We show that every graph has an induced pseudoforest of at least $n-m/4.5$
vertices, an induced partial 2-tree of at least $n-m/5$ vertices, and an
induced planar subgraph of at least $n-m/5.2174$ vertices. These results are
constructive, implying linear-time algorithms to find the respective induced
subgraphs. We also show that the size of the largest $K_h$-minor-free graph in
a given graph can sometimes be at most $n-m/6+o(m)$.Comment: Accepted by Graph Drawing 2014. To appear in Journal of Graph
Algorithms and Application
Designing network protocols that work well under a variety of network conditions typically involves a large amount of manual tuning and guesswork, particularly when choosing dynamic update strategies for numeric parameters. The situation is made more complex by adding the Quality of Service (QoS) requirements to a network protocol. A fundamentally different approach for designing protocols is via Reinforcement Learning (RL) algorithms which allow protocols to be automatically optimized through network simulation. However, getting RL to work well in practice requires considerable expertise and carries a significant implementation overhead. To help overcome this challenge, recent work has developed the programming paradigm of Adaptation-Based Programming (ABP), which allows programmers who are not RL-experts to write self-optimizing "adaptive programs". In this work, we study the potential of applying ABP to the problem of designing network protocols via simulation. We demonstrate the flexibility of our design method via a number of case studies, each of which investigates the performance of an adaptive program written for the backoff mechanism of the MAC layer in the 802.11 standard. Our results show that the learned protocols typically outperform 802.11 on a number of evaluation metrics and network conditions.
We show that every graph has an induced pseudoforest of at least n − m/4.5 vertices, an induced partial 2-tree of at least n − m/5 vertices, and an induced planar subgraph of at least n−m/5.2174 vertices. These results are constructive, implying linear-time algorithms to find the respective induced subgraphs. We also show that the size of the largest K h -minorfree graph in a given graph can sometimes be at most n − m/6 + o(m).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.