Related papers: On-The-Fly Static Analysis via Dynamic Bidirected …
Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently,…
Connectivity related concepts are of fundamental interest in graph theory. The area has received extensive attention over four decades, but many problems remain unsolved, especially for directed graphs. A directed graph is 2-edge-connected…
In (fully) dynamic set cover, the goal is to maintain an approximately optimal solution to a dynamically evolving instance of set cover, where in each step either an element is added to or removed from the instance. The two main desiderata…
Static code analysis is a powerful approach to detect quality deficiencies such as performance bottlenecks, safety violations or security vulnerabilities already during a software system's implementation. Yet, as current software systems…
The topologies of predictable dynamic networks are continuously dynamic in terms of node position, network connectivity and link metric. However, their dynamics are almost predictable compared with the ad-hoc network. The existing routing…
Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…
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…
Updatable timed automata (UTA) are extensions of classic timed automata that allow special updates to clock variables, like x:= x - 1, x := y + 2, etc., on transitions. Reachability for UTA is undecidable in general. Various subclasses with…
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.…
In the classic online graph balancing problem, edges arrive sequentially and must be oriented immediately upon arrival, to minimize the maximum in-degree. For adversarial arrivals, the natural greedy algorithm is $O(\log n)$-competitive,…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
The nonlinear filtering problem is concerned with finding the conditional probability distribution (posterior) of the state of a stochastic dynamical system, given a history of partial and noisy observations. This paper presents a…
In this paper we study the problem of fully dynamic maximal matching with lookahead. In a fully dynamic $n$-vertex graph setting, we have to handle updates (insertions and removals of edges), and answer queries regarding the current graph,…
We study dynamic network flows with uncertain input data under a robust optimization perspective. In the dynamic maximum flow problem, the goal is to maximize the flow reaching the sink within a given time horizon $T$, while flow requires a…
Computing a maximum independent set (MaxIS) is a fundamental NP-hard problem in graph theory, which has important applications in a wide spectrum of fields. Since graphs in many applications are changing frequently over time, the problem of…
This paper presents a method for incorporating control analysis into design optimization for highly-maneuverable aircraft. By studying reachable sets for aircraft dynamics, we ensure that the optimizer will take the aircraft's controlled…
We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic…
We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\log^3 n)$ per edge insertion, $O(\log^4 n)$ per edge…
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…
In this paper we introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive…