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Provably efficient scheduling for languages with finegrained parallelism
 IN PROC. SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 1995
"... Many highlevel parallel programming languages allow for finegrained parallelism. As in the popular worktime framework for parallel algorithm design, programs written in such languages can express the full parallelism in the program without specifying the mapping of program tasks to processors. A ..."
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Cited by 82 (25 self)
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Many highlevel parallel programming languages allow for finegrained parallelism. As in the popular worktime framework for parallel algorithm design, programs written in such languages can express the full parallelism in the program without specifying the mapping of program tasks to processors. A common concern in executing such programs is to schedule tasks to processors dynamically so as to minimize not only the execution time, but also the amount of space (memory) needed. Without careful scheduling, the parallel execution on p processors can use a factor of p or larger more space than a sequential implementation of the same program. This paper first identifies a class of parallel schedules that are provably efficient in both time and space. For any
Recursion Versus Iteration at HigherOrders
, 1997
"... . We extend the wellknown analysis of recursionremoval in firstorder program schemes to a higherorder language of finitely typed and polymorphically typed functional programs, the semantics of which is based on callbyname parameterpassing. We introduce methods for recursionremoval, i.e. for ..."
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Cited by 6 (0 self)
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. We extend the wellknown analysis of recursionremoval in firstorder program schemes to a higherorder language of finitely typed and polymorphically typed functional programs, the semantics of which is based on callbyname parameterpassing. We introduce methods for recursionremoval, i.e. for translating higherorder recursive programs into higherorder iterative programs, and determine conditions under which this translation is possible. Just as finitely typed recursive programs are naturally classified by their orders, so are finitely typed iterative programs. This syntactic classification of recursive and iterative programs corresponds to a semantic (or computational) classification: the higher the order of programs, the more functions they can compute. 1 Background and Motivation Although our analysis is entirely theoretical, as it combines methods from typed calculi, from abstract recursion theory and from denotational semantics, the problems we consider have a strong pra...
On Separators, Segregators and Time versus Space
"... We give the first extension of the result due to Paul, Pippenger, Szemeredi and Trotter [24] that deterministic linear time is distinct from nondeterministic linear time. We show that N T IM E(n ..."
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Cited by 6 (0 self)
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We give the first extension of the result due to Paul, Pippenger, Szemeredi and Trotter [24] that deterministic linear time is distinct from nondeterministic linear time. We show that N T IM E(n
Partitioning Graphs with Costs and Weights on Vertices: Algorithms and Applications
 of Lecture Notes in Computer Science
"... We prove separator theorems in which the size of the separator is minimized with respect to nonnegative vertex costs. We show that for any planar graph G there exists a vertex separator of total vertex cost at most c qP v2V (G) (cost(v)) 2 and that this bound is optimal within a constant factor ..."
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Cited by 4 (0 self)
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We prove separator theorems in which the size of the separator is minimized with respect to nonnegative vertex costs. We show that for any planar graph G there exists a vertex separator of total vertex cost at most c qP v2V (G) (cost(v)) 2 and that this bound is optimal within a constant factor. Moreover such a separator can be found in linear time. This theorem implies a variety of other separation results discussed in the paper. We describe application of our separator theorems to graph embedding problems, graph pebbling, and multi commodity flow problems. 1 Introduction Background. A separator is a small set of vertices or edges whose removal divides a graph into two roughly equal parts. The existence of small separators for some important classes of graphs such as planar graphs can be used in the design of efficient divideandconquer algorithms for problems on such graphs. Formally, a separator theorem for a given class of graphs S states that any nvertex graph from S ca...
On the Relative Strength of Pebbling and Resolution
, 2010
"... The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven to be a useful tool for studying resolutionbased proof systems when comparing the strength of different subsystems, showing bounds on proof space, and establishing sizespace trade ..."
