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Basic Graph Algorithms

Jun 29, 2015 ... Outline. Graphs. Adjacency Matrix and Adjacency List. Special Graphs. Depth- First and Breadth-First Search. Topological Sort. Eulerian Circuit. Minimum Spanning Tree (MST). Strongly Connected Components (SCC). Graphs. 2 ...


Parallel breadth-first search algorithms for trees and graphs

(Received February 1983, in final form January 1984). Parallel Breadth-First Search (BFS) algorithms for ordered trees and graphs on a shared memory model of a Single Instruction-stream Multiple Data-stream computer are proposed. The parallel BFS algorithm for trees computes the BFS rank of each node of an ordered ...


Verification of the Schorr-Waite algorithm – From trees to graphs

Verification of the Schorr-Waite algorithm –. From trees to graphs. Mathieu Giorgino, Martin Strecker, Ralph Matthes, and Marc Pantel. IRIT (Institut de Recherche en Informatique de Toulouse). Université de Toulouse. Abstract. This article proposes a method for proving the correctness of graph algorithms by manipulating ...


A Node-Positioning Algorithm for General Trees

This algorithm addresses the problem of drawing tree structures. Trees are a common method of representing a hierarchically-organized structure. In com- puter science, trees are ... Several algorithms for the positioning of general trees have been published; in the works of Sweet" ... Depth-first spanning trees (graph theory).


Lecture 7: Minimum Spanning Trees and Prim's Algorithm

Generic approach: A tree is an acyclic graph. The idea is to start with an empty graph and try to add edges one at a time, always making sure that what is built remains acyclic. And if we are sure every time the resulting graph always is a subset of some minimum spanning tree, we are done. 7 ...


Improved Algorithms for Some Competitive Location Centroid

For the (r,1)-centroid problem, we show that it is strongly NP-hard for a general graph, but can be approximated within a factor e/(e−1). On the other hand, when the graph is a tree, we provide strongly polynomial algorithms for the (r,p)- centroid model, whenever p is fixed. For the (1,1)-centroid problem on a general graph, ...


A Linear Algorithm for Embedding Planar Graphs Using PO-Trees

Cederbaum (“Theory of Graphs,” Intl. Sympos. Rome, July 1966, pp. 21>232, Gordon &. Breach, New York, 1967) for the planarity testing, and is a modification of Booth and. Lueker's (J. Comput. System Sci. 13 (1976), 335379) implementation of the testing algorithm using a PQ-tree. Compared with the known embedding ...

A Linear Algorithm for Embedding Planar Graphs Using PQ-Trees.pdf

Algorithms for Finding Dominators in Directed Graphs

1979, Lengauer and Tarjan presented a fast algorithm for finding dominators. [ LT79]. This approach creates a tree structure for the graphs and uses this to find an approximated immediate dominator for each vertex, after this it uses these approximated immediate dominators alongside observation of the tree structure to find ...


UNIT 6C Organizing Data: Trees and Graphs Last Lecture

2. This Lecture. • Non-linear data structures. – Trees, specifically, binary trees. – Graphs. 15110 Principles of Computing,. Carnegie Mellon University. 3. Trees .... Building a Max-Heap. • To build a max-heap, just insert each element one at a time into the heap using the previous algorithm. 15110 Principles of Computing,.



Jan 31, 1979 ... and compute a coding for forests, interval graphs, outerplanar graphs, and planar graphs. Key words, automorphism partition, graph automorphism, interval graph, outerplanar graph. 1. Preliminaries. Starting from an algorithm for tree isomorphism we show how to build efficient algorithms whichcan answer ...


Dynamic Algorithms for Graphs with Treewidth 2?

In this paper, we con- sider dynamic algorithms for graphs with treewidth at most 2, (also known as partial. 2-trees or series-parallel graphs.) These contain all outerplanar graphs. Many problems become linear time solvable for graphs, given together with a tree-decomposition with treewidth bounded by some constant k.


Amorphous Data-parallelism in Irregular Algorithms

Abstract. Most client-side applications running on multicore processors are likely to be irregular programs that deal with complex, pointer- based data structures such as large sparse graphs and trees. How- ever, we understand very little about the nature of parallelism in irregular algorithms, let alone how to exploit it ...


Tree-based reparameterization framework for analysis of sum

Abstract—We present a tree-based reparameterization (TRP) framework that provides a new conceptual view of a large class of algorithms for computing approximate marginals in graphs with cycles. This class includes the belief propagation (BP) or sum-product algorithm as well as variations and extensions of. BP.


Algorithms Finding Tree-Decompositions of Graphs Jirı Matoušek

Abstract. A graph G has tree-width at most w if it admits a tree-decomposition of width ≤ w. It is known that once we have a tree-decomposition of a graph G of bounded width, many NP-hard problems can be solved for G in linear time. For w ≤ 3 we give a linear- time algorithm for finding such a decomposition and for a ...


Algorithmics and Applications of Tree and Graph Searching

knowledge of strings, and thousands of machines. Several research efforts have attemptedto generalize keyword search to keytree and keygraph searching, because trees and graphs have many applications in next-generation database sys- tems. This paper surveys both algorithms and applications, giving some emphasis ...


Multirobot Tree and Graph Exploration

Abstract—In this paper, we present an algorithm for the ex- ploration of an unknown graph by multiple robots, which is never worse than depth-first search with a single robot. On trees, we prove that the algorithm is optimal for two robots. For k robots, the algorithm has an optimal dependence on the size of the tree but not on ...


Tree Algorithms

Another spanning tree? Why? For weighted graphs: tree of minimal costs... useful building block (approximation algorithms etc.)! MST. Tree with edges of minimal total weight. Assume all links have different weights. So... MST is unique. How to compute in a distributed manner. (synchronously...)?! (How to do it classically?)


CHR-Graph: A Platform for Animating Tree and Graph Algorithms

Abstract—Trees and graphs are two data structures that are commonly used in representing different kinds of data. They also have many associated algorithms taught in many courses. It is thus beneficial to have a tool that could be used by students, teachers and programmers to visually trace how their algorithms work.



50 V GRAPH ALGORITHMS. 50 5.1 Computational Complexity of Algorithms. 52 5.2 Reachability: Warshall's Algorithm. 53 5.3 Depth-First and Breadth-First Searches. 61 5.4 The Lightest Path: Dijkstra's Algorithm. 63 5.5 The Lightest Path : Floyd's Algorithm. 66 5.6 The Lightest Spanning Tree: Kruskal's and Prim's ...



O(V+E+EN) and the space is O( V+E), where V, E, and N represent the number of vertices, edges, and spanning trees, respectively. If the graph is undirected, the time decreases to O(V + E + VN), which is optimal to within a constant factor. The previously best-known algorithm for undirected graphs requires time O( V + E + ...