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LinearTime PointerMachine Algorithms for Least Common Ancestors, MST Verification, and Dominators
 IN PROCEEDINGS OF THE THIRTIETH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1998
"... We present two new data structure toolsdisjoint set union with bottomup linking, and pointerbased radix sortand combine them with bottomlevel microtrees to devise the first lineartime pointermachine algorithms for offline least common ancestors, minimum spanning tree (MST) verification, ..."
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Cited by 29 (4 self)
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We present two new data structure toolsdisjoint set union with bottomup linking, and pointerbased radix sortand combine them with bottomlevel microtrees to devise the first lineartime pointermachine algorithms for offline least common ancestors, minimum spanning tree (MST) verification, randomized MST construction, and computing dominators in a flowgraph.
A New, Simpler LinearTime Dominators Algorithm
 ACM Transactions on Programming Languages and Systems
, 1998
"... this article is organized as follows. Section 2 outlines Lengauer and Tarjan's approach. Section 3 gives a broad overview of our algorithm and dierentiates it from previous work. Section 4 presents our algorithm in detail, and Section 5 analyzes its running time. Section 6 presents our new path ..."
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Cited by 25 (5 self)
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this article is organized as follows. Section 2 outlines Lengauer and Tarjan's approach. Section 3 gives a broad overview of our algorithm and dierentiates it from previous work. Section 4 presents our algorithm in detail, and Section 5 analyzes its running time. Section 6 presents our new pathcompression result, on which the analysis relies. Section 7 describes our implementation, and Section 8 reports experimental results. We conclude in Section 9
Splay trees, DavenportSchinzel sequences, and the deque conjecture
, 2007
"... We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence S, none of whose subsequences are isomorphic to fixed forbidden subsequence. We direct ..."
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Cited by 20 (6 self)
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We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence S, none of whose subsequences are isomorphic to fixed forbidden subsequence. We direct this technique towards Tarjan’s deque conjecture and prove that n deque operations require O(nα ∗ (n)) time, where α ∗ (n) is the minimum number of applications of the inverseAckermann function mapping n to a constant. We are optimistic that this approach could be directed towards other open conjectures on splay trees such as the traversal and split conjectures.
Data Structural Bootstrapping, Linear Path Compression, and Catenable Heap Ordered Double Ended Queues
 SIAM Journal on Computing
, 1992
"... A deque with heap order is a linear list of elements with realvalued keys which allows insertions and deletions of elements at both ends of the list. It also allows the findmin (equivalently findmax) operation, which returns the element of least (greatest) key, but it does not allow a general delet ..."
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Cited by 19 (7 self)
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A deque with heap order is a linear list of elements with realvalued keys which allows insertions and deletions of elements at both ends of the list. It also allows the findmin (equivalently findmax) operation, which returns the element of least (greatest) key, but it does not allow a general deletemin (deletemax) operation. Such a data structure is also called a mindeque (maxdeque) . Whereas implementing mindeques in constant time per operation is a solved problem, catenating mindeques in sublogarithmic time has until now remained open. This paper provides an efficient implementation of catenable mindeques, yielding constant amortized time per operation. The important algorithmic technique employed is an idea which is best described as data structural bootstrapping: We abstract mindeques so that their elements represent other mindeques, effecting catenation while preserving heap order. The efficiency of the resulting data structure depends upon the complexity of a special case of pa...
A new framework for exhaustive and incremental data flow analysis using DJ graphs
 ACM SIGPLAN CONF. ON PLDI
, 1995
"... In this paper we propose a new framework for eliminationbased exhaustive and incremental data flow analysis using DJ graphs. In this paper we give an overview of our framework. The details can be found in our two long reports [SGL95a, SG95a]. These two reports are available from our WWW URL http:/ ..."
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Cited by 12 (0 self)
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In this paper we propose a new framework for eliminationbased exhaustive and incremental data flow analysis using DJ graphs. In this paper we give an overview of our framework. The details can be found in our two long reports [SGL95a, SG95a]. These two reports are available from our WWW URL http://wwwacaps.cs.mcgill.ca/~sreedhar/pubs.html OR http://wwwacaps.cs.mcgill.ca/doc/memos.html
Applications of forbidden 01 matrices to search tree and path compression based data structures
, 2009
"... In this paper we improve, reprove, and simplify a variety of theorems concerning the performance of data structures based on path compression and search trees. We apply a technique very familiar to computational geometers but still foreign to many researchers in (nongeometric) algorithms and data s ..."
