In this paper the properties of node-node adjacency matrix in acyclic digraphs are considered. It is shown that topological ordering and node-node adjacency matrix are closely related. In fact, first the one to one correspondence between upper triangularity of node-node adjacency matrix and existence of directed cycles in digraphs is proved and then with this correspondence other properties of ...

We call a topological ordering of a weighted directed acyclic graph non-negative if the sum of weights on the vertices in any prefix of the ordering is non-negative. We investigate two processes for constructing non-negative topological orderings of weighted directed acyclic graphs. The first process is called a mark sequence and the second is a generalization called a mark-unmark sequence. We ...

In Bayesian Network Structure Learning (BNSL), we are given a variable set and parent scores for each aim to compute DAG, called network, that maximizes the sum of scores, possibly under some structural constraints. Even very restricted special cases BNSL computationally hard, and, thus, in practice heuristics such as local search used. typical algorithm, solution ask whether there is better wi...

ÐScheduling DAGs to multiprocessors is one of the key issues in high-performance computing. Most realistic scheduling algorithms are heuristic and heuristic algorithms often have room for improvement. The quality of a scheduling algorithm can be effectively improved by a local search. In this paper, we present a fast local search algorithm based on topological ordering. This is a compaction alg...

Ramalingam, G. and Reps, T., On competitive on-line algorithms for the dynamic priority-ordering problem. The vertices of a directed acyclic graph (DAG) are said to be correctly prioritized if every vertex v in the graph is assigned a priority, denoted by priority(v), such that if there is an edge in the DAG from vertex v to vertex w then priority(v) < priority(w). The dynamic priority-ordering...

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences enc...

We are here dealing with the problem of space layout planning. We present an approach based on an intermediate topological level with dynamic space ordering (dso) heuristics. Our software ARCHiPLAN proceeds through a number of steps. First, all the topologically different solutions, without presuming any precise dimension, are enumerated. Next, we may evolve in this topological solution space, ...

A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...