In the afternoon, we have a meeting to discuss the short paper for CleanDB. 

First of all, we made some corrections about the description of problems in the section 5.2.1. 

1. replace the "sorting paths based on ..." with "calculate the properties of paths based on ...";

2. change the last problem, by "calculate the max number of universes decreased by removing some node in the compatibility graph".

Secondly, we came up with some basic ideas to deal with the problems we have so far. 

1. When calculating the number of universes that a node belongs to, we check the cliques composed by neighbors of that nodes. 

2. In order to calculate the number of universes which decreases by removing some node in the compatibility graph, we first assign to each nodes in the graph with the number of universes it belongs, and then recalculate the changes of these numbers after removing that node. The changes reflect the changes of the number of universes in the graph. 

On the other hand, we discuss about the possibility to introduce some concepts like independent sets, distance etc. into the analysis of the compatibility graph we get from the path instances. 

We didn't make clear decisions yet. We'd better find some related work by other people, to get some hints for our research.