Showing papers on "Communication complexity published in 1985"

Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity (Extended Abstract)

Abstract: A new model for weak random physical sources is presented. The new model strictly generalizes previous models (e.g., the Santha and Vazirani model [27]). The sources considered output strings according to probability distributions in which no single string is too probable.The new model provides a fruitful viewpoint on problems studied previously such as: • Extracting almost-perfect bits from sources of weak randomness. The question of possibility as well as the question of efficiency of such extraction schemes are addressed. • Probabilistic communication complexity. It is shown that most functions have linear communication complexity in a very strong probabilistic sense. • Robustness of BPP with respect to sources of weak randomness (generalizing a result of Vazirani and Vazirani [32], [33]).

Theory of algorithms

Abstract: On Parallel Algorithms of some Orthogonal Transforms (S.S. Agaian and D.Z. Gevorkian). An Efficient Algorithm for Finding Peripheral Nodes (I. Arany). Computational Aspects of Assigning Characteristic Semigroup of Asynchronous Automata and Their Extensions (S. Bocian and B. Mikolajczak). Reichenbach's Propositional Logic in Algorithmic Form (P. Borowik). The Complexity of Weighted Multi-Constrained Spanning Tree Problems (P. Camerini, G. Galbiati and F. Maffioli). An Algorithm for Finding SC-Preimages of a Deterministic Finite Automaton (K. Chmiel). On Entropy Decomposition Methods and Algorithm Design (Th. Fischer). An Efficient Algorithm for Dynamic String-Storage Allocation (D. Fox). Covering Intervals with Intervals under Containment Constraints (M.R. Garey and R.Y. Pinter). How to Construct Random Functions (O. Goldreich, S. Goldwasser and S. Micali). Four Pebbles Don't Suffice to Search Planar Infinite Labyrinths (F. Hoffmann). Parallel Algorithms: The Impact of Communication Complexity (F. Hossfeld). Tight Worst-Case Bounds for Bin-Packing Algorithms (A. Ivanyi). Hypergraph Planarity and the Complexity of Drawing Venn Diagrams (D.S. Johnson and H.O. Pollak). Convolutional Charaterization of Computability and Complexity of Computations (S. Jukna). Succinct Data Representations and the Complexity of Computations (S. Jukna). Lattices, Basis Reduction and the Shortest Vector Problem (R. Kannan). The Characterization of Some Complexity Classes by Recursion Schemata (M. Liskiewicz, K. Lorys and M. Piotrow). Some Algorithmic Problems on Lattices (L. Lovasz). Linear Proofs in the Non-Negative Cone (J. Moravek). Characterizing Some Low Arithmetic Classes (J.B. Paris, W.G. Handley and A.J. Wilkie). Constructing a Simplex Form of a Rational Matrix (A. Rycerz and J. Jegier). Computing N with a Few Number of Additions (I. Ruzsa and Zs. Tuza). A Hierarchy of Polynomial Time Basis Reduction Algorithms (C.P. Schnorr). A Topological View of Some Problems in Complexity Theory (M. Sipser). v-Computations on Turing Machines and the Accepted Languages (L. Staiger). On the Greedy Algorithm for an Edge-Partitioning Problem (Gy. Turan). The Complexity of Linear Quadtrees (T.R. Walsh).

Unbiased bits from sources of weak randomness and probabilistic communication complexity

Abstract: We introduce a general model for physical sources or weak randomness. Loosely speaking, we view physical sources as devices which output strings according to probability distributions in which no single string is too probable. The main question addressed is whether it is possible to extract alrnost unbiased random bits from such "probability bounded" sources. We show that most or the functions can be used to extract almost unbiased and independent bits from the output of any two independent "probability-bounded" sources. The number of extractable bits is within a constant factor of the information theoretic bound. We conclude this paper by establishing further connections between communication complexity and the problem discussed above. This allows us to show that most Boolean functions have linear communication complexity in a very strong sense.

Towards a strong communication complexity theory or generating quasi-random sequences from two communicating slightly-random sources

Abstract: Several computational applications, such as randomizing algorithms [Ra], stochastic simulation [SC, KG] and cryptographic protocols [B11, GM, W] assume a fast source of unbiased, independent coin flips. Unfortunately, the available physical sources of randomness, such as noise diodes and geiger counters are at best imperfect [Mu]. Santha and Vazirani [SV] consider a very general model for such imperfect sources of randomness: the slightly random source. A slightly random source is a black box

