By the DAG breakdown, we mean the decomposition of a supervised acyclic graph G into a underrated set of node-disjoint chains, that cover all the nodes of G. For some two nodes u and v on a chain, if u is above v before there is a way from u to v in G. In this paper, we discuss an efficient treasure for this problem. Its period complexity is middle from two points O(max{k, } ×n2) while best choice algorithm for this question up to now needs O(n3) time, place n is the number of the nodes of G, and k is G’s breadth, defined expected the size of a best node subset U of G specific that for every pair of growth x, y Î U, there does not endure a path from x to y or from y to x. k is usually much smaller than n. In addition, for one existing algorithm, Q(n2) extra room (besides the space for G itself) is necessary to maintain the transitive seal of G to do the task while ours needs only O(k×n) extra scope. This is particularly important for few nowadays requests with large graphs including heaps and even billions of knots, like the facebook, twitter, and some other friendly networks.

**Author(s) Details:**

**Yangjun Chen,
**Department of Mathematics, Sindhi College, Bangalore-560024, India.

**Yibin Chen,
**The University of Winnipeg, Canada.

**Please see the link here: **https://stm.bookpi.org/RATMCS-V1/article/view/10692

**Keywords: **Micropolar, pressure, lubrication, squeeze film