algorithmcreativity - say that an -vertex directed acyclic graph is compact if there is some way of numbering the vertices of with the integers from to such that contains the edge (ijif and only if jfor all ij in [ give an ( )time algorithm for detecting if is compact - justify proposition - describein pseudo-codean ( )-time algorithm for computing all the connected components of an undirected graph with vertices and edges - let be the spanning tree rooted at the start vertex produced by the depth-first search of connectedundirected graph argue why every edge of not in goes from vertex in to one of its ancestorsthat isit is back edge - suppose we wish to represent an -vertex graph using the edge list structureassuming that we identify the vertices with the integers in the set { , describe how to implement the collection to support (log )-time performance for the areadjacent method how are you implementing the method in this casec- tamarindo university and many other schools worldwide are doing joint project on multimedia computer network is built to connect these schools using communication links that form free tree the schools decide to install file server at one of the schools to share data among all the schools since the transmission time on link is dominated by the link setup and synchronizationthe cost of data transfer is proportional to the number of links used henceit is desirable to choose "centrallocation for the file server given free tree and node of tthe eccentricity of is the length of longest path from to