All previously known efficient maximum-flow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortest-length augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the preflow concept of Karzanov is introduced. A preflow is like a flow, except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out. The method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths. The algorithm and its analysis are simple and intuitive, yet the algorithm runs as fast as any other known method on dense graphs, achieving an O(n3) time bound on an n-vertex graph. By incorporating the dynamic tree data structure of Sleator and Tarjan, we obtain a version of the algorithm running in O(nm log(n2/m)) time on an n-vertex, m-edge graph. This is as fast as any known method for any graph density and faster on graphs of moderate density. The algorithm also admits efficient distributed and parallel implementations. A parallel implementation running in O(n2log n) time using n processors and O(m) space is obtained. This time bound matches that of the Shiloach-Vishkin algorithm, which also uses n processors but requires O(n2) space.

/pdf/a-new-approach-to-the-maximum-flow-problem-1guoakm9e8.pdf

A new approach to the maximum-flow problem

Written by an authority in the field, this book provides an introduction to the design and analysis of parallel algorithms. The emphasis is on the application of the PRAM (parallel random access machine) model of parallel computation, with all its variants, to algorithm analysis. Special attention is given to the selection of relevant data structures and to algorithm design principles that have proved to be useful. Features *Uses PRAM (parallel random access machine) as the model for parallel computation. *Covers all essential classes of parallel algorithms. *Rich exercise sets. *Written by a highly respected author within the field. 0201548569B04062001

/pdf/an-introduction-to-parallel-algorithms-c3tag3zjaf.pdf

An introduction to parallel algorithms

A vast body of theoretical research has focused either on overly simplistic models of parallel computation, notably the PRAM, or overly specific models that have few representatives in the real world. Both kinds of models encourage exploitation of formal loopholes, rather than rewarding development of techniques that yield performance across a range of current and future parallel machines. This paper offers a new parallel machine model, called LogP, that reflects the critical technology trends underlying parallel computers. it is intended to serve as a basis for developing fast, portable parallel algorithms and to offer guidelines to machine designers. Such a model must strike a balance between detail and simplicity in order to reveal important bottlenecks without making analysis of interesting problems intractable. The model is based on four parameters that specify abstractly the computing bandwidth, the communication bandwidth, the communication delay, and the efficiency of coupling communication and computation. Portable parallel algorithms typically adapt to the machine configuration, in terms of these parameters. The utility of the model is demonstrated through examples that are implemented on the CM-5.

/pdf/logp-towards-a-realistic-model-of-parallel-computation-2hpmqi5j0f.pdf

LogP: towards a realistic model of parallel computation

We investigate the complexity of the classical problem of optimal policy computation in Markov decision processes. All three variants of the problem finite horizon, infinite horizon discounted, and infinite horizon average cost were known to be solvable in polynomial time by dynamic programming finite horizon problems, linear programming, or successive approximation techniques infinite horizon. We show that they are complete for P, and therefore most likely cannot be solved by highly parallel algorithms. We also show that, in contrast, the deterministic cases of all three problems can be solved very fast in parallel. The version with partially observed states is shown to be PSPACE-complete, and thus even less likely to be solved in polynomial time than the NP-complete problems; in fact, we show that, most likely, it is not possible to have an efficient on-line implementation involving polynomial time on-line computations and memory of an optimal policy, even if an arbitrary amount of precomputation is allowed. Finally, the variant of the problem in which there are no observations is shown to be NP-complete.

/pdf/the-complexity-of-markov-decision-processes-51wd5q31f7.pdf

The Complexity of Markov Decision Processes

All previously known efftcient maximum-flow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortest-length augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the preflow concept of Karzanov is introduced. A preflow is like a flow, except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out. The method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths. The algorithm and its analysis are simple and intuitive, yet the algorithm runs as fast as any other known method on dense. graphs, achieving an O(n)) time bound on an n-vertex graph. By incorporating the dynamic tree data structure of Sleator and Tarjan, we obtain a version of the algorithm running in O(nm log(n'/m)) time on an n-vertex, m-edge graph. This is as fast as any known method for any graph density and faster on graphs of moderate density. The algorithm also admits efticient distributed and parallel implementations. A parallel implementation running in O(n'log n) time using n processors and O(m) space is obtained. This time bound matches that of the Shiloach-Vishkin

/pdf/a-new-approach-to-the-maximum-flow-problem-4cox1zcghr.pdf

A new approach to the maximum flow problem

http://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-get.cgi/1980/CS/CS0178.pdf

An O(logn) parallel connectivity algorithm

A model for synchronized parallel computation is described in which all p processors have access to a common memory. this model is used to solve the problems of finding the maximum, merging, and sorting by p processors.

Yossi Shiloach

Papers

An O(logn) parallel connectivity algorithm

Finding the maximum, merging and sorting in a parallel computation model

An O ( n 2 log n ) parallel max-flow algorithm

Finding the maximum, merging, and sorting in a parallel computation model

Fast canonization of circular strings