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12
SelfAdjusting Computation
 In ACM SIGPLAN Workshop on ML
, 2005
"... From the algorithmic perspective, we describe novel data structures for tracking the dependences ina computation and a changepropagation algorithm for adjusting computations to changes. We show that the overhead of our dependence tracking techniques is O(1). To determine the effectiveness of change ..."
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Cited by 35 (13 self)
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From the algorithmic perspective, we describe novel data structures for tracking the dependences ina computation and a changepropagation algorithm for adjusting computations to changes. We show that the overhead of our dependence tracking techniques is O(1). To determine the effectiveness of changepropagation, we present an analysis technique, called trace stability, and apply it to a number of applications.
An experimental analysis of selfadjusting computation
 In Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI
, 2006
"... Selfadjusting computation uses a combination of dynamic dependence graphs and memoization to efficiently update the output of a program as the input changes incrementally or dynamically over time. Related work showed various theoretical results, indicating that the approach can be effective for a r ..."
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Cited by 34 (18 self)
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Selfadjusting computation uses a combination of dynamic dependence graphs and memoization to efficiently update the output of a program as the input changes incrementally or dynamically over time. Related work showed various theoretical results, indicating that the approach can be effective for a reasonably broad range of applications. In this article, we describe algorithms and implementation techniques to realize selfadjusting computation and present an experimental evaluation of the proposed approach on a variety of applications, ranging from simple list primitives to more sophisticated computational geometry algorithms. The results of the experiments show that the approach is effective in practice, often offering orders of magnitude speedup from recomputing the output from scratch. We believe this is the first experimental evidence that incremental computation of any type is effective in practice for a reasonably broad set of applications.
An Experimental Analysis of Change Propagation in Dynamic Trees
, 2005
"... Change propagation is a technique for automatically adjusting the output of an algorithm to changes in the input. The idea behind change propagation is to track the dependences between data and function calls, so that, when the input changes, functions affected by that change can be reexecuted to u ..."
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Cited by 20 (12 self)
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Change propagation is a technique for automatically adjusting the output of an algorithm to changes in the input. The idea behind change propagation is to track the dependences between data and function calls, so that, when the input changes, functions affected by that change can be reexecuted to update the computation and the output. Change propagation makes it possible for a compiler to dynamize static algorithms. The practical effectiveness of change propagation, however, is not known. In particular, the cost of dependence tracking and change propagation may seem significant. The contributions of the paper are twofold. First, we present some experimental evidence that change propagation performs well when compared to direct implementations of dynamic algorithms. We implement change propagation on treecontraction as a solution to the dynamic trees problem and present an experimental evaluation of the approach. As a second contribution, we present a library for dynamictrees that support a general interface and present an experimental evaluation by considering a broad set of applications. The dynamictrees library relies on change propagation to handle edge insertions/deletions. The applications that we consider include path queries, subtree queries, leastcommonancestor queries, maintenance of centers and medians of trees, nearestmarkedvertex queries, semidynamic minimum spanning trees, and the maxflow algorithm of Sleator and Tarjan.
Dynamic parallel tree contraction
 In Proceedings 5th Annual ACM Symp. on Parallel Algorithms and Architectures
, 1994
"... Parallel tree contraction has been found to be a useful and quite powerful tool for the design of a wide class of efficient graph algorithms. We propose a corresponding technique for the parallel solution of problems with incremental changes in the data. In dynamic tree contraction problems, we are ..."
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Cited by 16 (2 self)
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Parallel tree contraction has been found to be a useful and quite powerful tool for the design of a wide class of efficient graph algorithms. We propose a corresponding technique for the parallel solution of problems with incremental changes in the data. In dynamic tree contraction problems, we are given an initial tree T, and then an online algorithm processes requests regarding T. Requests may be either incremental changes to T or requests for certain values computed using the tree. A simple example is maintaining the preorder numbering on a tree. The online algorithm would then have to handle incremental changes to the tree, and would also have to quickly answer queries about the preorder number of any tree node. Our dynamic algorithms are based on the prior parallel tree contraction algorithms, and hence we call such algorithms incremental tree contraction algorithms. By maintaining the connection between our incremental algorithms and the parallel tree contraction algorithm, we create incremental algorithms for tree contraction. We consider a dynamic binary tree T of ≤ n nodes and unbounded depth. We describe a procedure, which we call the dynamic parallel tree contraction algorithm, which incrementally processes various parallel modification requests and queries: (1) parallel requests to add or delete leaves of T, or modify labels of internal nodes or leaves of T, and also (2) parallel tree contraction queries which require recomputing values at specified nodes. Each modification or query is with respect to a set of nodes U in T. We make use of a random splitting tree as an aid
Maintaining Center and Median in Dynamic Trees
, 2000
"... We show how to maintain centers and medians for a collection of dynamic trees where edges may be inserted and deleted and node and edge weights may be changed. All updates are supported in O(log n) time, where n is the size of the tree(s) involved in the update. ..."
