Directed Acyclic

Documents about Directed Acyclic

	lec17.2p Maryland, CMSC 430 Excerpt: ... Common subexpressions Consider the tree for the expression a + a * b - c + b - c * d Directed acyclic graphs The directed acyclic graph is a useful representation for such expressions a + a * b - c + b - c * d + + a a b c b c a b * d * + * + * d Both a and b-c are common subexpressions cse compute the same value should compute the value once A simple and general form of code improvement CMSC 430 Lecture 17, Page 1 c The dag clearly exposes the cses Aho, Sethi, and Ullman, x5.2, x9.8, : : : CMSC 430 Lecture 17, Page 2 Directed acyclic graphs A directed acyclic graph is a tree with sharing Directed acyclic graphs a tree is a directed acyclic graph where each node has at most one parent a dag allows multiple parents for each node both a tree and a dag have a distinguished root no cycles in the graph! How do we build a dag for an expression? use construction primitives for building tree teach primitives to catch cse's \| mkleaf and mknode \| hash on op,l,r unique name for each node \| its v ...
	375-4 Michigan Flint, CSC 375 Excerpt: ... unweighted. * Adjacent, incident, path, simple path, length of a path, cycle, simple cycle. * subgraph, connected, acyclic, Directed Acyclic Graph (DAG), free tree. Graph implementations: * Adjacency matrix: given a graph, show the representation. * Adjacency list: given a graph, show the representation. Graph traversals: * DFS ...
	Lec_Part_16 Alabama, CS 470 Excerpt: ... Lecture Notes for CS470 Fall 2004 Part 16 (preliminary draft) Topological sort [Give a realistic example of events, dependencies between them, and their ordering the events - building a home] Suppose that you have a certain set of tasks to perform, and there are dependencies between some of these task [so that a task can be executed only after certain tasks have been executed]. Today, we will find out how to sequence the execution of the tasks so as not to violate the dependencies, if possible. A cycle is a path of length at least one in which v0=vk. A directed graph with no cycles is called directed acyclic graph (dag). Applications modeling precedence among events / tasks. [give example of a cycle and dag] Definition Topological sort is a linear ordering of vertices consistent with the edges of a directed graph i.e., if there is an edge (u,v) in the graph, then u occurs (strictly) before v in the ordering [this implies that if there is an edge (v,v) then v should occur before v - impossible] ...
	sl-17 Texas Tech, CS 5353 Excerpt: ... he scanner and parser: The scanner-will modify the symbol table code to enter the correct types for variables (INT, REAL or undefined) The parser-will embed in each parsing procedure calls to semantic code generation procedures-must understand how the parser works Lecture 17: Intermediate Code Generation 4 Modifying the Symbol Table Handler The Symbol Table You Have Used So Far: Name Begin . Sum X Y Each record has two fields. Need to introduce a third field to represent the type Code BeginSym ID ID ID Lecture 17: Intermediate Code Generation 5 Name Begin . Sum X Y Will come back to this in Lecture 21. Code BeginSym ID ID ID Kind IntVar RealVar undefined Lecture 17: Intermediate Code Generation 6 Lecture 17: Intermediate Representation Reading Lecture Notes: Chapter 7 1. The role of the intermediate code generator Semantic analysis (using the symbol table) Translation 2. Four Typical Representations: Syntax trees Directed acyclic graphs (DAGs) Postfix notation Three-address code (3 ...
	Lec_06 Alabama, CS 470 Excerpt: ... Lecture Notes for CS470 Fall 2005 Part 6 (preliminary draft) Topological sort [Give a realistic example of events, dependencies between them, and their ordering the events - building a home] Suppose that you have a certain set of tasks to perform, and there are dependencies between some of these tasks [so that a task can be executed only after certain tasks have been executed]. Today, we will find out how to sequence the execution of the tasks so as not to violate the dependencies, if possible. In a directed graph, a cycle is a path of length at least one in which v0=vk. The definition is different from the definition of a cycle for undirected graphs, because in the following directed graph b a d (c,c) is a cycle, so is (a,b,a), so is (b,c,d,b,c,d,b). A directed graph with no cycles is called directed acyclic graph (dag). Applications modeling precedence among events / tasks. c a b c d Definition Topological sort is a linear ordering of vertices consistent with the edges of a directed graph i.e., ...
