Covering Graphs Using Trees and Stars

  title={Covering Graphs Using Trees and Stars},
  author={Guy Even and Naveen Garg and Jochen K{\"o}nemann and Ramamoorthi Ravi and Amitabh Sinha},
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… 

Approximation to the Minimum Rooted Star Cover Problem

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

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

  • M. Khani
  • 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

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

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

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

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.


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

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.



Approximation Algorithms for Min-sum p-clustering

Clustering to minimize the sum of cluster diameters

This work presents a primal-dual based constant factor approximation algorithm that achieves a logarithmic approximation which also applies when the distance function is asymmetric and an incremental clustering algorithm that maintains a solution whose cost is at most a constant factors times that of optimal with a constant factor blowup in the number of clusters.

The k-traveling repairman problem

An 8.497α-approximation algorithm is given for this generalization of the metric traveling repairman problem, also known as the minimum latency problem, to multiple repairmen, where α denotes the best achievable approximation factor for the problem of finding the least cost rooted tree spanning i vertices (i-MST) problem.

Approximation algorithms for some routing problems

Several polynomial time approximation algorithms for some NP-complete routing problems are presented, and the worst-case ratios of the cost of the obtained route to that of an optimal are determined.

Approximating min-sum k-clustering in metric spaces

The first polynomial time non-trivial approximation algorithm for the min-sum k-clustering problem in general metric spaces is given, based on embedding of metric spaces into hierarchically separated trees.

A simple heuristic for the p-centre problem

An approximation algorithm for the generalized assignment problem

The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing jobj on machinei

Approximation algorithms for facility location problems

This thesis improves a long line of previous results and gives a 1.52-approximation algorithm for the uncapacitated facility location problem and considers several important generalizations of the unccapacitated problem, including: (1) Capacitate facility location: Each facility can serve only a certain amount of clients.

Approximation algorithms for facility location problems

This note is intended as companion to the lecture at CONF 2000, mainly to give pointers to the appropriate references.

Computers and Intractability: A Guide to the Theory of NP-Completeness

It is proved here that the number ofrules in any irredundant Horn knowledge base involving n propositional variables is at most n 0 1 times the minimum possible number of rules.