Self-stabilizing Hierarchical Construction of Bounded Size Clusters

2011 ◽  
pp. 54-65 ◽  
Author(s):  
Alain Bui ◽  
Simon Clavière ◽  
Ajoy K. Datta ◽  
Lawrence L. Larmore ◽  
Devan Sohier
Keyword(s):  
Bounded Size

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.

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.

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 Improper colouring of graphs with no odd clique minor

2019 ◽  
Vol 28 (5) ◽  
pp. 740-754
Author(s):  
Dong Yeap Kang ◽  
Sang-Il Oum
Keyword(s):  
Maximum Degree ◽  
Hadwiger's Conjecture ◽  
Vertex Set ◽  
Bounded Size ◽  
Hadwiger’S Conjecture

AbstractAs a strengthening of Hadwiger’s conjecture, Gerards and Seymour conjectured that every graph with no oddKtminor is (t− 1)-colourable. We prove two weaker variants of this conjecture. Firstly, we show that for eacht⩾ 2, every graph with no oddKtminor has a partition of its vertex set into 6t− 9 setsV1, …,V6t−9such that eachViinduces a subgraph of bounded maximum degree. Secondly, we prove that for eacht⩾ 2, every graph with no odd Kt minor has a partition of its vertex set into 10t−13 setsV1,…,V10t−13such that eachViinduces a subgraph with components of bounded size. The second theorem improves a result of Kawarabayashi (2008), which states that the vertex set can be partitioned into 496tsuch sets.

Non-uniformity issues and workarounds in bounded-size sampling

2013 ◽  
Vol 22 (6) ◽  
pp. 753-772 ◽  
Author(s):  
Rainer Gemulla ◽  
Peter J. Haas ◽  
Wolfgang Lehner
Keyword(s):  
Bounded Size
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