Results 1  10
of
16
Soft kinetic data structures
 In SODA ’01: Proceedings of the twelfth annual ACMSIAM symposium on Discrete algorithms
"... We introduce the framework of soft kinetic data structures (SKDS). A soft kinetic data structure is an approximate data structure that can be used to answer queries on a set of moving objects with unpredictable motion. We analyze the quality of a soft kinetic data structure by giving a competitive a ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
(Show Context)
We introduce the framework of soft kinetic data structures (SKDS). A soft kinetic data structure is an approximate data structure that can be used to answer queries on a set of moving objects with unpredictable motion. We analyze the quality of a soft kinetic data structure by giving a competitive analysis with respect to the dynamics of the system. We illustrate our approach by presenting soft kinetic data structures for maintaining classical data structures: sorted arrays, balanced search trees, heaps, and range trees. We also describe soft kinetic data structures for maintaining the Euclidean minimum spanning trees. 1 Introduction. The need of storing and processing continuously moving data arises in a broad variety of applications, including
Minimizing Randomness in Minimum Spanning Tree, Parallel Connectivity, and Set Maxima Algorithms
 In Proc. 13th Annual ACMSIAM Symposium on Discrete Algorithms (SODA'02
, 2001
"... There are several fundamental problems whose deterministic complexity remains unresolved, but for which there exist randomized algorithms whose complexity is equal to known lower bounds. Among such problems are the minimum spanning tree problem, the set maxima problem, the problem of computing conne ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
There are several fundamental problems whose deterministic complexity remains unresolved, but for which there exist randomized algorithms whose complexity is equal to known lower bounds. Among such problems are the minimum spanning tree problem, the set maxima problem, the problem of computing connected components and (minimum) spanning trees in parallel, and the problem of performing sensitivity analysis on shortest path trees and minimum spanning trees. However, while each of these problems has a randomized algorithm whose performance meets a known lower bound, all of these randomized algorithms use a number of random bits which is linear in the number of operations they perform. We address the issue of reducing the number of random bits used in these randomized algorithms. For each of the problems listed above, we present randomized algorithms that have optimal performance but use only a polylogarithmic number of random bits; for some of the problems our optimal algorithms use only log n random bits. Our results represent an exponential savings in the amount of randomness used to achieve the same optimal performance as in the earlier algorithms. Our techniques are general and could likely be applied to other problems.
Approximate Sorting ⋆
"... Abstract. We show that any randomized algorithm to approximate any given ranking of n items within expected Spearman’s footrule distance n 2 /ν(n) needs at least n (min{log ν(n), log n} − 6) comparisons. This bound is tight up to a constant factor since there exists a deterministic algorithm that s ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We show that any randomized algorithm to approximate any given ranking of n items within expected Spearman’s footrule distance n 2 /ν(n) needs at least n (min{log ν(n), log n} − 6) comparisons. This bound is tight up to a constant factor since there exists a deterministic algorithm that shows that 6n(log ν(n) + 1) comparisons are always sufficient. Keywords. Sorting, Ranking, Spearman’s footrule metric, Kendall’s tau metric
An InverseAckermann Style Lower Bound for Online Minimum Spanning Tree Verification
 Combinatorica
"... 1 Introduction The minimum spanning tree (MST) problem has seen a flurry of activity lately, driven largely by the success of a new approach to the problem. The recent MST algorithms [20, 8, 29, 28], despite their superficial differences, are all based on the idea of progressively improving an appro ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
1 Introduction The minimum spanning tree (MST) problem has seen a flurry of activity lately, driven largely by the success of a new approach to the problem. The recent MST algorithms [20, 8, 29, 28], despite their superficial differences, are all based on the idea of progressively improving an approximately minimum solution, until the actual minimum spanning tree is found. It is still likely that this progressive improvement approach will bear fruit. However, the current
A Simpler Implementation and Analysis of Chazelle’s Soft Heaps
 In Proc. of the 19th ACMSIAM Symposium on Discrete Algorithms
, 2009
