Hitting Diamonds and Growing Cacti
نویسندگان
چکیده
We consider the following NP-hard problem: in a weighted graph, find a minimum cost set of vertices whose removal leaves a graph in which no two cycles share an edge. We obtain a constant-factor approximation algorithm, based on the primaldual method. Moreover, we show that the integrality gap of the natural LP relaxation of the problem is Θ(logn), where n denotes the number of vertices in the graph.
منابع مشابه
Increasing Diamonds
A class of diamond-shaped combinatorial structures is studied whose enumerating generating functions satisfy differential equations of the form f2 “ Gpfq, for some function G. In addition to their own interests and being natural extensions of increasing trees, the study of such DAG-structures was motivated by modelling executions of seriesparallel concurrent processes; they may also be used in ...
متن کاملRock Weathering, Plant Growth-promoting Bacteria from Desert Plants Allow the Growth of Cactus Seedling in Rocks
ABSTRACT Light, fluorescent, and field emission scanning electron microscopy, combined with microbial counts on culture media, revealed the presence of numerous microorganisms (bacteria, fungi, and actimomycetes) living as rhizoplane populations of roots of at least three species of cactus and a wild fig tree growing in rocks without soil. These plants are responsible for weathering of volcanic...
متن کاملA note on the zeroth-order general randić index of cacti and polyomino chains
The present note is devoted to establish some extremal results for the zeroth-order general Randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.
متن کاملMantle Rocks and Diamond-Associated Phases: Role in Diamond Origin
The components of rock-forming and accessory minerals of the upper mantle, transition zone and lower mantle rocks have been involved into the processes of diamond genesis. Through their dissolving in primary carbonate melts, the mantle minerals have turned into components of the parental silicate-(±oxide)carbonate-carbon melts-solutions for diamonds and co-crystallized paragenetic minerals. The...
متن کاملMantle Rocks and Diamond-Associated Phases: Role in Diamond Origin
The components of rock-forming and accessory minerals of the upper mantle, transition zone and lower mantle rocks have been involved into the processes of diamond genesis. Through their dissolving in primary carbonate melts, the mantle minerals have turned into components of the parental silicate-(±oxide)carbonate-carbon melts-solutions for diamonds and co-crystallized paragenetic minerals. The...
متن کامل