	lec20 Texas A&M, PEOPLE 434 Excerpt: ... Better code generation Goal is to produce more e cient code for expressions We consider directed acyclic graphs (DAG) \optimal" register allocation for trees Sethi-Ullman \more optimal" register allocation for trees Proebsting-Fischer CPSC 434 Lecture 20, Page 1 Common subexpressions Consider the tree for the expression a + a * ( b - c ) + ( b - c ) * d + + a a b * c d b * c Both a and b-c are common subexpressions (cse ) compute the same value should compute the value once A simple and general form of code improvement CPSC 434 Lecture 20, Page 2 Directed acyclic graphs The directed acyclic graph is a useful representation for such expressions a + a * ( b - c ) + ( b - c ) * d + + * a b The dag clearly exposes the cses Aho, Sethi, and Ullman, x5.2, x9.8, : : : CPSC 434 Lecture 20, Page 3 * d c Directed acyclic graphs A directed acyclic graph is a tree with sharing a tree is a directed acyclic graph where each node has at most one parent a dag allows multiple parents for each node both a tree an ...
	graph5 Concordia Chicago, STAT 36500 Excerpt: ... 5 Directed acyclic graphs (5.1) Introduction In many statistical studies we have prior knowledge about a temporal or causal ordering of the variables. In this chapter we will use directed graphs to incorporate such knowledge into a graphical model for the variables. Let XV = (Xv )vV be a vector of real-valued random variables with probability distribution P and density p. Then the density p can always be decomposed into a product of conditional densities, d p(x) = p(xd \|x1 , . . . , xd-1 )p(x1 , . . . , xd-1 ) = . . . = v=1 p(xv \|x1 , . . . , xv-1 ). (5.1) Note that this can be achieved for any ordering of the variables. Now suppose that the conditional density of some variable Xv does not depend on all its predecessors, namely X1 , . . . , Xv-1 , but only on a subset XUv , that is, Xv is conditionally independent of its predecessors given XUv . Substituting p(xv \|xUv ) for p(xv \|x1 , . . . , xv-1 ) in the product (5.1), we obtain d p(x) = v=1 p(xv \|xUv ). (5.2) This recursive dependence structure c ...
	lec14_notes Iowa State, EE 520 Excerpt: ... Iowa State University Lecturer: Aditya Ramamoorthy EE 520: Topics in Communications: Network Coding October 15, 2007 Scribe: Seth Stanley Lecture 14 Graphs with cycles In the presentation up until this point, we have exclusively considered directed acyclic graphs. All the code construction algorithms that we have considered have implicitly used the assumption of acyclicity. For example, in the Linear-Information-Flow (LIF) algorithm, the assignment of a code vector for a given edge can be done because we assume that the assignment for edges that feed into it has already been done. In acyclic graphs, a numbering of the edges can be done so that only lower-numbered edges feed into higher-numbered edges. The code vectors can then be assigned according to this order. However, in cyclic graphs, such an ordering is impossible. Also, the algebraic approach that we presented earlier needs to be modied by introducing a delay parameter. There are also some technicalities the need to be taken care of (please see the ...
	EEG_Final_Presentation Temple, C 4339 Excerpt: ... d using the first half of data over time for the first model and the second half of over time for the second model Co pa ed each ode and created Compared eac model a d c eated a weight matrix e g t at Normalized the data 5/9/2008 17 OSB algorithm OSB : Optimal Subsequence Bijection It is an algorithm that determines the optimal subsequence bijection between two sequences of real numbers. We were given a code `tsDAGjump4' that worked for only one channels and we modified so it can work for more than 1 channels.( works for 40 channels) Modification: Created difference matrix with each entry containing differences of corresponding elements. 5/9/2008 18 Why OSB algorithm? The OSB is efficient because we use DAG( Directed Acyclic Graph), cheapest path to find the solution. By using DAG in OSB, we get p y g , g perfect and correct results on Time Series dataset. DAG helps us to get rid of outlier elements and get one-to-one or one-toonto bijection of a sequences. Comparing OSB with DTW using warping window OSB ...
