scholarly journals Longest Path Distance in Random Circuits

2012 ◽  
Vol 21 (6) ◽  
pp. 856-881
Author(s):  
NICOLAS BROUTIN ◽  
OMAR FAWZI
Keyword(s):  
Large Deviation ◽  
Directed Acyclic Graphs ◽  
Branching Random Walk ◽  
Acyclic Graphs ◽  
Large Numbers ◽  
Path Distance ◽  
Multiple Paths ◽  
Minimum Depth ◽  
Random Circuits ◽  
Distance Properties

We study distance properties of a general class of random directed acyclic graphs (dags). In a dag, many natural notions of distance are possible, for there exist multiple paths between pairs of nodes. The distance of interest for circuits is the maximum length of a path between two nodes. We give laws of large numbers for the typical depth (distance to the root) and the minimum depth in a random dag. This completes the study of natural distances in random dags initiated (in the uniform case) by Devroye and Janson. We also obtain large deviation bounds for the minimum of a branching random walk with constant branching, which can be seen as a simplified version of our main result.

scholarly journals Large deviation estimates for branching random walks

2019 ◽  
Vol 23 ◽  
pp. 823-840
Author(s):  
Dariusz Buraczewski ◽  
Mariusz Maślanka
Keyword(s):  
Random Walk ◽  
Law Of Large Numbers ◽  
Large Deviation ◽  
First Passage Time ◽  
Passage Time ◽  
Branching Random Walk ◽  
First Passage ◽  
Branching Random Walks ◽  
The Central Limit Theorem ◽  
Large Numbers

For the branching random walk drifting to −∞ we study large deviations-type estimates for the first passage time. We prove the corresponding law of large numbers and the central limit theorem.

Probabilistic and Fuzzy based Efficient Routing Protocol for Mobile Ad Hoc Networks

2020 ◽  
Vol 13 (3) ◽  
pp. 422-432
Author(s):  
Madan Mohan Agarwal ◽  
Hemraj Saini ◽  
Mahesh Chandra Govil
Keyword(s):  
Fuzzy Logic ◽  
Energy Consumption ◽  
Routing Protocol ◽  
Queue Length ◽  
Ad Hoc ◽  
Fuzzy Controller ◽  
Second Phase ◽  
Path Distance ◽  
Fixed Threshold ◽  
Multiple Paths

Background: The performance of the network protocol depends on number of parameters like re-broadcast probability, mobility, the distance between source and destination, hop count, queue length and residual energy, etc. Objective: In this paper, a new energy efficient routing protocol IAOMDV-PF is developed based on the fixed threshold re-broadcast probability determination and best route selection using fuzzy logic from multiple routes. Methods: In the first phase, the proposed protocol determines fixed threshold rebroadcast probability. It is used for discovering multiple paths between the source and the destination. The threshold probability at each node decides the rebroadcasting of received control packets to its neighbors thereby reducing routing overheads and energy consumption. The multiple paths list received from the first phase and supply to the second phase that is the fuzzy controller selects the best path. This fuzzy controller has been named as Fuzzy Best Route Selector (FBRS). FBRS determines the best path based on function of queue length, the distance between nodes and mobility of nodes. Results: Comparative analysis of the proposed protocol named as "Improved Ad-Hoc On-demand Multiple Path Distance Vector based on Probabilistic and Fuzzy logic" (IAOMDV-PF) shows that it is more efficient in terms of overheads and energy consumption. Conclusion: The proposed protocol reduced energy consumption by about 61%, 58% and 30% with respect to FF-AOMDV, IAOMDV-F and FPAOMDV routing protocols, respectively. The proposed protocol has been simulated and analyzed by using NS-2.

scholarly journals Directed acyclic graphs: An under-utilized tool for child maltreatment research

2019 ◽  
Vol 91 ◽  
pp. 78-87 ◽  
Author(s):  
Anna E. Austin ◽  
Tania A. Desrosiers ◽  
Meghan E. Shanahan
Keyword(s):  
Child Maltreatment ◽  
Directed Acyclic Graphs ◽  
Acyclic Graphs

scholarly journals On directed analogues of expander and hyperfinite graph sequences

2021 ◽  
pp. 1-14
Author(s):  
Endre Csóka ◽  
Łukasz Grabowski
Keyword(s):  
Directed Acyclic Graphs ◽  
Acyclic Graphs ◽  
Probabilistic Construction

Abstract We introduce and study analogues of expander and hyperfinite graph sequences in the context of directed acyclic graphs, which we call ‘extender’ and ‘hypershallow’ graph sequences, respectively. Our main result is a probabilistic construction of non-hypershallow graph sequences.

PATTERN MATCHING CODE MINIMIZATION IN REWRITING-BASED PROGRAMMING LANGUAGES

2002 ◽  
Vol 13 (06) ◽  
pp. 873-887
Author(s):  
NADIA NEDJAH ◽  
LUIZA DE MACEDO MOURELLE
Keyword(s):  
Programming Languages ◽  
Pattern Matching ◽  
Term Rewriting ◽  
Directed Acyclic Graphs ◽  
Tree Automaton ◽  
Minimal Tree ◽  
Term Rewriting Systems ◽  
Rewriting Systems ◽  
Acyclic Graphs ◽  
Space Requirements

We compile pattern matching for overlapping patterns in term rewriting systems into a minimal, tree matching automata. The use of directed acyclic graphs that shares all the isomorphic subautomata allows us to reduce space requirements. These are duplicated in the tree automaton. We design an efficient method to identify such subautomata and avoid duplicating their construction while generating the dag automaton. We compute some bounds on the size of the automata, thereby improving on previously known equivalent bounds for the tree automaton.

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