If there exists a projective birational morphism f: Y [right arrow] X from a smooth variety Y such that the f-exceptional locus Exc(f) and Exc(f) [union] Supp [f.sup.-1.sub.*] [DELTA] are simple normal crossing divisors on Y and that a(E, X, [DELTA]) > -1 for every f-exceptional divisor E, then (X, [DELTA]) is called a divisorial log terminal pair.
This means that g is a projective birational morphism such that [K.sub.Z] + [[DELTA].sub.Z] = [g.sub.*] ([K.sub.X] + [DELTA]) and that (Z, [[DELTA].sub.Z]) is a divisorial log terminal pair. It is well known that Z has only rational singularities.
Let (X, [DELTA]) be a projective kawamata log terminal pair. Assume that X has maximal Albanese dimension.
By taking a suitable crepant pull-back, we may further assume that the pair (X, [DELTA]) is a Q-factorial terminal pair. In particular, X has only terminal singularities.
The project entails construction of three multimodal terminals (Varanasi, Sahibganj and Haldia); two intermodal terminals; five Roll On - Roll Off (Ro-Ro) terminal pairs
; new navigation lock at Farakka; assured depth dredging; integrated vessel repair & maintenance facility, Differential Global Positioning System (DGPS), River Information System (RIS), river training & river conservancy works.
In such problems, an edge weighted graph with a set of source terminal pairs
is given; we need to modify the lengths of edges by a minimum cost under a given norm.
Now, we start to explore the effect of the parameters [s.sub.p], [s.sub.0], [s.sub.i], and n in a [PSN.sub.SU](n, n, [s.sub.p], [s.sub.0], [s.sub.i]) on the switch-efficiency, and we try to find proper [s.sub.p], [s.sub.0], [s.sub.i], and n values to minimize the number of switches needed in a rearrangeable [PSN.sub.SU] (n, n, [s.sub.p], [s.sub.0], [s.sub.i]) to interconnect terminal pairs from the three sets of [P.sub.P], [P.sub.O], and [P.sub.I] We assume that the set of [P.sub.P], [P.sub.O], and [P.sub.I] have NP = [s.sub.p] x n, [N.sub.O] = [s.sub.0] xn, and [N.sub.I] = [s.sub.i] x n external terminals, respectively.
We not only provide the designers with a rearrangeable [PSN.sub.SU](n, m,[s.sub.p],[s.sub.0],[s.sub.i]) with m [greater than or equal to] n for connecting terminal pairs from three disjoint terminal sets to each other but also determinate the important parameter n to minimize the number of switches needed in that network.