Tel Aviv University
The Raymond and Beverly Sackler
Faculty of Exact Sciences
Scho ol of Mathematical Sciences
Complexity and Approximation of
Some Graph Mo di cation Problems
Thesis submitted in partial ful llment
of graduate requirements for the degree
M Sc in Tel Aviv University
Department of Computer Science
By
Assaf Natanzon Prepared under the sup ervision of Prof Ron Shamir
Acknowledgments
Iwould like to thank my advisor Prof Ron Shamir for directing me and giving me
a helping hand and for his clarifying comments and reformulations
Iwould liketothankmy b eloved Mom and Dad for their supp ort
Abstract
In an edge mo di cation problem one has to change the edge set of a given graph as
little as p ossible so as to satisfy a certain prop erty We prove in this pap er the NP
hardness of a variety of edge mo di cation problems with resp ect to some well studied
classes of graphs These include p erfect chordal comparability split threshold and
cluster graphs Weshow that some of these problems b ecome p olynomial when the
input graph has b ounded degree We give a general constant factor approximation
algorithm for deletion and editing problems on b ounded degree graphs with resp ect
to prop erties that can b e characterized by a nite set of forbidden induced subgraphs
We giveanapproximation algorithm for Cluster Deletion and Editing We also prove
some combinatorial b ounds on the sizes of the minimum completion and deletion sets of a graph
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