MATHEMATICAL ENGINEERING TECHNICAL REPORTS Enumerating Spanning and Connected Subsets in Graphs and Matroids

نویسندگان

  • Leonid Khachiyan
  • Endre Boros
  • Konrad Borys
  • Khaled Elbassioni
  • Vladimir Gurvich
  • Kazuhisa Makino
چکیده

We show that enumerating all minimal spanning and connected subsets of a given matroid can be solved in incremental quasi-polynomial time. In the special case of graphical matroids, we improve this complexity bound by showing that all minimal 2-vertex connected subgraphs of a given graph can be generated in incremental polynomial time.

برای دانلود 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

Enumerating Spanning and Connected Subsets in Graphs and Matroids

We show that enumerating all minimal spanning and connected subsets of a given matroid can be solved in incremental quasipolynomial time. In the special case of graphical matroids, we improve this complexity bound by showing that all minimal 2-vertex connected edge subsets of a given graph can be generated in incremental polynomial time.

متن کامل

ENUMERATING SPANNING AND CONNECTED SUBSETS IN GRAPHS AND MATROIDS ̃y

We show that enumerating all minimal spanning and connected subsets of a given matroid can be solved in incremental quasi-polynomial time. In the special case of graphical matroids, we improve this complexity bound by showing that all minimal 2-vertex connected subgraphs of a given graph can be generated in incremental polynomial time.

متن کامل

On Generation of Cut Conjunctions, Minimal K-connected Spanning Subgraphs, Minimal Connected and Spanning Subsets and Vertices

OF THE DISSERTATION On Generation of Cut Conjunctions, Minimal k-Connected Spanning Subgraphs, Minimal Connected and Spanning Subsets and Vertices by Konrad Borys Dissertation Director: Professor Endre Boros We consider the following problems: • Cut conjunctions in graphs: given an undirected graphG = (V,E) and a collection of vertex pairs B ⊆ V × V generate all minimal edge sets X ⊆ E such tha...

متن کامل

Energy of Graphs, Matroids and Fibonacci Numbers

The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.

متن کامل

On the Complexity of Some Enumeration Problems for Matroids

Let M be a matroid defined by an independence oracle on ground set S, and let A ⊆ S. We present an incremental polynomial-time algorithm for enumerating all minimal (maximal) subsets of S which span (do not span) A. Special cases of these problems include the generation of bases, circuits, hyperplanes, flats of given rank, circuits through a given element, generalized Steiner trees and multiway...

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

برای دانلود 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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007