Bounded size dictionary compression: SCk-completeness and NC algorithms

1998 ◽  
pp. 522-532 ◽  
Author(s):  
Sergio De Agostino ◽  
Riccardo Silvestri
Keyword(s):  
Bounded Size ◽  
Nc Algorithms

scholarly journals Bounded size dictionary compression: SCk-completeness and NC algorithms

2003 ◽  
Vol 180 (2) ◽  
pp. 101-112 ◽  
Author(s):  
Sergio De Agostino ◽  
Riccardo Silvestri
Keyword(s):  
Bounded Size ◽  
Nc Algorithms

scholarly journals A Synopsis Based Approach for Itemset Frequency Estimation over Massive Multi-Transaction Stream

2021 ◽  
Vol 16 (2) ◽  
pp. 1-30
Author(s):  
Guangtao Wang ◽  
Gao Cong ◽  
Ying Zhang ◽  
Zhen Hai ◽  
Jieping Ye
Keyword(s):  
Frequency Estimation ◽  
Frequent Itemsets ◽  
Frequent Itemset ◽  
Experimental Results ◽  
Closure Property ◽  
Frequent Itemset Mining ◽  
Itemset Mining ◽  
Minimum Value ◽  
Downward Closure ◽  
Bounded Size

The streams where multiple transactions are associated with the same key are prevalent in practice, e.g., a customer has multiple shopping records arriving at different time. Itemset frequency estimation on such streams is very challenging since sampling based methods, such as the popularly used reservoir sampling, cannot be used. In this article, we propose a novel k -Minimum Value (KMV) synopsis based method to estimate the frequency of itemsets over multi-transaction streams. First, we extract the KMV synopses for each item from the stream. Then, we propose a novel estimator to estimate the frequency of an itemset over the KMV synopses. Comparing to the existing estimator, our method is not only more accurate and efficient to calculate but also follows the downward-closure property. These properties enable the incorporation of our new estimator with existing frequent itemset mining (FIM) algorithm (e.g., FP-Growth) to mine frequent itemsets over multi-transaction streams. To demonstrate this, we implement a KMV synopsis based FIM algorithm by integrating our estimator into existing FIM algorithms, and we prove it is capable of guaranteeing the accuracy of FIM with a bounded size of KMV synopsis. Experimental results on massive streams show our estimator can significantly improve on the accuracy for both estimating itemset frequency and FIM compared to the existing estimators.

Parallel algorithms for matroid intersection and matroid parity

2015 ◽  
Vol 07 (02) ◽  
pp. 1550019
Author(s):  
Jinyu Huang
Keyword(s):  
Parallel Algorithms ◽  
Polynomial Identity ◽  
Black Box ◽  
Matroid Intersection ◽  
Polynomial Identity Testing ◽  
Identity Testing ◽  
Common Base ◽  
Graphic Matroid ◽  
Matroid Parity ◽  
Nc Algorithms

A maximum linear matroid parity set is called a basic matroid parity set, if its size is the rank of the matroid. We show that determining the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity) is in NC2, provided that there are polynomial number of common bases (basic matroid parity sets). For graphic matroids, we show that finding a common base for matroid intersection is in NC2, if the number of common bases is polynomial bounded. To our knowledge, these algorithms are the first deterministic NC algorithms for matroid intersection and matroid parity. We also give a new RNC2 algorithm that finds a common base for graphic matroid intersection. We prove that if there is a black-box NC algorithm for Polynomial Identity Testing (PIT), then there is an NC algorithm to determine the existence of a common base (basic matroid parity set) for linear matroid intersection (linear matroid parity).

