SUMMARY An s-t ow in a directed network is called \un-controllable", when the ow is representable as a positive sum of elementary s-t path ows. In this paper, we discuss the problem \Is a given ow uncontrollable?". We show that the problem is NP-complete. 1. Introduction Recently, Iri proposed a new type of network ow theory [1], where only those ows which are representable as a positive sum of...

Given an undirected graph G = (V,E), two distinguished vertices s and t of G, and a diameter bound D, a D-s, t-path is a path between s and t composed of at most D edges. An edge e or vertex u are called Dirrelevant if e or u does not belong to anyD-s, t-path ofG. In this paper we study the problem of efficiently detecting D-irrelevant edges and vertices and also study the computational complex...

in this short article, we observe that the path of particle of mass $m$ moving along $mathbf{r}= mathbf{r}(t)$ under pseudo-force $mathbf{a}(t)$, $t$ denotes the time, is given by $mathbf{r}_d= int(frac{dmathbf{r}}{dt} mathbf{a}(t)) dt +mathbf{c}$. we also observe that the effective force $mathbf{f}_e$ on that particle due to pseudo-force $mathbf{a}(t)$, is given by $ mathbf{f}_e= mathbf{f} mat...

We show that the operational semantics for HOPLA is in strong correspondence with its presheaf semantics [2, 1]. The proof is a fairly standard logical relations proof, exploiting the path semantics of the language [3, 4]. Strong correspondence can be proved for full HOPLA by making use of the path semantics to get a logical relations proof off the ground. We’ll use the notation J−K for the pat...

Let S be a set of n points in IR and let t > 1 be a real number. A t-spanner for S is a directed graph having the points of S as its vertices, such that for any pair p and q of points there is a path from p to q of length at most t times the Euclidean distance between p and q. Such a path is called a t-spanner path. The spanner diameter of such a spanner is defined as the smallest integer D suc...

Ab initio electronic structure calculations with RHF, MP2, and CCSD(T) wave functions have been used to investigate a reaction path for the hydrosilation reaction catalyzed by divalent titanium (modeled by TiH2). Optimized structures and energies are presented. All levels of theory predict a barrierless reaction path compared to a barrier of 78 kcal/mol for the uncatalyzed reaction. The use of ...

n : Number of tasks m : Number of machines k : Current iteration T : Set of tasks = {1,..,n} M : Set of machines = {1,..,m} Tj : j task node, j ∈ T Mij : Node for machine i connected from Tj, i ∈ M, j ∈ T Lj : Level of Tj, j ∈ T (number of tasks in the remaining path till the final node) LETj : Level with estimated time of Tj, j ∈ T (processing rime of the remaining path) ωj : Weight on the lin...

It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on t vertices, for fixed t. We propose an algorithm that, given a 3-colorable graph without an induced path on t vertices, computes a coloring with max { 5, 2 ⌈ t−1 2 ⌉ − 2 } many colors. If the input graph is triangle-free, we only need max { 4, ⌈ t−1...

In this paper, the maximum capacity path problem in time-varying network is presented, where waiting times at vertices are not allowable. Moreover, the capacities are considered the generalized trapezoidal fuzzy number. An exact algorithm is proposed which can find a optimal solution of problem subject to the time of path is at most T, where T is a given time horizon.

Let S be a set of n points in IRd and let t > 1 be a real number. A t-spanner for S is a directed graph having the points of S as its vertices, such that for any pair p and q of points there is a path from p to q of length at most t times the Euclidean distance between p and q. Such a path is called a t-spanner path. The spanner diameter of such a spanner is de ned as the smallest integer D suc...