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Cited by 2 (1 self)
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The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven to be a useful tool for studying resolutionbased proof systems when comparing the strength of different subsystems, showing bounds on proof space, and establishing sizespace tradeoffs. The typical approach has been to encode the pebble game played on a graph as a CNF formula and then argue that proofs of this formula must inherit (various aspects of) the pebbling properties of the underlying graph. Unfortunately, the reductions used here are not tight. To simulate resolution proofs by pebblings, the full strength of nondeterministic blackwhite pebbling is needed, whereas resolution is only known to be able to simulate deterministic black pebbling. To obtain strong results, one therefore needs to find specific graph families which either have essentially the same properties for black and blackwhite pebbling (not at all true in general) or which admit simulations of blackwhite pebblings in resolution. This paper contributes to both these approaches. First, we design a restricted form of blackwhite pebbling that can be simulated in resolution and show that there are graph families for which such restricted pebblings can be asymptotically better than black pebblings. This proves that, perhaps somewhat unexpectedly, resolution can strictly beat blackonly pebbling, and in particular that the space lower bounds on pebbling formulas in [BenSasson and Nordström 2008] are tight. Second, we present a versatile parametrized graph family with essentially the same properties for black and blackwhite pebbling, which gives sharp simultaneous tradeoffs for black and blackwhite pebbling for various parameter settings. Both of our contributions have been instrumental in obtaining the timespace tradeoff results for resolutionbased proof systems in [BenSasson and Nordström 2009].
An Infinite Pebble Game And Applications
, 1996
"... this paper might not have been written. We express our thanks to them all, as well as to M.A. Taitslin for his valuable comments. 2 The Infinite Pebble Game ..."
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this paper might not have been written. We express our thanks to them all, as well as to M.A. Taitslin for his valuable comments. 2 The Infinite Pebble Game
Partially supported by the European Grant BRAQMIPS of CEC DG XIII.
, 2004
"... We consider a system of uniform recurrence equations (URE) of dimension one. We show how its computation can be carried out using minimal memory size with several synchronous processors. This result is then applied to register minimization for digital circuits and parallel computation of task graphs ..."
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We consider a system of uniform recurrence equations (URE) of dimension one. We show how its computation can be carried out using minimal memory size with several synchronous processors. This result is then applied to register minimization for digital circuits and parallel computation of task graphs.
Efficient pebbling for list traversal synopses ∗
, 2003
"... We show how to support efficient back traversal in a unidirectional list, using small memory and with essentially no slowdown in forward steps. Using O(lg n) memory for a list of size n, the i’th backstep from the farthest point reached so far takes O(lg i) time in the worst case, while the overhea ..."
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We show how to support efficient back traversal in a unidirectional list, using small memory and with essentially no slowdown in forward steps. Using O(lg n) memory for a list of size n, the i’th backstep from the farthest point reached so far takes O(lg i) time in the worst case, while the overhead per forward step is at most ǫ for arbitrary small constant ǫ> 0. An arbitrary sequence of forward and back steps is allowed. A full tradeoff between memory usage and time per backstep is presented: k vs. kn 1/k and vice versa. Our algorithms are based on a novel pebbling technique which moves pebbles on a virtual binary, or tary, tree that can only be traversed in a preorder fashion. The compact data structures used by the pebbling algorithms, called list traversal synopses, extend to general directed graphs, and have other interesting applications, including memory efficient hashchain implementation. Perhaps the most surprising application is in showing that for any program, arbitrary rollback steps can be efficiently supported with small overhead in memory, and marginal overhead in its ordinary execution. More concretely: Let P be a program that runs for at most T steps, using memory of size M. Then, at the cost of recording the input used by the program, and increasing the memory by a factor of O(lg T) to O(M lg T), the program P can be extended to support an arbitrary sequence of forward execution and rollback steps: the i’th rollback step takes O(lg i) time in the worst case, while forward steps take O(1) time in the worst case, and 1 + ǫ amortized time per step. 1