"... Chazelle (JACM 47(6), 2000) devised an approximate meldable priority queue data structure, called Soft Heaps, and used it to obtain the fastest known deterministic comparisonbased algorithm for computing minimum spanning trees, as well as some new algorithms for selection and approximate sorting pr ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Chazelle (JACM 47(6), 2000) devised an approximate meldable priority queue data structure, called Soft Heaps, and used it to obtain the fastest known deterministic comparisonbased algorithm for computing minimum spanning trees, as well as some new algorithms for selection and approximate sorting problems. If n elements are inserted into a collection of soft heaps, then up to εn of the elements still contained in these heaps, for a given error parameter ε, maybecorrupted, i.e., have their keys artificially increased. In exchange for allowing these corruptions, each soft heap operation is performed in O(log 1 ε) amortized time. Chazelle’s soft heaps are derived from the binomial heaps data structure in which each priority queue is composed of a collection of binomial trees. We describe a simpler and more direct implementation of soft heaps in which each priority queue is composed of a collection of standard binary trees. Our implementation has the advantage that no cleanup operations similar to the ones used in Chazelle’s implementation are required. We also present a concise and unified potentialbased amortized analysis of the new implementation. 1
An InverseAckermann Type Lower Bound for Online Minimum Spanning Tree Verification
 Combinatorica
"... Given a spanning tree T of some graph G, the problem of minimum spanning tree verication is to decide whether T = MST(G). A celebrated result of Komlos shows that this problem can be solved in linear time. Somewhat unexpectedly, MST verication turns out to be useful in actually computing minimum spa ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Given a spanning tree T of some graph G, the problem of minimum spanning tree verication is to decide whether T = MST(G). A celebrated result of Komlos shows that this problem can be solved in linear time. Somewhat unexpectedly, MST verication turns out to be useful in actually computing minimum spanning trees from scratch. It is this application that has led some to wonder whether a more flexible version of MST Verification could be used to derive a faster deterministic minimum spanning tree algorithm.
A Lightweight Infrastructure for Graph Analytics ∗
"... Several domainspecific languages (DSLs) for parallel graph analytics have been proposed recently. In this paper, we argue that existing DSLs can be implemented on top of a generalpurpose infrastructure that (i) supports very finegrain tasks, (ii) implements autonomous, speculative execution of th ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Several domainspecific languages (DSLs) for parallel graph analytics have been proposed recently. In this paper, we argue that existing DSLs can be implemented on top of a generalpurpose infrastructure that (i) supports very finegrain tasks, (ii) implements autonomous, speculative execution of these tasks, and (iii) allows applicationspecific control of task scheduling policies. To support this claim, we describe such an implementation called the Galois system. We demonstrate the capabilities of this infrastructure in three ways. First, we implement more sophisticated algorithms for some of the graph analytics problems tackled by previous DSLs and show that endtoend performance can be improved by orders of magnitude even on powerlaw graphs, thanks to the better algorithms facilitated by a more general programming model. Second, we show that, even when an algorithm can be expressed in existing DSLs, the implementation of that algorithm in the more general system can be orders of magnitude faster when the input graphs are road networks and similar graphs with high diameter, thanks to more sophisticated scheduling. Third, we implement the APIs of three existing graph DSLs on top of the common infrastructure in a few hundred lines of code and show that even for powerlaw graphs, the performance of the resulting implementations often exceeds that of the original DSL systems, thanks to the lightweight infrastructure.
Randomized Minimum Spanning Tree Algorithms Using Exponentially Fewer Random Bits
"... For many fundamental problems there exist randomized algorithms that are asymptotically optimal and are superior to the best known deterministic algorithm. Among these are the minimum spanning tree (MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel mi ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
For many fundamental problems there exist randomized algorithms that are asymptotically optimal and are superior to the best known deterministic algorithm. Among these are the minimum spanning tree (MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel minimum spanning tree problems, and the local sorting and set maxima problems. (For the first two problems there are provably optimal deterministic algorithms with unknown, and possibly superlinear running times.) One downside of the randomized methods for solving these problems is that they use a number of random bits linear in the size of the input. In this paper we develop some general methods for reducing exponentially the consumption of random bits in comparison based algorithms. In some cases we are able to reduce the number of random bits from linear to nearly constant without affecting the expected running time. Most of our results are obtained by adjusting or reorganizing existing randomized algorithms to work well with a pairwise or O(1)wise independent sampler. The prominent exception — and the main focus of this paper — is a lineartime randomized minimum spanning tree algorithm that is not derived from the well known KargerKleinTarjan algorithm. In many ways it resembles more closely the deterministic minimum spanning tree algorithms based on Soft Heaps. Further,