منابع مشابه
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...
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For any given > 0 we provide an algorithm for the Densest k-Subhypergraph Problem with an approximation ratio of at most O(nm ) for θm = 1 2 m − 1 2 − 1 2m and run time at most O(nm−2+1/ ), where the hyperedges have at most m vertices. We use this result to give an algorithm for the Set Union Knapsack Problem with an approximation ratio of at most O(nm ) for αm = 2 3 [m − 1 − 2m−2 m2+m−1 ] and ...
متن کاملDensest Subgraphs THE DENSE K SUBGRAPH PROBLEM
Given a graph G = (V, E) and a parameter k, we consider the problem of finding a subset U ⊆ V of size k that maximizes the number of induced edges (DkS). We improve upon the previously best known approximation ratio for DkS, a ratio that has not seen any progress during the last decade. Specifically, we improve the approximation ratio from n to n. The improved ratio is obtained by studying a va...
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Given an n-vertex graph G and a parameter k, we are to nd a k-vertex subgraph with the maximum number of edges. This problem is N P-hard. We show that the problem remains N P-hard even when the maximum degree in G is three. When G contains a k-clique, we give an algorithm that for any > 0 nds a k-vertex subgraph with at least (1 ?) ? k 2 edges, in time n O((1+log n k)==). We study the applicabi...
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In the Densest k-Subgraph problem (DSP), we are given an undirected weighted graph G = (V, E) with n vertices (v1, ..., vn). We seek to find a subset of k vertices (k belonging to {1, ..., n}) which maximizes the number of edges which have their two endpoints in the subset. This problem is NP-hard even for bipartite graphs, and no polynomial-time algorithm with a fixed performance guarantee is ...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2018
ISSN: 0895-4801,1095-7146
DOI: 10.1137/16m1096402