	cse460_lecture12 Washington University in St. Louis, CSE 460 Excerpt: ... CSE 460 : Switching Theory Lecture 12: Binary Decision Diagrams (BDDs) Washington University Spring 2006 http:/www.arl.wustl.edu/~lockwood/class/cse460/ Copyright 2006, John W Lockwood CSE460 : Lockwood 1 Binary Decision Diagrams (BDDs) Reading Chapter 6 of text Properties of BDDs Canonical Same circuits will have same BDD given the same ordering of terms! Scalable Can decompose large circuits Reduced BDDs Isomorphic subgraphs Remove redundant nodes CSE460 : Lockwood 2 Directed Acyclic Graph (DAG) Directed Acyclic Graph (DAG) Directed Edges are of one direction Acyclic No cycles between Nodes Binary Decision Diagram Nodes are Multiplexors Root node is the function Leaf nodes are {0,1} Literals are the selectors CSE460 : Lockwood 3 Creating a BDD (1) Choose an Order Ordered BDD Literals appear in same order along all paths from root to leaves Prefer largest split first Generate Root Node Apply ...
	ee460_lecture13 Washington University in St. Louis, COE 460 Excerpt: ... CoE/EE460 Switching Theory Lecture 13 Washington University Spring 2001 http:/www.arl.wustl.edu/~lockwood/class/coe460/ Copyright 2001, John W Lockwood CoE/EE460 : Lockwood 1 Announcements Homework 4 Points lost for missing e-f-g-h-i-j Resubmit to Henry before Wednesday for credit Homework 5 Problems 1 - 4 require 3 Solutions NMOS + resistor(s) only PMOS + resistor(s) only NMOS + PMOS = CMOS only Problem Consider 2LUT, 3LUT Solution Consider 3LUT, 2LUT Solution CoE/EE460 : Lockwood 2 Binary Decision Diagrams (BDDs) Properties of BDDs Canonical Same circuits will have same BDD Assuming the same ordering of terms! Effective for large sets Chapter 6 of text CoE/EE460 : Lockwood 3 Directed Acyclic Graph (DAG) Directed Acyclic Graph (DAG) Directed Edges are of one direction Acyclic No cycles between Nodes Binary Decision Diagram Nodes are Multipexors Root node is the function Leaf nodes are {0,1} Literals are the selectors CoE/EE460 : Lockwood 4 ...
	hw6 RIT, CS 800 Excerpt: ... Algorithms, Spring 2008-09, Homework 6 due Wednesday 4/29/09, 11:59pm For every problem include the pseudocode of your algorithm and a short verbal description. Briefly argue your algorithm's correctness and explain its running time. Problem 1 Give a linear-time algorithm (i.e., O(n + m) that decides whether a given undirected graph is cyclic. Problem 2 Give an O(n2 ) algorithm that computes the length of the longest path in a given directed acyclic graph. Hint: use topological sort and dynamic programming. Note: the problem of computing the longest path in undirected graphs or directed graphs with cycles, is known to be NP-complete. This means that we do not know whether a polynomial-time algorithm exists or not (most people think that it does not exist). However, if the input is a directed acyclic graph, this problem can be solved in polynomial-time. Problem 3 Given is a weighted undirected graph G = (V, E) with positive weights and a subset of its edges F E. An F -containing spanning tree of G is a sp ...
	Notes1-2 CSU LA, CS 386 Excerpt: ... O(N) = how long the program takes to run with N inputs, or how fast it experiences growth, in terms of time for algorithms. As number of inputs increases, algorithms with differentrunning times increase in different proportions. O(1) O(lg n) O(n) O(n lg n) O(n2) O(nk) O(kn) O(nn) O(n!) Constant time Logarithmic time Quadratic time Polynomial time Exponential time Super polynomial time Factorial time Tower of Hanoi - puzzle solution has a running time of factorial. Graphs Graphs are composed of vertices and edges Digraph has edges with direction V={v1, v2, v3, v4} set or vertices E={e1, e2, e3, e4} set of edges e1={vj, vk} edge defined by vertices. A Walk is a sequence of visits from vertices vi to vj A Walk where NO EDGE is repeated is a Path. A Path where no VERTEX is repeated is a Simple Path. (no cycles) A Walk from v1 to itself is a cycle (no edge repeated). Simple Cycle = no vertices are repeated. Loop = an edge from a vertex to itself. DAG = Directed Acyclic Graph No cycles, directed edges. Fu ...
