a recent h-index of 63 (since 2020), a distinguished researcher at Princeton University, specializes in the field of data structures, graph algorithms, analysis of algorithms.
His recent articles reflect a diverse array of research interests and contributions to the field:
Fast and Simple Sorting Using Partial Information
Minimum-cost paths for electric cars
Digital rights management systems and methods using efficient messaging schemes
A nearly-tight analysis of multipass pairing heaps
Finding strong components using depth-first search
Optimal resizable arrays
Zip-Zip Trees: Making Zip Trees More Balanced, Biased, Compact, or Persistent
Efficiency of Self-Adjusting Heaps
Professor Information
University | Princeton University |
---|---|
Position | Professor of Computer Science |
Citations(all) | 93629 |
Citations(since 2020) | 15587 |
Cited By | 83378 |
hIndex(all) | 119 |
hIndex(since 2020) | 63 |
i10Index(all) | 310 |
i10Index(since 2020) | 171 |
University Profile Page | Princeton University |
Research & Interests List
data structures
graph algorithms
analysis of algorithms
Top articles of Robert Tarjan
Fast and Simple Sorting Using Partial Information
We consider the problem of sorting a set of items having an unknown total order by doing binary comparisons of the items, given the outcomes of some pre-existing comparisons. We present a simple algorithm with a running time of , where , , and are the number of items, the number of pre-existing comparisons, and the number of total orders consistent with the outcomes of the pre-existing comparisons, respectively. The algorithm does comparisons. Our running time and comparison bounds are best possible up to constant factors, thus resolving a problem that has been studied intensely since 1976 (Fredman, Theoretical Computer Science). The best previous algorithm with a bound of on the number of comparisons has a time bound of and is significantly more complicated. Our algorithm combines three classic algorithms: topological sort, heapsort with the right kind of heap, and efficient insertion into a sorted list.
Authors
Bernhard Haeupler,Richard Hladík,John Iacono,Vaclav Rozhon,Robert Tarjan,Jakub Tětek
Journal
arXiv preprint arXiv:2404.04552
Published Date
2024/4/6
Minimum-cost paths for electric cars
An electric car equipped with a battery of a finite capacity travels on a road network with an infrastructure of charging stations. Each charging station has a possibly different cost per unit of energy. Traversing a given road segment requires a specified amount of energy that may be positive, zero or negative. The car can only traverse a road segment if it has enough charge to do so (the charge cannot drop below zero), and it cannot charge its battery beyond its capacity. To travel from one point to another the car needs to choose a travel plan consisting of a path in the network and a recharging schedule that specifies how much energy to charge at each charging station on the path, making sure of having enough energy to reach the next charging station or the destination. The cost of the plan is the total charging cost along the chosen path. We reduce the problem of computing plans between every two junctions of the …
Authors
Dani Dorfman,Haim Kaplan,Robert E Tarjan,Mikkel Thorup,Uri Zwick
Published Date
2024
Digital rights management systems and methods using efficient messaging schemes
This disclosure relates to systems and methods for managing protected electronic content that employ relatively efficient messaging schemes. Rights management architectures are described that may, among other things, provide end-to-end protection of content keys from their point of origination at a content creator and/or content service to end user devices. Certain embodiments may further provide for message protocols where fewer messages are sent in connection with a protected content license request process, thereby reducing latency associated with license request and provisioning processes.
Published Date
2023/11/16
A nearly-tight analysis of multipass pairing heaps
The pairing heap, introduced by Fredman et al. [3], is a self-adjusting heap data structure that is both simple and efficient. A variant introduced in the same paper is the multipass pairing heap. Standard pairing heaps do just two linking passes during delete-min, a pairing pass and an assembly pass. In contrast, multipass pairing heaps do repeated pairing passes, in which nodes are linked in adjacent pairs, until only a minimum-key node remains. We obtain the following amortized time bounds for operations on n-item multipass pairing heaps: O(log n) for delete-min and delete; O(log log n log log log n) for decrease-key; and O(1) for all other heap operations, including insert and meld. This is the first analysis giving an O(log n) bound for delete-min. Our analysis is tight for all operations except possibly decrease-key, for which Fredman [2] and separately Iacono and Ozkan [6] proved an Ω(log log n) lower bound.
