Related papers: Completing the Node-Averaged Complexity Landscape …
Tree-width has been proven to be a useful parameter to design fast and efficient algorithms for intractable problems. However, while tree-width is low on relatively sparse graphs can be arbitrary high on dense graphs. Therefore, we…
Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…
A standard model in network synchronised distributed computing is the LOCAL model. In this model, the processors work in rounds and, in the classic setting, they know the number of vertices of the network, $n$. Using $n$, they can compute…
A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of…
Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…
Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [JT07]. However, for graphs of tree-width larger than 2, no bound better than NL is known. In this paper, we…
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…
We focus on the average-case analysis: A function w : V -> Z+ is given which defines the likelihood for a node to be the one marked, and we want the strategy that minimizes the expected number of queries. Prior to this paper, very little…
Triangle-free graphs play a central role in graph theory, and triangle detection (or triangle finding) as well as triangle enumeration (triangle listing) play central roles in the field of graph algorithms. In distributed computing,…
Consider a graph problem that is locally checkable but not locally solvable: given a solution we can check that it is feasible by verifying all constant-radius neighborhoods, but to find a solution each node needs to explore the input graph…
We study \emph{local computation algorithms (LCAs)} for constructing spanning trees. In this setting, the goal is to locally determine, for each edge $ e \in E $, whether it belongs to a spanning tree $ T $ of the input graph $ G $, where $…
In this work we introduce the graph-theoretic notion of mendability: for each locally checkable graph problem we can define its mending radius, which captures the idea of how far one needs to modify a partial solution in order to "patch a…
This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree $\Delta$, and each node has up to $L$ units of load. The task is to distribute the load more evenly so that the loads of…
We connect three distinct lines of research that have recently explored extensions of the classical LOCAL model of distributed computing: A. distributed quantum computing and non-signaling distributions [e.g. STOC 2024], B.…
In this paper, we study the graph realization problem in the Congested Clique model of distributed computing under crash faults. We consider {\em degree-sequence realization}, in which each node $v$ is associated with a degree value $d(v)$,…
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…
Shared randomness is a valuable resource in distributed computing, allowing some form of coordination between processors without explicit communication. But what happens when the shared random string can affect the inputs to the system?…
One of the cornerstones of the distributed complexity theory is the derandomization result by Chang, Kopelowitz, and Pettie [FOCS 2016]: any randomized LOCAL algorithm that solves a locally checkable labeling problem (LCL) can be…
The graph model checking problem consists in testing whether an input graph satisfies a given logical formula. In this paper, we study this problem in a distributed setting, namely local certification. The goal is to assign labels to the…