相关论文: Dynamic complexity of Reachability: How many chang…
Recently it was shown that the transitive closure of a directed graph can be updated using first-order formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework by Dong, Su, and Topor, and…
Reachability, distance, and matching are some of the most fundamental graph problems that have been of particular interest in dynamic complexity theory in recent years [DKMSZ18, DMVZ18, DKMTVZ20]. Reachability can be maintained with…
In this paper we show a new algorithm for the decremental single-source reachability problem in directed planar graphs. It processes any sequence of edge deletions in $O(n\log^2{n}\log\log{n})$ total time and explicitly maintains the set of…
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of Dyck reachability problems in directed and undirected graphs, where updates may add or delete…
Which dynamic queries can be maintained efficiently? For constant-size changes, it is known that constant-depth circuits or, equivalently, first-order updates suffice for maintaining many important queries, among them reachability, tree…
This paper studies dynamic complexity under definable change operations in the DynFO framework by Patnaik and Immerman. It is shown that for changes definable by parameter-free first-order formulas, all (uniform) $AC^1$ queries can be…
We propose a fully dynamic algorithm for maintaining reachability information in directed graphs. The proposed deterministic dynamic algorithm has an update time of $O((ins*n^{2}) + (del * (m+n*log(n))))$ where $m$ is the current number of…
Graph databases in many applications---semantic web, transport or biological networks among others---are not only large, but also frequently modified. Evaluating graph queries in this dynamic context is a challenging task, as those queries…
In the sensitive distance oracle problem, there are three phases. We first preprocess a given directed graph $G$ with $n$ nodes and integer weights from $[-W,W]$. Second, given a single batch of $f$ edge insertions and deletions, we update…
Graph algorithms applied in many applications, including social networks, communication networks, VLSI design, graphics, and several others, require dynamic modifications -- addition and removal of vertices and/or edges -- in the graph.…
Patnaik and Immerman introduced the dynamic complexity class DynFO of database queries that can be maintained by first-order dynamic programs with the help of auxiliary relations under insertions and deletions of edges (Patnaik and Immerman…
With the ubiquity of large-scale graph data in a variety of application domains, querying them effectively is a challenge. In particular, reachability queries are becoming increasingly important, especially for containment, subsumption, and…
Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with $o(mn)$ total update time, where $m$ is the number of edges and $n$ is the…
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…
We consider the problems of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the result of the modification satisfies some property definable in first-order logic. We establish a number…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
One of the most fundamental problems in computer science is the reachability problem: Given a directed graph and two vertices s and t, can s reach t via a path? We revisit existing techniques and combine them with new approaches to support…
This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space. The fully dynamic graph connectivity problem is the following: given a graph on a fixed set of n nodes, process an online…
Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…
Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability however their space complexity is…