NC-ALGORITHMS FOR OPERATIONS ON BINARY DECISION DIAGRAMS

1993 ◽  
Vol 03 (01) ◽  
pp. 3-12 ◽  
Author(s):  
DETLEF SIELING ◽  
INGO WEGENER
Keyword(s):  
Binary Decision Diagrams ◽  
Pattern Generation ◽  
Decision Diagrams ◽  
Equivalence Test ◽  
Ordered Binary Decision Diagrams ◽  
Binary Decision ◽  
Verification Test ◽  
Logical Synthesis ◽  
Redundancy Test ◽  
Nc Algorithms

(Ordered) binary decision diagrams are a powerful representation for Boolean functions and are widely used in logical synthesis, verification, test pattern generation or as part of CAD tools. NC-algorithms are presented for the most important operations on this representation, e.g. evaluation for a given input, minimization, satisfiability, redundancy test, replacement of variables by constants or functions, equivalence test and synthesis. The algorithms have logarithmic run time on CRCW COMMON PRAMs with a polynomial number of processors.

scholarly journals Twin-width I: Tractable FO Model Checking

2022 ◽  
Vol 69 (1) ◽  
pp. 1-46
Author(s):  
Édouard Bonnet ◽  
Eun Jung Kim ◽  
Stéphan Thomassé ◽  
Rémi Watrigant
Keyword(s):  
Model Checking ◽  
Elementary Function ◽  
First Order ◽  
Fpt Algorithm ◽  
Fixed Parameter ◽  
Dimension 2 ◽  
Bounded Size ◽  
Map Graphs ◽  
Dimensional Ball ◽  
Bounded Width

Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA’14], we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, K t -free unit d -dimensional ball graphs, posets with antichains of bounded size, and proper subclasses of dimension-2 posets all have bounded twin-width. On all these classes (except map graphs without geometric embedding) we show how to compute in polynomial time a sequence of d -contractions , witness that the twin-width is at most d . We show that FO model checking, that is deciding if a given first-order formula ϕ evaluates to true for a given binary structure G on a domain D , is FPT in |ϕ| on classes of bounded twin-width, provided the witness is given. More precisely, being given a d -contraction sequence for G , our algorithm runs in time f ( d ,|ϕ |) · |D| where f is a computable but non-elementary function. We also prove that bounded twin-width is preserved under FO interpretations and transductions (allowing operations such as squaring or complementing a graph). This unifies and significantly extends the knowledge on fixed-parameter tractability of FO model checking on non-monotone classes, such as the FPT algorithm on bounded-width posets by Gajarský et al. [FOCS’15].

Algorithm for Decision Procedure in Temporal Logic Treating Uncertainty, Plausibility, Knowledge and Interacting Agents

2012 ◽  
pp. 32-46
Author(s):  
V. Rybakov
Keyword(s):  
Normal Form ◽  
Temporal Logic ◽  
Decision Procedure ◽  
Linear Temporal Logic ◽  
Satisfiability Problem ◽  
Global Knowledge ◽  
Interacting Agents ◽  
Logical Operations ◽  
Multi Agent ◽  
Bounded Size

Our paper studies a logic UIALTL, which is a combination of the linear temporal logic LTL, a multi-agent logic with operation for passing knowledge via agents’ interaction, and a suggested logic based on operation of logical uncertainty. The logical operations of UIALTL also include (together with operations from LTL) operations of strong and weak until, agents’ knowledge operations, operation of knowledge via interaction, operation of logical uncertainty, the operations for environmental and global knowledge. UIALTL is defined as a set of all formulas valid at all Kripke-Hintikka like models NC. Any frame NC represents possible unbounded (in time) computation with multi-processors (parallel computational units) and agents’ channels for connections between computational units. The main aim of our paper is to determine possible ways for computation logical laws of UIALTL. Principal problems we are dealing with are decidability and the satisfiability problems for UIALTL. We find an algorithm which recognizes theorems of UIALTL (so we show that UIALTL is decidable) and solves satisfiability problem for UIALTL. As an instrument we use reduction of formulas to rules in the reduced normal form and a technique to contract models NC to special non-UIALTL-models, and, then, verification of validity these rules in models of bounded size. The paper uses standard results from non-classical logics based on Kripke-Hintikka models.

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