Authors
Corwin Sinnamon,Robert E Tarjan
Published Date
2023
Finding strong components using depth-first search
We survey three algorithms that use depth-first search to find the strong components of a directed graph in linear time: (1) Tarjan’s algorithm; (2) a cycle-finding algorithm; and (3) a bidirectional search algorithm.
Authors
Robert E Tarjan,Uri Zwick
Journal
European Journal of Combinatorics
Published Date
2023/10/19
Optimal resizable arrays
A resizable array is an array that can grow and shrink by the addition or removal of items from its end, or both its ends, while still supporting constant-time access to each item stored in the array given its index. Since the size of an array, i.e., the number of items in it, varies over time, space-efficient maintenance of a resizable array requires dynamic memory management. A standard doubling technique allows the maintenance of an array of size N using only O(N) space, with O(1) amortized time, or even O(1) worst-case time, per operation. Sitarski and Brodnik et al. describe much better solutions that maintain a resizable array of size N using only N + O(√N) space, still with O(1) time per operation. Brodnik et al. give a simple proof that this is best possible. We distinguish between the space needed for storing a resizable array, and accessing its items, and the temporary space that may be needed while growing or …
Authors
Robert E Tarjan,Uri Zwick
Published Date
2023
Zip-Zip Trees: Making Zip Trees More Balanced, Biased, Compact, or Persistent
We define simple variants of zip trees, called zip-zip trees, which provide several advantages over zip trees, including overcoming a bias that favors smaller keys over larger ones. We analyze zip-zip trees theoretically and empirically, showing, e.g., that the expected depth of a node in an n-node zip-zip tree is at most , which matches the expected depth of treaps and binary search trees built by uniformly random insertions. Unlike these other data structures, however, zip-zip trees achieve their bounds using only bits of metadata per node, w.h.p., as compared to the bits per node required by treaps. In fact, we even describe a “just-in-time” zip-zip tree variant, which needs just an expected O(1) number of bits of metadata per node. Moreover, we can define zip-zip trees to be strongly history independent, whereas treaps are generally only weakly history independent. We also introduce biased …
Authors
Ofek Gila,Michael T Goodrich,Robert E Tarjan
Published Date
2023/7/28
Efficiency of Self-Adjusting Heaps
Since the invention of the pairing heap by Fredman et al., it has been an open question whether this or any other simple "self-adjusting" heap supports decrease-key operations on -item heaps in time. Using powerful new techniques, we answer this question in the affirmative. We prove that both slim and smooth heaps, recently introduced self-adjusting heaps, support heap operations on an -item heap in the following amortized time bounds: for delete-min and delete, for decrease-key, and for all other heap operations, including insert and meld. We also analyze the multipass pairing heap, a variant of pairing heaps. For this heap implementation, we obtain the same bounds except for decrease-key, for which our bound is . Our bounds significantly improve the best previously known bounds for all three data structures. For slim and smooth heaps our bounds are tight, since they match lower bounds of Iacono and Ozkan; for multipass pairing heaps our bounds are tight except for decrease-key, which by the lower bounds of Fredman and Iacono and \"Ozkan must take amortized time if delete-min takes time.
Authors
Corwin Sinnamon,Robert E Tarjan
Journal
arXiv preprint arXiv:2307.02772
Published Date
2023/7/6
Professor FAQs
What is Robert Tarjan's h-index at Princeton University?
The h-index of Robert Tarjan has been 63 since 2020 and 119 in total.
What are Robert Tarjan's top articles?
The articles with the titles of
Fast and Simple Sorting Using Partial Information
Minimum-cost paths for electric cars
Digital rights management systems and methods using efficient messaging schemes
A nearly-tight analysis of multipass pairing heaps
Finding strong components using depth-first search
Optimal resizable arrays
Zip-Zip Trees: Making Zip Trees More Balanced, Biased, Compact, or Persistent
Efficiency of Self-Adjusting Heaps
...
are the top articles of Robert Tarjan at Princeton University.
What are Robert Tarjan's research interests?
The research interests of Robert Tarjan are: data structures, graph algorithms, analysis of algorithms
What is Robert Tarjan's total number of citations?
Robert Tarjan has 93,629 citations in total.
What are the co-authors of Robert Tarjan?
The co-authors of Robert Tarjan are Mihalis Yannakakis, James B. Orlin, Loukas Georgiadis.