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12
Applying parallel computation algorithms in the design of serial algorithms
 J. ACM
, 1983
"... Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for design ..."
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Cited by 232 (7 self)
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Abstract. The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for designing an efficient serial algorithm for another problem. A d ~ eframework d for cases like this is presented. Particular cases, which are discussed in this paper, provide motivation for examining parallelism in sorting, selection, minimumspanningtree, shortest route, maxflow, and matrix multiplication problems, as well as in scheduling and locational problems.
Deciding Bisimilarity and Similarity for Probabilistic Processes
, 2000
"... This paper deals with probabilistic and nondeterministic processes represented by a variant of labelled transition systems where any outgoing transition of a state s is augmented with probabilities for the possible successor states. Our main contribution are algorithms for computing the bisimulatio ..."
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Cited by 25 (4 self)
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This paper deals with probabilistic and nondeterministic processes represented by a variant of labelled transition systems where any outgoing transition of a state s is augmented with probabilities for the possible successor states. Our main contribution are algorithms for computing the bisimulation equivalence classes as introduced by Larsen & Skou [44] and the simulation preorder `a la Segala & Lynch [57]. The algorithm for deciding bisimilarity is based on a variant of the traditional partitioning technique [43, 51] and runs in time O(mn(log m+ log n)) where m is the number of transitions and n the number of states. The main idea for computing the simulation preorder is the reduction to maximum flow problems in suitable networks. Using the method of Cheriyan, Hagerup & Mehlhorn [15] for computing the maximum flow, the algorithm runs in time O((mn 6 +m 2 n 3 )= log n). Moreover, we show that the networkbased technique is also applicable to compute the simulationlike relation...
The Pseudoflow algorithm: A new algorithm for the maximum flow problem
 Operations Research
, 2008
"... We introduce the pseudoflow algorithm for the maximumflow problem that employs only pseudoflows and does not generate flows explicitly. The algorithm solves directly a problem equivalent to the minimumcut problem—the maximum blockingcut problem. Once the maximum blockingcut solution is available ..."
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Cited by 20 (10 self)
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We introduce the pseudoflow algorithm for the maximumflow problem that employs only pseudoflows and does not generate flows explicitly. The algorithm solves directly a problem equivalent to the minimumcut problem—the maximum blockingcut problem. Once the maximum blockingcut solution is available, the additional complexity required to find the respective maximumflow is O�mlog n�. A variant of the algorithm is a new parametric maximumflow algorithm generating all breakpoints in the same complexity required to solve the constant capacities maximumflow problem. The pseudoflow algorithm has also a simplex variant, pseudoflowsimplex, that can be implemented to solve the maximumflow problem. One feature of the pseudoflow algorithm is that it can initialize with any pseudoflow. This feature allows it to reach an optimal solution quickly when the initial pseudoflow is “close ” to an optimal solution. The complexities of the pseudoflow algorithm, the pseudoflowsimplex, and the parametric variants of pseudoflow and pseudoflowsimplex algorithms are all O�mnlog n � on a graph with n nodes and m arcs. Therefore, the pseudoflowsimplex algorithm is the fastest simplex algorithm known for the parametric maximumflow problem. The pseudoflow algorithm is also shown to solve the maximumflow problem on s�ttree networks in linear time, where s�ttree networks are formed by joining a forest of capacitated arcs, with nodes s and t adjacent to any subset of the nodes. Subject classifications: flow algorithms; parametric flow; normalized tree; lowest label; pseudoflow algorithm; maximum flow.
Polynomial Time Algorithms for Testing Probabilistic Bisimulation and Simulation
 Proc. CAV'96, LNCS 1102
, 1996
"... . Various models and equivalence relations or preorders for probabilistic processes are proposed in the literature. This paper deals with a model based on labelled transition systems extended to the probabalistic setting and gives an O(n 2 \Delta m) algorithm for testing probabilistic bisimula ..."
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Cited by 19 (4 self)
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. Various models and equivalence relations or preorders for probabilistic processes are proposed in the literature. This paper deals with a model based on labelled transition systems extended to the probabalistic setting and gives an O(n 2 \Delta m) algorithm for testing probabilistic bisimulation and an O(n 5 \Delta m 2 ) algorithm for testing probabilistic simulation where n is the number of states and m the number of transitions in the underlying probabilistic transition systems. 1 Introduction Transition systems have proved to be very useful for modelling concurrent processes. A variety of widely accepted equivalence relations and preorders for such systems support the use of transition systems for the design and verification of concurrent systems. In this context, testing equivalences and preorders become important and have been studied e.g. in [3, 4, 8, 11, 17]. For instance, (strong) bisimulation can be decided in time O(m \Delta log n) [22], weak bisimulation in t...
A Computational Study of the Pseudoflow and Pushrelabel Algorithms for the Maximum Flow Problem
"... We present the results of a computational investigation of the pseudoflow and pushrelabel algorithms for the maximum flow and minimum st cut problems. The two algorithms were tested on several problem instances from the literature. Our results show that our implementation of the pseudoflow algorit ..."