Solving narrow banded systems on ensemble architectures

Abstract: We present concurrent algorithms for the solution of narrow banded systems on ensemble architectures, and analyze the communication and arithmetic complexities of the algorithms. The algorithms consist of three phases. In phase 1, a block tridiagonal system of reduced size is produced through largely local operations. Diagonal dominance is preserved. If the original system is positive, definite, and symmetric, so is the reduced system. It is solved in a second phase, and the remaining variables obtained through local back substitution in a third phase. With a sufficient number of processing elements, there is no first and third phase. We investigate the arithmetic and communicationcomplexity of Gaussian elimination and block cyclic reduction for the solution of the reduced system on boolean cubes, perfect shuffle and shuffle-exchange networks, binary trees, and linear arrays.With an optimum number of processors, the minimum solution time on a linear array is of an order that ranges from O(m2√Nm) to O(m3 + m3log2(N/m)) depending on the bandwidth, the dimension of the problem, and the times for communication and arithmetic. For boolean cubes, cube-connected cycles, prefect shuffle and shuffle-exchange networks, and binary trees, the minimum time is O(m3+m3log2(N/m)) including the communication complexity

Distributed Sorting

Abstract: The problem of sorting a file distributed over a number of sites of a communication network is examined. Two versions of this problem are investigated; distributed solution algorithms are presented; and their communication complexity analyzed both in the worst and in the average case. The worst case bounds are shown to be sharp, with respect to order of magnitude, for large files.

Distributed BFS algorithms

Abstract: This paper develops a new distributed BFS algorithm for an asynchronous communication network. This paper presents two new BFS algorithms with improved communication complexity. The first algorithm has complexity O((E+V1.5)?logV) in communication and O(V1.5?logV) in time. The second algorithm uses the technique of the first recursively and achieves O(E?2 √logVloglogV) in communication and O(V?2√logVloglogV) in time.

Concurrent Broadcast for Information Dissemination

Abstract: Concurrent broadcast involves the dissemination of a database, consisting of messages initially distributed among the nodes of a network, so that a copy of the entire database eventually resides at each node. One application is the dissemination of network status information for adaptive routing in a communications network. This paper examines the time complexity and communication complexity of several distributed procedures for concurrent broadcast. The procedures do not use information depending on the network topology. The worst-case time complexity of a flooding procedure for concurrent broadcast is shown to be linear in the number of nodes plus the number of messages, and no other procedure for concurrent broadcast has a better worst-case time complexity. A variant of flooding is proposed to eliminate redundant message receipts from the flooding process by real-time signaling between neighbors concerning messages residing at each. This variant can reduce communication complexity, while having a worst-case time complexity similar in form to that of the flooding procedure. Special properties of concurrent broadcast in a tree are also given. The present time complexity results can be used to bound the time during which inconsistent databases may reside at different nodes, to evaluate and compare procedures for (or including) concurrent broadcast, and to schedule a sequence of instances of concurrent broadcast so that the instances do not overlap and there is no need for sequence numbers.

Distributed algorithms for election in unidirectional and complete networks (traversal, synchronous, leader, asynchronous, complexity)

Abstract: Consider a data communication network of n nodes, each of which has a unique identifier (id); otherwise the nodes are identical. The nodes are asleep and have no global information about network topology, number and ids of other nodes, etc. A distributed election algorithm is a means by which the nodes of the network distinguish one among them as the leader. The problem of distributively electing a leader in a network is viewed as a problem of synchronization among potential candidates for leadership. Each candidate tries to capture all the nodes. To guarantee that only one succeeds, all but one candidate are killed. Following this view election algorithms in a general, two component framework are designed. Component one is a capturing and termination detection mechanism, assuming only one candidate. Component two is a synchronization mechanism, to eliminate all but one candidate. In arbitrary networks the synchronization is complicated by the uncertainties of nodes about the network topology and the relative location of candidates. Two network models are considered: first, a complete network in which a bidirectional communication link connects every node with every other, thus eliminating topological uncertainties; and second, the opposite extreme in which topological uncertainties are at maximum--a strongly connected unidirectional network with some or all links transmitting messages in one direction only. The study produces an O(n(.)log n) messages O(log n) time synchronous and O(n(.)log n) messages O(n) time asynchronous election algorithm in complete networks. For unidirectional networks we derive a distributed election algorithm whose communication complexity is O(n(.)(VBAR)E(VBAR) + n('2)log n) bits, where (VBAR)E(VBAR) is the total number of links. We also establish that (OMEGA)(n(.)log n) is a lower bound on the total number of messages transmitted for achieving election in synchronous complete networks. Moreover, it is shown that the time complexity of message-optimal synchronous algorithms is (OMEGA)(log n), hence the optimality of our synchronous complete network algorithm. It remains open whether a sublinear time, message-optimal, asynchronous complete network election algorithm exists.