# Covering Graphs Using Trees and Stars

@inproceedings{Even2003CoveringGU, title={Covering Graphs Using Trees and Stars}, author={Guy Even and Naveen Garg and Jochen K{\"o}nemann and Ramamoorthi Ravi and Amitabh Sinha}, booktitle={RANDOM-APPROX}, year={2003} }

A tree cover of a graph G is defined as a collection of trees such that their union includes all the vertices of G. The cost of a tree cover is the weight of the maximum weight tree in the tree cover. Given a positive integer k, the k-tree cover problem is to compute a minimum cost tree cover which has no more than k trees. Star covers are defined analogously. Additionally, we may also be provided with a set of k vertices which are to serve as roots of the trees or stars. In this paper, we…

## 25 Citations

### Approximation to the Minimum Rooted Star Cover Problem

- MathematicsTAMC
- 2007

This paper presents a constant ratio approximation algorithm for finding a minimum cardinality set of rooted stars, that covers all vertices in V such that the length of each rooted star is at most D.

### Improved Approximation Algorithms for the Min-max Tree Cover and Bounded Tree Cover Problems

- Computer Science, MathematicsAlgorithmica
- 2012

Improved approximation algorithms for the Min-Max Tree Cover and Bounded Tree Cover problems are provided improving the 3-approximation bound in Arkin et al. (J. Algorithms 59:1–18, 2006).

### Improved approximation algorithms for Min-Max Tree Cover, Bounded Tree Cover, Shallow-Light and Buy-at-Bulk k-Steiner Tree, and (k, 2)-Subgraph

- Computer Science, Mathematics
- 2011

This thesis provides improved approximation algorithms for the Min-Max k-Tree Cover, Bounded Tree Cover and Shallow-Light k-Steiner Tree, (k, 2)-subgraph problems and shows the approximation algorithm for BBkST implies approximation factors for some other network design problems.

### Min-max cover of a graph with a small number of parts

- Computer Science, MathematicsDiscret. Optim.
- 2015

### Improved Approximations for Buy-at-Bulk and Shallow-Light k-Steiner Trees and (k, 2)-Subgraph

- Mathematics, Computer ScienceISAAC
- 2011

Improved approximation algorithms for some network design problems are given, including the problem of finding a minimum cost 2-edge-connected subgraph with at least k vertices, which is introduced as the (k,2)-subgraph problem in [14].

### Approximations for minimum and min-max vehicle routing problems

- Mathematics, Computer ScienceJ. Algorithms
- 2006

### D S ] 3 D ec 2 01 9 Approximating Star Cover Problems

- Physics, Mathematics
- 2019

Given a metric space (F ∪ C, d), we consider star covers of C with balanced loads. A star is a pair (f, Cf ) where f ∈ F and Cf ⊆ C, and the load of a star is ∑ c∈Cf d(f, c). In minimum load k-star…

### Approximation Algorithms for Min-Max Cycle Cover Problems

- Computer ScienceIEEE Transactions on Computers
- 2015

Improved approximation algorithms for the vehicle routing problem, which has wide application backgrounds and has been paid lots of attentions in past decades, are studied by devising improved approximate algorithms for it and its variants.

### A PPROXIMATION A LGORITHMS FOR SOME M IN - MAX V EHICLE R OUTING P ROBLEMS

- Computer Science, Mathematics
- 2013

This thesis considers min-max vehicle routing problems, in which the maximum cost incurred by the subgraph corresponding to each vehicle is to be minimized, and study two types of covering problems and present new or improved approximation algorithms for them.

### A Sublogarithmic Approximation for Highway and Tollbooth Pricing

- Computer ScienceICALP
- 2010

The main result is a deterministic algorithm for the tollbooth problem on trees whose approximation ratio is O(log m/log logm), where m denotes the number of edges in the underlying graph.

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