Answering reachability queries in directed acyclic graphs is an operation required by many applications. In this paper, we present efficient algorithms to construct and search a space-efficient data structure in the k-dimensional space that is based on Graph Dominance Drawing. Our algorithms construct this data structure in O(km) time, while it can be stored in O(kn) space. Any reachability query is answered in constant time, since no "falsely implied paths (fips)" are introduced. We also present experimental results that show that the number of dimensions, k, in the solutions produced by our techniques is low. Additionally, we present a new method for constructing random DAGs with prespecified structure and density. The analysis of our experimental results reveals an interesting interplay between density and structure.

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We present a new heuristic algorithm for computing a minimum Feedback Arc Set in directed graphs. The new technique produces solutions that are better than the ones produced by the best previously known heuristics, often reducing the FAS size by more than 50%. It is based on computing the PageRank score of the nodes of the directed line graph of the input directed graph. Although the time required by our heuristic is heavily influenced by the size of the produced line graph, our experimental results show that it runs very fast even for very large graphs used in graph drawing.

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