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Cited by 16 (3 self)
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We show how to maintain centers and medians for a collection of dynamic trees where edges may be inserted and deleted and node and edge weights may be changed. All updates are supported in O(log n) time, where n is the size of the tree(s) involved in the update.
Maintaining information in fullydynamic trees with top trees
 ACM Transactions on Algorithms
, 2003
"... We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fullydynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we show how to maintain the diameter, center, and median of eac ..."
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Cited by 12 (0 self)
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We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fullydynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we show how to maintain the diameter, center, and median of each tree in the forest. The forest can be updated by insertion and deletion of edges and by changes to vertex and edge weights. Each update is supported in O(log n) time, where n is the size of the tree(s) involved in the update. Also, we show how to support nearest common ancestor queries and level ancestor queries with respect to arbitrary roots in O(log n) time. Finally, with marked and unmarked vertices, we show how to compute distances to a nearest marked vertex. The later has applications to approximate nearest marked vertex in general graphs, and thereby to static optimization problems over shortest path metrics. Technically speaking, top trees are easily implemented either with Frederickson’s topology trees [Ambivalent Data Structures for Dynamic 2EdgeConnectivity and k Smallest Spanning Trees, SIAM J. Comput. 26 (2) pp. 484–538, 1997] or with Sleator and Tarjan’s dynamic
Clustering for Faster Network Simplex Pivots
, 2000
"... We show how to use a combination of treeclustering techniques and computational geometry to improve the time bounds for optimal pivot selection in the primal network simplex algorithm for minimumcost flow and related problems and for pivot execution in the dual network simplex algorithm, from O(m) ..."
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Cited by 7 (2 self)
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We show how to use a combination of treeclustering techniques and computational geometry to improve the time bounds for optimal pivot selection in the primal network simplex algorithm for minimumcost flow and related problems and for pivot execution in the dual network simplex algorithm, from O(m) to O (√m) per pivot. Our techniques can also speed up network simplex algorithms for generalized flow, shortest paths with negative edges, maximum flow, the assignment problem, and the transshipment problem.
Dynamic Trees in Practice ⋆
"... 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 seve ..."
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Cited by 5 (1 self)
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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: STtrees, ETtrees, RCtrees, and two variants of top trees (selfadjusting and worstcase). We quantify their strengths and weaknesses through tests with various workloads, most stemming from practical applications. We observe that a simple, lineartime implementation is remarkably fast for graphs of small diameter, and that worstcase and randomized data structures are best when queries are very frequent. The best overall performance, however, is achieved by selfadjusting STtrees. 1
Design and Analysis of Data Structures for Dynamic Trees
, 2006
"... The dynamic trees problem is that of maintaining a forest that changes over time through edge insertions and deletions. We can associate data with vertices or edges and manipulate this data, individually or in bulk, with operations that deal with whole paths or trees. Efficient solutions to this pr ..."
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Cited by 5 (1 self)
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The dynamic trees problem is that of maintaining a forest that changes over time through edge insertions and deletions. We can associate data with vertices or edges and manipulate this data, individually or in bulk, with operations that deal with whole paths or trees. Efficient solutions to this problem have numerous applications, particularly in algorithms for network flows and dynamic graphs in general. Several data structures capable of logarithmictime dynamic tree operations have been proposed. The first was Sleator and Tarjan’s STtree, which represents a partition of the tree into paths. Although reasonably fast in practice, adapting STtrees to different applications is nontrivial. Frederickson’s topology trees, Alstrup et al.’s top trees, and Acar et al.’s RCtrees are based on tree contractions: they progressively combine vertices or edges to obtain a hierarchical representation of the tree. This approach is more flexible in theory, but all known implementations assume the trees have bounded degree; arbitrary trees are supported only after ternarization. This thesis shows how these two approaches can be combined (with very little overhead) to produce a data structure that is at least as generic as any other, very easy to
SelfAdjusting Computation with Delta ML
"... Abstract. In selfadjusting computation, programs respond automatically and efficiently to modifications to their data by tracking the dynamic data dependences of the computation and incrementally updating the output as needed. In this tutorial, we describe the selfadjustingcomputation model and pr ..."
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Cited by 2 (0 self)
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Abstract. In selfadjusting computation, programs respond automatically and efficiently to modifications to their data by tracking the dynamic data dependences of the computation and incrementally updating the output as needed. In this tutorial, we describe the selfadjustingcomputation model and present the language ∆ML (Delta ML) for writing selfadjusting programs. 1