Showing papers on "Decision tree model published in 1987"

Information-based complexity

Abstract: Information-based complexity seeks to develop general results about the intrinsic difficulty of solving problems where available information is partial or approximate and to apply these results to specific problems. This allows one to determine what is meant by an optimal algorithm in many practical situations, and offers a variety of interesting and sometimes surprising theoretical results.

Lower bounds on communication complexity in distributed computer networks

Abstract: The main result of this paper is a general technique for determining lower bounds on the communication complexity of problems on various distributed computer networks This general technique is derived by simulating the general network by a linear array and then using a lower bound on the communication complexity of the problem on the linear array Applications of this technique yield optimal bounds on the communication complexity of merging, ranking, uniqueness, and triangle-detection problems on a ring of processors Nontrivial near-optimal lower bounds on the communication complexity of distinctness, merging, and ranking on meshes and complete binary trees are also derived

The power of randomness for communication complexity

Abstract: Improving a result of Mehlhorn and Schmidt, a function f with deterministic communication complexity n2 is shown to have Las Vegas communication complexity O(n). This is the best possible, because the deterministic complexity cannot be more than the square of the Las Vegas communication complexity for any function.

Making Distributed Spanning Tree Algorithms Fault-Resilient

Abstract: We study distributed algorithms for networks with undetectable fail-stop failures, assuming that all of them had occurred before the execution started (It was proved that distributed agreement cannot be reached when a node may fail during execution) Failures of this type are encountered, for example, during a recovery from a crash in the network We study the problems of leader election and spanning tree construction, that have been characterized as fundamental for this environment We point out that in presence of faults just duplicating messages in an existing algorithm does not suffice to make it resilient; actually, this redundancy gives rise to synchronization problems and also might increase the message complexity In this paper we investigate the problem of making existing spanning tree algorithms fault-resilient, and still overcome these difficulties Several lower bounds and optimal fault-resilient algorithms are presented for the first timeHowever, we believe that the main contribution of the paper is twofold: First, in designing the algorithms we use tools that thus argued to be rather general (for example, we extend the notion of token algorithms to multiple-token algorithms) In fact we are able to use them on several different algorithms, for several different families of networks Second, following the amortized computational complexity, we introduce amortized message complexity as a tool for analyzing the message complexity

Some completeness results on decision trees and group testing

Abstract: The computational complexity of the group testing problem is investigated under the minimax measure and the decision tree model. We consider the generalizations of the group testing problem in which partial information about the decision tree of the problem is given. Using this approach, we demonstrate the NP-hardness of several decision problems related to various models of the group testing problem. For example, we show that, for several models of group testing, the problem of recognizing a set of queries that uniquely determines each object is co-NP-complete.

On the Complexity of Branching Programs and Decision Trees for Clique Functions

Abstract: Because of the slow progress in proving lower bounds on the circuit complexity of Boolean functions one is interested in restricted models of Boolean circuits like depth restricted circuits, decision trees, branching programs, width-k branching programs and k-times-only branching programs. We prove here exponentiallower bounds on the decision tree complexity of clique functions. For one-time-only branching programs we prove for k-clique functions large polynomial lower bounds if k is fixed and exponential lower bounds for k increasing with n. Finally we introduce the hierarchy of the classes BPk (P) of all sequences of Boolean functions which may be computed by k-times-only branching programs of polynomial size. We show constructively that BP1(P) is a proper subset of BP2(P).

Experiments on genetic risk perception and decision making: explorative studies.

Abstract: In cognitive psychology, considerable attention has recently been given to studies on risk perception and decision making under uncertainty. The attempt to apply the cognitive frameworks to the genetic counseling setting is a major challenge. After reviewing the relevant literature in cognitive psychology, the aim of our first study was to understand how people process and memorize genetic information about Huntington's disease. Although we did not obtain clear-cut data about the mental representation of this genetic information in our subjects, the context in which the information was given was a surprisingly strong variable affecting its memorability. Pauker and Pauker (1979) developed a tree model helping the prospective parents to use the probabilities as well as the costs of different outcomes to decide on having an amniocentesis performed. Specific attention was paid to the estimation of the costs of the outcomes. While repeating the same experiment, the goal of our second study was to investigate whether the subjects agree with the advice given by the model and whether their final decision was affected by using the technique or not. In a third experiment, we scrutinized the joint decision process of two persons as compared with the decision process of people not discussing together. They all received genetic information, either about Hemophilia or about Down syndrome. The joint decision process was completely different for the two genetic diseases. As the two diseases have highly different risk probabilities, we had to unravel the influence of the importance of the risk and the burden of the disease on the ongoing decision of two persons. The set of findings at least suggests that the existing models in the literature have overlooked the importance of the context in providing the information and the complexities of the decision process when two people have to agree. Moreover, the serious problems in carrying out an experiment when a decision tree is imposed upon the subjects, reveal the potential inadequacy of the assumed total rationality of the decision maker.