Dominator

Abstract: A linear time algorithm is presented for nding dominators in control ow graphs.

Abstract: A simple, iterative bit propagation algorithm for solving global data flow analysis problems such as “available expressions” and “live variables” is presented and shown to be quite comparable in speed to the corresponding interval analysis algorithm. This comparison is facilitated by a result relating two parameters of a reducible flow graph (rfg). Namely, if G is an rfg, d is the largest number of back edges found in any cycle-free path in G, and k is the length of the interval derived sequence of G, then $k \geqq d$. (Intuitively, k is the maximum nesting depth of loops in a computer program, while d is a measure of the maximum loop-interconnectedness.) The node ordering employed by the simple algorithm is the reverse of the order in which a node is last visited while growing any depth-first spanning tree of the flow graph. In addition, a dominator algorithm for an rfg is presented which takes O(edges) bit vector steps.

Abstract: Branch testing a program involves generating a set of paths that will cover every arc in the program flowgraph, called a path cover, and finding a set of program inputs that will execute every path in the path cover. This paper presents a generalized algorithm that finds a path cover for a given program flowgraph. The analysis is conducted on a reduced flowgraph, called a ddgraph, and uses graph theoretic principles differently than previous approaches. In particular, the relations of dominance and implication which form two trees of the arcs of the ddgraph are exploited. These relations make it possible to identify a subset of ddgraph arcs, called unconstrained arcs, having the property that a set of paths exercising all the unconstrained arcs also cover all the arcs in the ddgraph. In fact, the algorithm has been designed to cover all the unconstrained arcs of a given ddgraph: the paths are derived one at a time, each path covering at least one as yet uncovered unconstrained arc. The greatest merits of the algorithm are its simplicity and its flexibility. It consists in just visiting recursively in combination the dominator and the implied trees, and is flexible in the sense that it can derive a path cover to satisfy different requirements, according to the strategy adopted for the selection of the unconstrained arc to be covered at each recursive iteration. This feature of the algorithm can be employed to address the problem of infeasible paths, by adopting the most suitable selection strategy for the problem at hand. Embedding of the algorithm into a software analysis and testing tool is recommended. >

Abstract: A data exploration tool which has a graphical user interface that employs directed graphs to provide histories of the data exploration operations. Nodes in the directed graphs represent operations on data; the edges represent relationships between the operations. One type of the directed graphs is the derivation graph, in which the root of the graph is a node representing a data set and an edge leading from a first node to a second node indicates that the operation represented by the second node is performed on the result of the operation represented by the first node. Operations include query, segmentation, aggregation, and data view operations. A user may edit the derivation graph and may select a node for execution. When that is done, all of the operations represented by the nodes between the root node and the selected node are performed as indicated in the graph. The operations are performed using techniques of lazy evaluation and encachement of results with the nodes. Anothertype of the directed graphs is the subsumption graph, in which an edge leading from a first node to a second node indicates that the second node stands in a subsumption relationship to the first node. If a result of the operation represented by the first node has been computed, the result is available to calculate the result of the operation represented by the second node.