GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Spring 2014
HW1
Jiyuan Yang,
Shuai Guo,
Zhijia Wang
Jan.23 2017
1. A
nswer: There are 2 different DFS trees.
a. xywzvu
b. x zvuw, y
3.
Proof:
According to the problem, we can easily know the number of vertices must more than 1,
it means V>=2.
When 2<=V<=4,
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
An index structure for efficient reverse nearest neighbor queries
KingIp Lin
Division of Computer Science,
Department of Mathematical Sciences
The University of Memphis,
Memphis, TN 38 152, USA
linki @msci.memphis.edu
Congjun Yang
Division of Computer Sc
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
A Separator Theorem for Planar Graphs
Author(s): Richard J. Lipton and Robert Endre Tarjan
Source: SIAM Journal on Applied Mathematics, Vol. 36, No. 2 (Apr., 1979), pp. 177189
Published by: Society for Industrial and Applied Mathematics
Stable URL: http:
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
CS271 Randomness & Computation
Fall 2011
Lecture 2: August 30
Lecturer: Alistair Sinclair
Based on scribe notes by:
Daniel Chen, Anand Kulkarni; Sudeep Juvekar Thomas Vidick
Disclaimer: These notes have not been subjected to the usual scrutiny reserved fo
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
SIAM J. COMPUT.
Vol. 24. No. 3, pp. 494504, June 1995
1995 Society for Industrial and Applied Mathematics
006
SCALING ALGORITHMS FOR THE SHORTEST PATHS PROBLEM*
ANDREW V. GOLDBERG
Abstract. We describe a new method for designing scaling algorithms for th
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
Separators for SpherePackings and Nearest Neighbor
Graphs
GARY L. MILLER
Carnegie Mellon University, Pittsburgh, Pennsylvania
SHANGHUA TENG
University of Minnesota, Minneapolis, Minnesota
WILLIAM THURSTON
University of California, Berkeley, California
A
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
15853:Algorithms in the Real World
Planar Separators I & II
Definitions
Separators of Trees
Planar Separator Theorem
15853
Page1
Planar Graphs
Definition: A graph is planar if it can be embedded in
the plane, i.e., drawn in the plane so that no two e
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
Design and Analysis of Algorithms
Lecture 18
Randomized Perfect Bipartite Matching
Lecturer: Daniel A. Spielman
18.1
March 22, 2012
Introduction
These are my notes for part of todays lecture. In this half, we will cover a new randomized algorithm
by Ashis
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
Sublinear Algorithms
Lecture 2
Sofya Raskhodnikova
Penn State University
Thanks to Madhav Jha (Penn State) for help with creating these slides.
1
Tentative Plan
Lecture 1. Background. Testing properties of images and lists.
Lecture 2. Testing properties o
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
Algorithms
Lecture 18: Basic Graph Algorithms [Fa14]
Thus you see, most noble Sir, how this type of solution bears little relationship to
mathematics, and I do not understand why you expect a mathematician to produce it,
rather than anyone else, for the s
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Spring 2014
CS420/520: Graph Theory with Applications to CS, Winter 2016
Homework 1
Due: Tue, Jan/24/17
Homework Policy:
1. Students should work on homework assignments in groups of preferably three people. Each group submits to
TEACH one set of typeset solutions, an
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
Notes for lecture #1: Introduction to sublinear algorithms
The focus of the course is on sublinear algorithm. This may mean more than one thing. In
particular well be interested in algorithms whose running time is sublinear in the size of the
input, and
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
Property Testing of Graphs:
Models and Results for Sparse Graphs (Part I)
Testing properties of graphs  dierent models
In what follows I will talk about undirected graphs. Later will also talk a bit about directed graphs.
There are several models for tes
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
Algorithms
Lecture 21: Shortest Paths [Fa14]
Well, ya turn left by the re station in the village and take the old post road by
the reservoir and. . . no, that wont do.
Best to continue straight on by the tar road until you reach the schoolhouse and
then t
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
Lecture notes for Analysis of Algorithms:
Minimum Spanning Trees
Lecturer: Uri Zwick
May 22, 2013
Abstract
We present a general framework for obtaining ecient algorithms for computing minimum
spanning trees. We use this framework to derive the classical a
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
Lecture notes on:
Maximum matching in
bipartite and nonbipartite graphs
(Draft)
Lecturer: Uri Zwick
June 5, 2013
1
The maximum matching problem
Let G = (V, E) be an undirected graph. A set M E is a matching if no two edges in M have
a common vertex. A ve
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
CHAPTER
1
Planar Graphs
2
Es nimmt mich Wunder, dass diese allgemeinen proprietates in der Stereometrie noch
von Niemand, so viel mir bekannt, sind angemerkt worden; doch viel mehr aber, dass die
frnehmsten davon als theor. 6 und theor. 11 so schwer zu be
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
Lecture notes for Analysis of Algorithms:
Computing shortest paths
and detecting negative cycles
Lecturer: Uri Zwick
Spring 2006
Abstract
We consider the problem of computing shortest paths in a weighted directed graph whose
edges have positive or negativ
GRAPH THEORY WITH APPLICATIONS TO COMPUTER SCIENCE
CS 520

Winter 2015
8
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