	Notes1-2 CSU LA, CS 386 Excerpt: ... o run with N inputs, or how fast it experiences growth, in terms of time for algorithms. As number of inputs increases, algorithms with differentrunning times increase in different proportions. O(1) O(lg n) O(n) O(n lg n) O(n2) O(nk) O(kn) O(nn) O(n!) Constant time Logarithmic time Quadratic time Polynomial time Exponential time Super polynomial time Factorial time Tower of Hanoi - puzzle solution has a running time of factorial. Graphs Graphs are composed of vertices and edges Digraph has edges with direction V={v1, v2, v3, v4} set or vertices E={e1, e2, e3, e4} set of edges e1={vj, vk} edge defined by vertices. A Walk is a sequence of visits from vertices vi to vj A Walk where NO EDGE is repeated is a Path. A Path where no VERTEX is repeated is a Simple Path. (no cycles) A Walk from v1 to itself is a cycle (no edge repeated). Simple Cycle = no vertices are repeated. Loop = an edge from a vertex to itself. DAG = Directed Acyclic Graph No cycles, directed edges. Fully Connected Graph Every node conn ...
	hw9 Wisconsin Milwaukee, CS 535 Excerpt: ... CS 535 HW 9 Due: April 30 (Th), in class. Undergrads and grads, please answer all the questions. 1. R-6.6. 2. Consider a grid board where some of the squares are shaded. (An example is shown below.) We wish to determine a knight's tour, if one exists, that starts at the square designated by s and, after visiting the minimum number of squares, ends at the square designated by t. (Note: A "knight" here is a chess piece and not a knight in King Arthur's court!) The tour must not visit any shaded square. Describe how this problem can be formulated on a graph; that is specify the vertices and edges of the graph, and the associated problem you have to solve. Next, design an algorithm for solving this problem. What is its running time? Why is it correct? s t 3. Given a directed acyclic graph G = (V, E) and two vertices s and t. Design an algorithm that returns the number of paths from s to t in G in O(\|V \| + \|E\|) time. 4. (Based on C-6.9) Given a tree T and a node v of T , the eccentricity of v is the length of a ...
	StudyGuide2 Kent State, CS 303 Excerpt: ... o conduct topological sorting? o What is a DAG ( Directed Acyclic Graph)? ...
	Figure1RIPRCWebsite-R Minnesota, ENHS 1 Excerpt: ... TheAssociationbetweenParentsPastAgriculturalInjuriesandtheirChildrensRiskofInjury: AnalysesfromtheRegionalRuralInjuryStudyII Kathleen Ferguson Carlson, MS; Deborah Langner, MS; Bruce H. Alexander, PhD; James G. Gurney, PhD; Susan Goodwin Gerberich, P ...
	seminar_recknor Iowa State, SEMINARS 2005 Excerpt: ... Seminar Notice Statistical Laboratory Iowa State University DATE AND TIME: PLACE: SPEAKER: Tuesday, July 25 Coover 1219 Justin Recknor 1:10 p.m. TITLE: Identification of Differentially Expressed Functional Categories in Microarray Studies Using Nonparametric Multivariate Analyses ABSTRACT Tests of differential expression across groups of genes, within a functional category, are performed using a method motivated by Barry, Nobel, and Wright (2005). Rather than comparing marginal distributions on a gene-by-gene basis across treatment groups, we use a test statistic that can detect general changes in multivariate distributions across treatment groups. Resampling-based methods and multiple-testing adjustments are used to obtain simultaneous inference for multiple groups of genes. Results are visualized on a directed acyclic al graph, and new methods for pinpointing genes of greatest interest are provided. Seminar schedules and abstracts are available via WWW: http:/www.stat.iastate.edu/ ...
	final-review Utah, CS 2420 Excerpt: ... Final Exam Study Guide 1 Balanced BSTs (Chapter 19) Rotations Single Rotations Double Rotations Inner vs. Outer cases AVL Trees Recursive Definition Insertion Red-Black Trees Definition Top-Down insertion Top-Down deletion AA trees Definition Split and Skew Algorithms Breadth First Search Depth First Search Topological Sort Single-Source Shortest paths Unweighted, positive weighted (Dijkstra's Algorithm), negative weighted Strongly Connected Components Minimum Spanning Trees (Kruskal's and Prim's algorithms) 3 Heaps (Chapter 21) Heap order property Storage (in an array) Insertion/Deletion making a heap from a binary tree 2 Graphs (Chapter 14) Definitions Vertices/nodes Edges/arcs Directed vs. Undirected Directed acyclic graph path path length edge cost/weight simple path Representation Adjacency Matrix Adjacency List 1 4 Hash Tables (Chapter 20) Hash Functions Collisions and Collision Handling Linear Probing Quadratic ...
