We introduce the notion of z-topological orderings for digraphs. We prove that given a digraph G on n vertices admitting a z-topological ordering, together with such an ordering, one may count the number of subgraphs of G that at the same time satisfy a monadic second order formula φ and are the union of k directed paths, in time f(φ, k, z) · n. Our result implies the polynomial time solvabilit...

In recent years, a few researchers have challenged past dogma and suggested methods (such as the IC algorithm) for inferring causal relationship among variables using steady state observations. In this paper, we present a modified IC (mIC) algorithm that uses entropy to test conditional independence and combines the steady state data with partial prior knowledge of topological ordering in gene ...

Because topological surface states of a single-crystal topological insulator can exist on all surfaces with different crystal orientations enclosing the crystal, mutual interactions among those states contiguous to each other through edges can lead to unique phenomena inconceivable in normal insulators. Here we show, based on a first-principles approach, that the difference in the work function...

Abstract For a connected graph, the first Zagreb eccentricity index $\xi _{1}$ ? 1 is defined as sum of squares eccentricities all vertices, and second _{2}$ 2 products pairs adjacent vertices. In this paper, we mainly present different universal approa...

Many applications like pointer analysis and incremental compilation require maintaining a topological ordering of the nodes of a directed acyclic graph (DAG) under dynamic updates. All known algorithms for this problem are either only analyzed for worst-case insertion sequences or only evaluated experimentally on random DAGs. We present the first averagecase analysis of incremental topological ...

We present two online algorithms for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm takes O(m) amortized time per arc and our second algorithm takes O(n/m) amortized time per arc, where n is the number of vertices and m is the total number of arcs. For sparse graphs, our O(m) bound improves the best p...

Topological relativity is a concept of interest in geographic information theory. One way of assessing the importance of topology in spatial reasoning is to analyze commonplace terms from natural language relative to conceptual neighborhood graphs, the alignment structures of choice for topological relations. Sixteen English-language spatial prepositions for regionregion relations were analyzed...

Using self-organizing wireless sensor networks for object tracking requires ordering events with regard to time and location. In labyrinth-shaped topologies, one-dimensional ordering suffices within the different parts of the network. We present an algorithm to derive this ordering without the use of location information. Local order knowledge in the nodes can then be additionally used to detec...

Motivated by the minimal tower problem, an earlier work studied diagonalizations of covers where the covers are related to linear quasiorders (τ -covers). We deal with two types of combinatorial questions which arise from this study. (1) Two new cardinals introduced in the topological study are expressed in terms of well known cardinals characteristics of the continuum. (2) We study the additiv...