A better approximation algorithm for the budget prize collecting tree problem

نویسنده

  • Asaf Levin
چکیده

Given an undirected graph G = (V,E), an edge cost c(e) ≥ 0 for each edge e ∈ E, a vertex prize p(v) ≥ 0 for each vertex v ∈ V , and an edge budget B. The budget prize collecting tree problem is to find a subtree T ′ = (V ′, E′) that maximizes ∑ v∈V ′ p(v), subject to ∑ e∈E′ c(e) ≤ B. We present a (4 + 2)-approximation algorithm.

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

Improved Approximation Algorithms for (Budgeted) Node-Weighted Steiner Problems

Moss and Rabani [13] study constrained node-weighted Steiner tree problems with two independent weight values associated with each node, namely, cost and prize (or penalty). They give an O(logn)-approximation algorithm for the prize-collecting node-weighted Steiner tree problem (PCST)—where the goal is to minimize the cost of a tree plus the penalty of vertices not covered by the tree. They use...

متن کامل

A 4-Approximation Algorithm for k-Prize Collecting Steiner Tree Problems

This paper studies a 4-approximation algorithm for k-prize collecting Steiner tree problems. This problem generalizes both k-minimum spanning tree problems and prize collecting Steiner tree problems. Our proposed algorithm employs two 2-approximation algorithms for k-minimum spanning tree problems and prize collecting Steiner tree problems. Also our algorithm framework can be applied to a speci...

متن کامل

Prize-Collecting Steiner Networks via Iterative Rounding

In this paper we design an iterative rounding approach for the classic prize-collecting Steiner forest problem and more generally the prize-collecting survivable Steiner network design problem. We show as an structural result that in each iteration of our algorithm there is an LP variable in a basic feasible solution which is at least one-third-integral resulting a 3-approximation algorithm for...

متن کامل

Primal-dual approximation algorithms for the Prize-Collecting Steiner Tree Problem

The primal-dual scheme has been used to provide approximation algorithms for many problems. Goemans and Williamson gave a (2−1/(n−1))-approximation for the Prize-Collecting Steiner Tree Problem that runs in O(n3 logn) time—it applies the primaldual scheme once for each of the n vertices of the graph. We present a primal-dual algorithm that runs in O(n2 logn), as it applies this scheme only once...

متن کامل

Approximation Algorithms for Constrained Node Weighted Steiner Tree Problems

We consider a class of optimization problems, where the input is an undirected graph with two weight functions dened for each node, namely the node's pro t and its cost. The goal is to nd a connected set of nodes of low cost and high pro t. We present approximation algorithms for three natural optimization criteria that arise in this context, all of which are NP-hard. The budget problem asks fo...

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:
  • Oper. Res. Lett.

دوره 32  شماره 

صفحات  -

تاریخ انتشار 2004