	StudyGuide2 Kent State, CS 303 Excerpt: ... o conduct topological sorting? o What is a DAG ( Directed Acyclic Graph)? ...
	hw2 UCSD, CSE 101 Excerpt: ... CSE 101: Homework 2 (Due Wednesday, Jan 23rd in Lecture) 1. Exercise 3.4 (ii) 2. Are the following statements true or false? If true, prove it; otherwise give a counter example. In a directed graph with two strongly connected components, it is alwa ...
	d7 UC Davis, ECS 122 Excerpt: ... ath between nodes 1 and 8 Keep a queue of nodes and a note of which nodes we have visited, and how we got to This algorithm passes along each edge at most once, so it has time complexity O(\|E\|) Depth First Search (DFS) Go as far as we can, if we don't have a solution, backtrack to an unvisited branch and try another route Backtracking is not found in BFS DFS uses stacks (Last In, First Out), not queues Example: topological sort - Finding the topological order of a directed acyclic graph Summary These searches are very common Adaptable to many problems But not all Used widely outside graphs E.g. backtracking and tree searching Topological Sort Topological order: A numbering of the vertices of a directed acyclic graph such that every edge from a vertex numbered i to a vertex numbered j satisfies i<j Topological Sort: Finding the topological order of a directed acyclic graph a, c, b, d Problem Given as input a weighted, directed, acyclic graph where the edge weights can be ...
	18 UPenn, CIS 121 Excerpt: ... ongly Connected Components Maximal subgraphs such that each vertex can reach all other vertices in the subgraph Finding them can be done in O(n+m) time using DFS, but is more complicated (similar to biconnectivity). a c d f Lecture Notes 18 g { a , c , g } e b { f , d , e , b } 9 DAGs and Topological Ordering A directed acyclic graph (DAG) is a digraph that has no directed cycles A topological ordering of a digraph is a numbering v1 , , vn of the vertices such that for every edge (vi , vj), we have i < j Topological ordering is not unique! Theorem A digraph admits a topological ordering if and only if it is a DAG D B C A v2 B v1 A C D v4 E DAG G v5 E v3 Topological ordering of G 10 4/10/09 Lecture Notes 18 5 Topological Sorting Number vertices, so that (u,v) in E implies u < v 1 wake up A typical student day eat 4 3 2 study computer sci. nap 7 play 5 more c.s. 8 write c.s. program at 10 sleep 9 throw epie professor 6 work out 11 dream about graphs Lecture No ...
	pa3 Binghamton, CS 333 Excerpt: ... udo described in pages 147 148 in the textbook or the pseudo code given in slide 16 of the lecture note on Prims algorithm. The algorithm in the textbook is easier, since it just uses a one dimensional array rather than a min-heap. Thus, you are only required to correctly implement the textbook algorithm. If you implement the min-heap version correctly in addition to implementing the required textbook algorithm, you will get 20% extra credit. 2. [40%] Implement the Dijkstras single-source shortest path algorithm. (pages 158 159 in the textbook) G2 G 1) Store the graph G2 above as a text file and read in the file to construct the adjacency matrix, similar to Programming Assignment 2. Also, specify the source node in the text file. Note that the TA will test your code using different graphs too; therefore, your code should work correctly for any connected directed acyclic graph. 2) Print the single source shortest paths. For example, your program should print out the shortest path from s to s1 ...
	knapsack Sanford-Brown Institute, CSCI 2580 Excerpt: ... w to generate and/or obtain benchmarks for the problems. 2.2 Dynamic Programming Algorithm Task: Write a dynamic programming algorithm to solve the knapsack problem. Study its practical performance on various benchmarks. Due Date: Thursday, February 7, Noon 2.3 Branch and Bound Algorithm Task: Write a branch and bound algorithm to solve the knapsack problem. Study the tradeo between pruning and searching on various benchmarks. Compare the performance with the dynamic programming approach on various classes of benchmarks. Due Date: Thursday, February 7, Noon 2.4 Local Search Algorithm Task: Write a local search algorithm to solve the knapsack problem. Study the quality of its solutions on various classes of benchmarks. Compare its running time with dynamic programming and branch & bound. Due Date: Thursday, February 14, Noon 3 Homework Task: Dynamic programming for knapsack can be interpreted as computing a longest path in a directed acyclic graph (dag). Consider the knapsack problem given at t ...