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Cited by 7 (5 self)
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In this paper we improve, reprove, and simplify a variety of theorems concerning the performance of data structures based on path compression and search trees. We apply a technique very familiar to computational geometers but still foreign to many researchers in (nongeometric) algorithms and data structures, namely, to bound the complexity of an object via its forbidden substructures. To analyze an algorithm or data structure in the forbidden substructure framework one proceeds in three discrete steps. First, one transcribes the behavior of the algorithm as some combinatorial object M; for example, M may be a graph, sequence, permutation, matrix, set system, or tree. (The size of M should ideally be linear in the running time.) Second, one shows that M excludes some forbidden substructure P, and third, one bounds the size of any object avoiding this substructure. The power of this framework derives from the fact that M lies in a more pristine environment and that upper bounds on the size of a Pfree object M may be reused in different contexts. All of our proofs begin by transcribing the individual operations of a dynamic data structure
Efficient data flow analysis using DJgraphs: Elimination methods revisited
, 1995
"... In this paper we present a new approach to elimination based data flow analysis that uses a program representation called the DJ Graph. The skeleton of the DJ graph of a program is the dominator tree of its flowgraph (whose edges are called D edges in this paper), and the tree skeleton is augmented ..."
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Cited by 3 (3 self)
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In this paper we present a new approach to elimination based data flow analysis that uses a program representation called the DJ Graph. The skeleton of the DJ graph of a program is the dominator tree of its flowgraph (whose edges are called D edges in this paper), and the tree skeleton is augmented with join edges (called J edges in this paper). Unlike the previous elimination methods, which first reduce a flowgraph to a single node, our approach only eliminate J edges from the DJ graph in a bottomup fashion during the reduction process, while maintainting the dominator tree structure (which may be compressed). We propose two methods for eliminating variables: (1) eager elimination method, and (2) delayed elimination method. With eager elimination, we first perform variable elimination on the DJgraph in a bottomup manner. Once we determine the solution for the root node, we propagate this information in a topdown fashion on the dominator tree and determine the corresponding solutio...
HewlettPackard Company and
"... In this article, we present a new framework for eliminationbased exhaustive and incremental data ow analysis using the DJ graph representation of a program. Unlike previous approaches to eliminationbased incremental data
ow analysis, our approach can handle arbitrary structural and nonstructural ..."
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In this article, we present a new framework for eliminationbased exhaustive and incremental data ow analysis using the DJ graph representation of a program. Unlike previous approaches to eliminationbased incremental data
ow analysis, our approach can handle arbitrary structural and nonstructural changes to program
owgraphs, including irreducibility. We show how our approach is related to dominance frontiers, and we exploit this relationship to establish the complexity of our exhaustive analysis and to aid the design of our incremental analysis.
and the Deque Conjecture
"... We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence, none of whose subsequences are isomorphic to a fixed forbidden subsequence. We direct ..."
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We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence, none of whose subsequences are isomorphic to a fixed forbidden subsequence. We direct this technique towards Tarjan’s deque conjecture and prove that n deque operations take only O(nα ∗ (n)) time, where α ∗ (n) is the minimum number of applications of the inverseAckermann function mapping n to a constant. We are optimistic that this approach could be directed towards other open conjectures on splay trees such as the traversal and split conjectures. 1
LBNL59102 Two Strategies to Speed up Connected Component Labeling Algorithms
"... Abstract — This paper presents two new strategies to speed up connected component labeling algorithms. The first strategy employs a decision tree to minimize the work performed in the scanning phase of connected component labeling algorithms. The second strategy uses a simplified unionfind data str ..."
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Abstract — This paper presents two new strategies to speed up connected component labeling algorithms. The first strategy employs a decision tree to minimize the work performed in the scanning phase of connected component labeling algorithms. The second strategy uses a simplified unionfind data structure to represent the equivalence information among the labels. For 8connected components in a twodimensional (2D) image, the first strategy reduces the number of neighboring pixels visited from 4 to 7/3 on average. In various tests, using a decision tree decreases the scanning time by a factor of about 2. The second strategy uses a compact representation of the unionfind data structure. This strategy significantly speeds up the labeling algorithms. We prove analytically that a labeling algorithm with our simplified unionfind structure has the same optimal theoretical time complexity as do the best labeling algorithms. By extensive experimental measurements, we confirm the expected performance characteristics of the new labeling algorithms and demonstrate that they are faster than other optimal labeling algorithms. Index Terms — Connected component labeling, optimization, unionfind algorithm, decision tree, equivalence relation. I.