A constant approximation algorithm for the densest k

نویسندگان

  • Maria Liazi
  • Ioannis Milis
  • Vassilis Zissimopoulos
چکیده

The Densest k-Subgraph (DkS) problem asks for a k-vertex subgraph of a given graph with the maximum number of edges. The DkS problem is NP-hard even for special graph classes including bipartite, planar, comparability and chordal graphs, while no constant approximation algorithm is known for any of these classes. In this paper we present a 3-approximation algorithm for the class of chordal graphs. The analysis of our algorithm is based on a graph theoretic lemma of independent interest.

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

Approximation schemes, cliques, colors and densest subgraphs

In this thesis we study the problem of finding the densest k-subgraph of a given graph G = (V, E). We present algorithms of polynomial time as well as approximation results on special graph classes. Analytically, we study polynomial time algorithms for the densest k-subgraph problem on weighted graphs of maximal degree two, on weighted trees even if the solution is disconnected, and on interval...

متن کامل

SDP-Hardness of Approximation for Densest k-subgraph

Densest k-subgraph is the problem of finding, giving a graph G and a number k, a k vertex subgraph of G with as many edges as possible. The best known poly-time algorithm for this problem gives a factor n1/4 approximation. Proving even constant factor hardness of approximation results for this problem has been done only with significantly stronger assumptions that P , NP. In 2011, however, Bhas...

متن کامل

The Densest k-Subhypergraph Problem

The Densest k-Subgraph (DkS) problem, and its corresponding minimization problem Smallest p-Edge Subgraph (SpES), have come to play a central role in approximation algorithms. This is due both to their practical importance, and their usefulness as a tool for solving and establishing approximation bounds for other problems. These two problems are not well understood, and it is widely believed th...

متن کامل

Finding Dense Subgraphs with Size Bounds

We consider the problem of finding dense subgraphs with specified upper or lower bounds on the number of vertices. We introduce two optimization problems: the densest at-least-k-subgraph problem (dalks), which is to find an induced subgraph of highest average degree among all subgraphs with at least k vertices, and the densest at-most-k-subgraph problem (damks), which is defined similarly. Thes...

متن کامل

Finding large and small dense subgraphs

We consider two optimization problems related to finding dense subgraphs, which are induced subgraphs with high average degree. The densest at-least-k-subgraph problem (DalkS) is to find an induced subgraph of highest average degree among all subgraphs with at least k vertices, and the densest at-most-k-subgraph problem (DamkS) is defined similarly. These problems are related to the well-known ...

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:
  • Inf. Process. Lett.

دوره 108  شماره 

صفحات  -

تاریخ انتشار 2008