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Cited by 13 (5 self)
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We present the results of a computational investigation of the pseudoflow and pushrelabel algorithms for the maximum flow and minimum st cut problems. The two algorithms were tested on several problem instances from the literature. Our results show that our implementation of the pseudoflow algorithm is faster than the best known implementation of pushrelabel on most of the problem instances within our computational study. Subject classifications: Flow algorithms; parametric flow; normalized tree; lowest label; pseudoflow algorithm; maximum flow Area of review: Networks/graphs 1.
On the complexity of the Whitehead minimization problem
 PREPRINT 721, CENTRE DE RECERCA MATEMÀTICA
, 2006
"... The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial b ..."
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Cited by 4 (3 self)
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The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.
Load balanced mapping of distributed objects to minimize network communication
 Journal of Parallel and Distributed Computing, Vol
, 1996
"... This paper introduces a new load balancing and communication minimizing heuristic used in the Inverse Remote Procedure Call (IRPC) system. While the paper briefly describes the IRPC system, the focus is on the new IRPC assignment heuristic. The IRPC compiler maps a distributed program to a graph tha ..."
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Cited by 3 (0 self)
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This paper introduces a new load balancing and communication minimizing heuristic used in the Inverse Remote Procedure Call (IRPC) system. While the paper briefly describes the IRPC system, the focus is on the new IRPC assignment heuristic. The IRPC compiler maps a distributed program to a graph that represents program objects and their dependencies (due to invocations and parameter passing) as nodes and edges, respectively. In the graph, the system preserves conditional and iterative flows, records network transmission and execution costs, and marks nodes that have to reside at specific network sites. The graph is then partitioned by the heuristic to derive a (sub)optimal node assignment to network sites minimizing load balancing and network data transport. The resulting program partition is then reflected in the physical object distribution, and remote and local object communication is transparently
Simplifications and speedups of the Pseudoflow algorithm. Networks
, 2012
"... The pseudoflow algorithm for solving the maximum flow and minimum cut problems was devised in Hochbaum (2008). The complexity of the algorithm was shown in (2008) to be O(nm log n). Chandran and Hochbaum, (2009) demonstrated that the pseudoflow algorithm is very efficient in practice, and that the h ..."
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Cited by 2 (2 self)
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The pseudoflow algorithm for solving the maximum flow and minimum cut problems was devised in Hochbaum (2008). The complexity of the algorithm was shown in (2008) to be O(nm log n). Chandran and Hochbaum, (2009) demonstrated that the pseudoflow algorithm is very efficient in practice, and that the highest label version of the algorithm tends to perform best. Here, we improve the running time of the highest label pseudoflow algorithm to O(n 3) using simple data structures and to O(nm log(n 2 /m)) using the dynamic trees data structure. Both these algorithms use a new form of DepthFirstSearch implementation that is likely to be fast in practice as well. In addition, we give a new simpler description of the pseudoflow algorithm by relating it to the simplex algorithm as applied to the maximum preflow problem defined here. The interpretation of the generic pseudoflow algorithm as a simplexlike algorithm for the maximum preflow problem motivates the pseudoflow algorithm and highlights differences between the pseudoflow algorithm and the preflowpush algorithm of Goldberg
Secret Key Generation for a Pairwise Independent Network Model
"... Abstract—We consider secret key generation for a “pairwise independent network ” model in which every pair of terminals observes correlated sources that are independent of sources observed by all other pairs of terminals. The terminals are then allowed to communicate publicly with all such communica ..."
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Cited by 1 (1 self)
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Abstract—We consider secret key generation for a “pairwise independent network ” model in which every pair of terminals observes correlated sources that are independent of sources observed by all other pairs of terminals. The terminals are then allowed to communicate publicly with all such communication being observed by all the terminals. The objective is to generate a secret key shared by a given subset of terminals at the largest rate possible, with the cooperation of any remaining terminals. Secrecy is required from an eavesdropper that has access to the public interterminal communication. A (singleletter) formula for secret key capacity brings out a natural connection between the problem of secret key generation and a combinatorial problem of maximal packing of Steiner trees in an associated multigraph. An explicit algorithm is proposed for secret key generation based on a maximal packing of Steiner trees in a multigraph; the corresponding maximum rate of Steiner tree packing is thus a lower bound for the secret key capacity. When only two of the terminals or when all the terminals seek to share a secret key, the mentioned algorithm achieves secret key capacity in which case the bound is tight. Index Terms—PIN model, private key, public communication, secret key capacity, security index, spanning tree packing, Steiner tree packing, wiretap secret key. I.
Algorithms and Complexity
, 1986
"... CONTENTS Chapter 0: What This Book Is About 0.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.2 Hard vs. easy problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0.3 A preview . . . . . . . . . . . . . . . . . . . . . . . . . . ..."
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CONTENTS Chapter 0: What This Book Is About 0.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.2 Hard vs. easy problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0.3 A preview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Chapter 1: Mathematical Preliminaries 1.1 Orders of magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Positional number systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Manipulations with series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 Recurrence relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5 Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.6 Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Chapter 2: Recursive Algorithms<F12.3