Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
CMPSCI 611: Advanced Algorithms Micah Adler
 

Summary: CMPSCI 611: Advanced Algorithms
Micah Adler
Problem Set 2 Out: October 10, 2001
Due: October 17, 2001
1. In lecture, we saw an algorithm for the bipartite matching problem. With some e ort, the general
technique we used can be extended to work for arbitrary graphs as well. In this question, you are
asked to provide an algorithm for an easier problem: directed matchings in arbitrary graphs.
Given a directed graph G = (V; E), a directed matching is a subset of the edges such that the indegree
of any node is at most 1, and the outdegree of any node is at most 1. Show how to use an e∆cient
algorithm for the (undirected) bipartite matching problem to nd the largest cardinality directed
matching in an arbitrary graph.
2. Intersection of matroids.
(a) Consider the following problem: we are given a graph G = (V; E), a vertex v 2 V , and an integer
k, and we want to determine whether or not there is a spanning tree of G in which v has degree k or
less. Show that this problem can be formulated as the intersection of two matroids. What does this
imply about how e∆ciently the problem can be solved?
(b) Consider now the following problem: we are given for each vertex i an integer k i
, and we want to
determine whether there is a spanning tree of G in which each vertex i has degree at most k i
. Note

  

Source: Adler, Micah - Department of Computer Science, University of Massachusetts at Amherst

 

Collections: Computer Technologies and Information Sciences