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A New Method for Functional Arrays
 Journal of Functional Programming
, 1997
"... Arrays are probably the most widely used data structure in imperative programming languages, yet functional languages typically only support arrays in a limited manner, or prohibit them entirely. This is not too surprising, since most other mutable data structures, such as trees, have elegant immuta ..."
Abstract

Cited by 13 (0 self)
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Arrays are probably the most widely used data structure in imperative programming languages, yet functional languages typically only support arrays in a limited manner, or prohibit them entirely. This is not too surprising, since most other mutable data structures, such as trees, have elegant immutable analogues in the functional world, whereas arrays do not. Previous attempts at addressing the problem have suffered from one of three weaknesses, either that they don't support arrays as a persistent data structure (unlike the functional analogues of other imperative data structures), or that the range of operations is too restrictive to support some common array algorithms efficiently, or that they have performance problems. Our technique provides arrays as a true functional analogue of imperative arrays with the properties that functional programmers have come to expect from their data structures. To efficiently support array algorithms from the imperative world, we provide O(1) operations for singlethreaded array use. Fully persistent array use can also be provided at O(1) amortized cost, provided that the algorithm satisfies a simple requirement as to uniformity of access. For those algorithms which do not access the array uniformly or singlethreadedly, array reads or updates take at most O(log n) amortized time, where n is the size of the array. Experimental results indicate that the overheads of our technique are acceptable in practice for many applications.
Persistent Triangulations
, 2001
"... Triangulations of a surface are of fundamental importance in computational geometry, computer graphics, and engineering and scientific simulations. Triangulations are ordinarily represented as mutable graph structures for which both adding and traversing edges take constant time per operation. These ..."
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Cited by 7 (2 self)
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Triangulations of a surface are of fundamental importance in computational geometry, computer graphics, and engineering and scientific simulations. Triangulations are ordinarily represented as mutable graph structures for which both adding and traversing edges take constant time per operation. These representations of triangulations make it di#cult to support persistence, including "multiple futures", the ability to use a data structure in several unrelated ways in a given computation; "time travel", the ability to move freely among versions of a data structure; or parallel computation, the ability to operate concurrently on a data structure without interference. We present a purely functional interface and representation of triangulated surfaces, and more generally of simplicial complexes in higher dimensions. In addition to being persistent in the strongest sense, the interface more closely matches the mathematical definition of triangulations (simplicial complexes) than do interfaces based on mutable representations. The representation, however, comes at the cost of requiring O(lg n) time for traversing or adding triangles (simplices), where n is the number of triangles in the surface. We show both analytically and experimentally that for certain important cases, this extra cost does not seriously a#ect endtoend running time. Analytically, we present a new randomized algorithm for 3dimensional Convex Hull based on our representations for which the running time matches the #(n lg n) lowerbound for the problem. This is achieved by using only O(n) traversals of the surface. Experimentally, we present results for both an implementation of the 3dimensional Convex Hull and for a terrain modeling algorithm, which demonstrate that, although there is some cost to persis...
Transparent, Distributed, and Replicated Dynamic Provable Data Possession
, 2013
"... With the growing trend toward using outsourced storage, the problem of efficiently checking and proving data integrity needs more consideration. Starting with PDP and POR schemes in 2007, many cryptography and security researchers have addressed the problem. After the first solutions for static data ..."
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Cited by 1 (1 self)
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With the growing trend toward using outsourced storage, the problem of efficiently checking and proving data integrity needs more consideration. Starting with PDP and POR schemes in 2007, many cryptography and security researchers have addressed the problem. After the first solutions for static data, dynamic versions were developed (e.g., DPDP). Researchers also considered distributed versions of such schemes. Alas, in all such distributed schemes, the client needs to be aware of the structure of the cloud, and possibly preprocess the file accordingly, even though the security guarantees in the real world are not improved. We propose a distributed and replicated DPDP which is transparent from the client’s viewpoint. It allows for real scenarios where the cloud storage provider (CSP) may hide its internal structure from the client, flexibly manage its resources, while still providing provable service to theclient. TheCSPdecides onhow many andwhich serverswill storethedata. Sincetheload is distributed on multiple servers, we observe onetotwo orders of magnitude better performance in our tests, while availability and reliability are also improved via replication. In addition, we use persistent rankbased authenticated skip lists to create centralized and distributed variants of a dynamic version control system with optimal complexity. 1
Under consideration for publication in J. Functional Programming 1 Persistent Triangulations∗
"... Triangulations of a surface are of fundamental importance in computational geometry, computer graphics, and engineering and scientific simulations. Triangulations are ordinarily represented as mutable graph structures for which both adding and traversing edges take constant time per operation. These ..."
Abstract
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Triangulations of a surface are of fundamental importance in computational geometry, computer graphics, and engineering and scientific simulations. Triangulations are ordinarily represented as mutable graph structures for which both adding and traversing edges take constant time per operation. These representations of triangulations make it difficult to support persistence, including “multiple futures”, the ability to use a data structure in several unrelated ways in a given computation; “time travel”, the ability to move freely among versions of a data structure; or parallel computation, the ability to operate concurrently on a data structure without interference. We present a purely functional interface and representation of triangulated surfaces, and more generally of simplicial complexes in higher dimensions. In addition to being persistent in the strongest sense, the interface more closely matches the mathematical definition of triangulations (simplicial complexes) than do interfaces based on mutable representations. The representation, however, comes at the cost of requiring O(lg n) time for traversing or adding triangles (simplices), where n is the number of triangles in the surface. We show both analytically and experimentally that for certain important cases, this extra cost does not seriously affect endtoend running time. Analytically, we present a new randomized algorithm for 3dimensional Convex Hull based on our representations for which the running time matches the Ω(n lg n) lowerbound for the problem. This is achieved by using only O(n) traversals of the surface. Experimentally, we present results for both an implementation of the 3dimensional Convex Hull and for a terrain modeling algorithm, which demonstrate that, although there is some cost to persistence, it seems to be a small constant factor. Capsule summary goes here.