Fast Algorithms for Hard Graph Problems: Bidimensionality, Minors, and Local Treewidth

نویسندگان

  • Erik D. Demaine
  • Mohammad Taghi Hajiaghayi
چکیده

This paper surveys the theory of bidimensional graph problems. We summarize the known combinatorial and algorithmic results of this theory, the foundational Graph Minor results on which this theory is based, and the remaining open problems.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Linearity of grid minors in treewidth with applications through bidimensionality

We prove that any H-minor-free graph, for a fixed graph H, of treewidth w has an Ω(w)× Ω(w) grid graph as a minor. Thus grid minors suffice to certify that H-minor-free graphs have large treewidth, up to constant factors. This strong relationship was previously known for the special cases of planar graphs and bounded-genus graphs, and is known not to hold for general graphs. The approach of thi...

متن کامل

Bidimensionality, Map Graphs, and Grid Minors

In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and the size of the largest grid minor. These bounds improve the running times of a broad class of fixed-parameter algorithms. Our novel technique of using appro...

متن کامل

The Bidimensional Theory of Bounded-Genus Graphs

Bidimensionality is a powerful tool for developing subexponential fixed-parameter algorithms for combinatorial optimization problems on graph families that exclude a minor. This paper completes the theory of bidimensionality for graphs of bounded genus (which is a minorexcluding family). Specifically we show that, for any problem whose solution value does not increase under contractions and who...

متن کامل

Subexponential-Time Parameterized Algorithm for Steiner Tree on Planar Graphs

The well-known bidimensionality theory provides a method for designing fast, subexponentialtime parameterized algorithms for a vast number of NP-hard problems on sparse graph classes such as planar graphs, bounded genus graphs, or, more generally, graphs with a fixed excluded minor. However, in order to apply the bidimensionality framework the considered problem needs to fulfill a special densi...

متن کامل

Treewidth and graph minors

We shall touch upon the theory of Graph Minors by Robertson and Seymour. This theory gives a very general condition under which a graph problem has a polynomial time algorithm (though the algorithms that come out of the theory are often not practical). We shall review a small part of this theory, and illustrate how dynamic programming can be used to solve some NP-hard problems on restricted cla...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004