Bidirectional data flow analysis has become the standard technique for solving bit-vector based code motion problems in the presence of critical edges. Unfortunately, bidirectional analyses have turned out to be conceptually and computationally harder than their unidirectional counterparts. In this paper we show that code motion in the presence of critical edges can be achieved without bidirect...

Let G be a graph without loops or multiple edges drawn in the plane. It is shown that, for any k, if G has at least Ckn edges and n vertices, then it contains three sets of k edges, such that every edge in any of the sets crosses all edges in the other two sets. Furthermore, two of the three sets can be chosen such that all k edges in the set have a common vertex.

among the various methods of clinical teaching, rounds and grand rounds are considered as the gold standards. clinical round includes some standard components and it plays an effective role in student's learning process. the aim of this study was to evaluate the content of teaching rounds in 40 clinical wards in 4 medical teaching hospitals affiliated to tehran university of medical sciences in...

We derive an upper bound on the number of vertices in graphs of diameter 3 and given degree arising from Abelian lifts of dipoles with loops and multiple edges.

. We think that if φ(e) = uv (short for {u, v}), then e connects u and v or equivalently e is incident to u and v. If there is at least one edge incident to u and v then we say that the vertices u and v are adjacent. If φ(e) = vv, then we call e a loop at v. If several edges e1, . . . , ej (j > 1) satisfy φ(e1) = · · · = φ(ej) = uv, then we say that there is a multiple edge between u and v. A g...

Simple equations are derived that give the shapes of various convex polyhedra. The five regular polyhedra, called Platonic solids (the tetrahedron, hexahedron or cube, octahedron, dodecahedron and icosahedron), and polyhedra composed of crystallographically low-index planes are treated. The equations also give shapes that are nearly polyhedral with round edges, or intermediate shapes between a ...

Consider the following game played by two players, called Waiter and Client, on edges of K n (where is divisible 3). Initially, all are unclaimed. In each round, picks yet unclaimed edges. Client then chooses one these to be added Waiter’s graph Client’s graph. wins if she forces create a 3 -factor in at some point, while does not manage do that, wins. It difficult see that for large enough , h...

The growing popularity and diversity of social network applications present new opportunities as well as new challenges. The resulting social networks have high value to business intelligence, sociological studies, organizational studies, epidemical studies, etc. The ability to explore and extract information of interest from the networks is thus crucial. However, these networks are often large...