For a graph G = (V,E), a function f : V (G) → {1, 2, . . . , k} is a kranking if f(u) = f(v) implies that every u−v path contains a vertex w such that f(w) > f(u). A k-ranking is minimal if decreasing any label violates the definition of ranking. The arank number, ψr(G), of G is the maximum value of k such that G has a minimal k-ranking. We completely determine the arank number of the Cartesian...

This paper is focussed on algorithms to solve the k-shortest path problem. Three codes were described and compared on rand and grid networks using random generators available on http://www.dis.uniroma1.it/∼challenge9 Codes were also tested on the USA road networks available on the same URL address. One million paths were ranked in less than 3 seconds on random instances with 10 000 nodes and 10...

In this study the intuitionistic fuzzy version of critical path method has been proposed to solve networking problems with uncertain activity durations. Intuitionistic set [1] is an extension theory [2] unlike set, it focuses on degree belonging, nonbelonging or non-membership function and hesitancy which helps decision maker adopt best among worst cases. Trapezoidal triangular numbers are util...

The Critical Path Method (CPM) is useful for planning and control of complex projects. The CPM identifies the critical activities in the critical path of an activity network. The successful implementation of CPM requires the availability of clear determined time duration for each activity. However, in practical situations this requirement is usually hard to fulfill since many of activities will...

The Critical Path Method (CPM) is a vital tool for the planning and control of complex projects. The successful implementation of CPM requires the availability of a clear determined time duration for each activity. However, in practical situations this requirement is usually hard to fulfill since many of activities will be executed for the first time. Hence, there is always uncertainty about th...

Recent research efforts have led to the development of a state-of-the-art supervised coreference model, the cluster-ranking model. However, it is not clear whether the features that have been shown to be useful when employed in traditional coreference models will fare similarly when used in combination with this new model. Rather than merely re-evaluate them using the cluster-ranking model, we ...

In this paper, we propose a new approach to critical path analysis in a project network whose activity times are uncertain. The uncertain parameters in the project network are represented by fuzzy numbers. We use fuzzy arithmetic and a fuzzy ranking method to determine the fuzzy critical path of the project network without converting the fuzzy activity times to classical numbers. The proposed m...