Related papers: Move Complexity of a Self-Stabilizing Algorithm fo…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
The combinatorial problem of learning directed acyclic graphs (DAGs) from data was recently framed as a purely continuous optimization problem by leveraging a differentiable acyclicity characterization of DAGs based on the trace of a matrix…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
Fomin and Villanger (STACS 2010) proved that Maximum Independent Set, Feedback Vertex Set, and more generally the problem of finding a maximum induced subgraph of treewith at most a constant $t$, can be solved in polynomial time on graph…
We consider the problem of maintaining an approximate maximum independent set of geometric objects under insertions and deletions. We present data structures that maintain a constant-factor approximate maximum independent set for broad…
We study the complexity of approximating the independent set polynomial $Z_G(\lambda)$ of a graph $G$ with maximum degree $\Delta$ when the activity $\lambda$ is a complex number. This problem is already well understood when $\lambda$ is…
It is confirmed in this work that the graph isomorphism can be tested in polynomial time, which resolves a longstanding problem in the theory of computation. The contributions are in three phases as follows. 1. A description graph…
Self-stabilizing protocols enable distributed systems to recover correct behavior starting from any arbitrary configuration. In particular, when processors communicate by message passing, fake messages may be placed in communication links…
We find a sharp bound for the order of the automorphism group of a stable curve of genus $g$ with $3g-3$ nodes, and a sharp bound for the order of the automorphism group of such a curve with all smooth components. Combined with the results…
A $t$-ruling set of a graph $G = (V, E)$ is a vertex-subset $S \subseteq V$ that is independent and satisfies the property that every vertex $v \in V$ is at a distance of at most $t$ from some vertex in $S$. A \textit{maximal independent…
Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriously hard both in the…
The 3-domatic number problem asks whether a given graph can be partitioned intothree dominating sets. We prove that this problem can be solved by a deterministic algorithm in time 2.695^n (up to polynomial factors). This result improves the…
A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these…
We show that spin systems with bounded degrees and coupling independence admit fully polynomial time approximation schemes (FPTAS). We design a new recursive deterministic counting algorithm to achieve this. As applications, we give the…
We study the self-stabilizing leader election problem in anonymous $n$-nodes networks. Achieving self-stabilization with low space memory complexity is particularly challenging, and designing space-optimal leader election algorithms remains…
A fundamental question is whether one can maintain a maximum independent set in polylogarithmic update time for a dynamic collection of geometric objects in Euclidean space. Already, for a set of intervals, it is known that no dynamic…
We present the first unsupervised learning model for Maximum-Independent-Set (MaxIS) in dynamic graphs where edges change over time. Our method combines structural learning from graph neural networks (GNNs) with a learned distributed update…
A graph $G$ is asymmetrizable if it has a set of vertices whose setwise stablizer only consists of the identity automorphism. The motion $m$ of a graph is the minimum number of vertices moved by any non-identity automorphism. It is known…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
A major impediment towards the industrial adoption of decentralized distributed systems comes from the difficulty to theoretically prove that these systems exhibit the required behavior. In this paper, we use probability theory to analyze a…