Related papers: Incremental Topological Ordering and Strong Compon…
We present two on-line algorithms for maintaining a topological order of a directed $n$-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles $m$ arc additions in $O(m^{3/2})$ time.…
We present two algorithms for maintaining the topological order of a directed acyclic graph with n vertices, under an online edge insertion sequence of m edges. Efficient algorithms for online topological ordering have many applications,…
We present an $\tilde{O}(n^{2.5})$-time algorithm for maintaining the topological order of a directed acyclic graph with $n$ vertices while inserting $m$ edges.
We consider the problem of detecting a cycle in a directed graph that grows by arc insertions, and the related problems of maintaining a topological order and the strong components of such a graph. For these problems, we give two…
We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in O(n^{2.75}) time, independent of the number of edges m inserted. For dense DAGs, this is…
We consider the problem of incremental cycle detection and topological ordering in a directed graph $G = (V, E)$ with $|V| = n$ nodes. In this setting, initially the edge-set $E$ of the graph is empty. Subsequently, at each time-step an…
This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph…
We modify the Pearce-Kelly algorithm that maintains a topological ordering for a directed acyclic graph in order to allow cycles to be tolerated. Cycles make topological orderings moot, of course, however tolerating them is useful in…
Recent works on machine learning for combinatorial optimization have shown that learning based approaches can outperform heuristic methods in terms of speed and performance. In this paper, we consider the problem of finding an optimal…
In this paper, we present an on-line fully dynamic algorithm for maintaining strongly connected component of a directed graph in a shared memory architecture. The edges and vertices are added or deleted concurrently by fixed number of…
The classical comparison-based sorting problem asks us to find the underlying total order of a given set of elements, where we can only access the elements via comparisons. In this paper, we study a restricted version, where, as a hint, a…
In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of…
Graph analytics attract much attention from both research and industry communities. Due to the linear time complexity, the $k$-core decomposition is widely used in many real-world applications such as biology, social networks, community…
The quest for efficient sorting is ongoing, and we will explore a graph-based stable sorting strategy, in particular employing comparison graphs. We use the topological sort to map the comparison graph to a linear domain, and we can…
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…
Graphs have been widely used in many applications such as social networks, collaboration networks, and biological networks. One important graph analytics is to explore cohesive subgraphs in a large graph. Among several cohesive subgraphs…
We describe two efficient on-line algorithms to simplify weighted graphs by eliminating degree-two vertices. Our algorithms are on-line in that they react to updates on the data, keeping the simplification up-to-date. The supported updates…
We present an algorithm for maintaining maximal matching in a graph under addition and deletion of edges. Our data structure is randomized that takes O(log n) expected amortized time for each edge update where n is the number of vertices in…
Canonical orderings serve as the basis for many incremental planar drawing algorithms. All these techniques, however, have in common that they are limited to undirected graphs. While $st$-orderings do extend to directed graphs, especially…
In this paper, we present enumeration algorithms to list all preferred extensions of an argumentation framework. This task is equivalent to enumerating all maximal semikernels of a directed graph. For directed graphs on $n$ vertices, all…