Related papers: Complexity landscape for local certification
In a labeling scheme the vertices of a given graph from a particular class are assigned short labels such that adjacency can be algorithmically determined from these labels. A representation of a graph from that class is given by the set of…
Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…
Given a network property or a data structure, a local certification is a labeling that allows to efficiently check that the property is satisfied, or that the structure is correct. The quality of a certification is measured by the size of…
We present a novel set of rigorous and computationally efficient topology-based complexity notions that exhibit a strong correlation with the generalization gap in modern deep neural networks (DNNs). DNNs show remarkable generalization…
In the real world a graph is often fragmented and distributed across different sites. This highlights the need for evaluating queries on distributed graphs. This paper proposes distributed evaluation algorithms for three classes of queries:…
There has been significant success in designing highly efficient algorithms for distance and shortest-path queries in recent years; many of the state-of-the-art algorithms use the hub labeling framework. In this paper, we study the…
By prior work, there is a distributed algorithm that finds a maximal fractional matching (maximal edge packing) in $O(\Delta)$ rounds, where $\Delta$ is the maximum degree of the graph. We show that this is optimal: there is no distributed…
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…
We give deterministic distributed $(1+\epsilon)$-approximation algorithms for Minimum Vertex Coloring and Maximum Independent Set on chordal graphs in the LOCAL model. Our coloring algorithm runs in $O(\frac{1}{\epsilon} \log n)$ rounds,…
Locally checkable labeling problems (LCLs) form the foundation of the modern theory of distributed graph algorithms. First introduced in the seminal paper by Naor and Stockmeyer [STOC 1993], these are graph problems that can be described by…
Property Testing is a formal framework to study the computational power and complexity of sampling from combinatorial objects. A central goal in standard graph property testing is to understand which graph properties are testable with…
We propose a general method for converting online algorithms to local computation algorithms by selecting a random permutation of the input, and simulating running the online algorithm. We bound the number of steps of the algorithm using a…
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…
A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being…
Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…
Graph-based representations such as Scene Graphs enable localization in structured indoor environments by matching a locally observed graph, constructed from sensor data, to a prior map. This process is particularly challenging in…
We give an almost complete characterization of the hardness of $c$-coloring $\chi$-chromatic graphs with distributed algorithms, for a wide range of models of distributed computing. In particular, we show that these problems do not admit…
We consider relations between the size, treewidth, and local crossing number (maximum number of crossings per edge) of graphs embedded on topological surfaces. We show that an $n$-vertex graph embedded on a surface of genus $g$ with at most…
This study examines clusterability testing for a signed graph in the bounded-degree model. Our contributions are two-fold. First, we provide a quantum algorithm with query complexity $\tilde{O}(N^{1/3})$ for testing clusterability, which…
Place classification is a fundamental ability that a robot should possess to carry out effective human-robot interactions. It is a nontrivial classification problem which has attracted many research. In recent years, there is a high…