Related papers: A Linear Time Algorithm for Constructing Hierarchi…
Fully dynamic graph algorithms that achieve polylogarithmic or better time per operation use either a hierarchical graph decomposition or random-rank based approach. There are so far two graph properties for which efficient algorithms for…
Let G = (V, E) be a planar triangulated graph (PTG) having every face triangular. A rectilinear dual or an orthogonal floor plan (OFP) of G is obtained by partitioning a rectangle into \mid V \mid rectilinear regions (modules) where two…
Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for…
Given an undirected graph $G$, the problem of deciding whether $G$ admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (G\"obel et al., 1991). In this article, we relax this problem and ask…
For any undirected and weighted graph $G=(V,E,w)$ with $n$ vertices and $m$ edges, we call a sparse subgraph $H$ of $G$, with proper reweighting of the edges, a $(1+\varepsilon)$-spectral sparsifier if \[…
Recently, a new set of multigraph parameters was defined, called "gonalities". Gonality bears some similarity to treewidth, and is a relevant graph parameter for problems in number theory and multigraph algorithms. Multigraphs of gonality 1…
We present ROBO (Riemannian Overlapping Block Optimization), a distributed and parallel approach to multi-robot pose graph optimization (PGO) based on the idea of overlapping domain decomposition. ROBO offers a middle ground between…
Recent years have witnessed a flurry of research activity in graph matching, which aims at finding the correspondence of nodes across two graphs and lies at the heart of many artificial intelligence applications. However, matching…
A homomorphism from a graph $G$ to a graph $H$ is an edge-preserving mapping from $V(G)$ to $V(H)$. Let $H$ be a fixed graph with possible loops. In the list homomorphism problem, denoted by \textsc{LHom}($H$), the instance is a graph $G$,…
The geodesic Voronoi diagram of m point sites inside a simple polygon of n vertices is a subdivision of the polygon into m cells, one to each site, such that all points in a cell share the same nearest site under the geodesic distance. The…
We give a generalized definition of stretch that simplifies the efficient construction of low-stretch embeddings suitable for graph algorithms. The generalization, based on discounting highly stretched edges by taking their $p$-th power for…
We show that the shortest $s$-$t$ path problem has the overlap-gap property in (i) sparse $\mathbf{G}(n,p)$ graphs and (ii) complete graphs with i.i.d. Exponential edge weights. Furthermore, we demonstrate that in sparse $\mathbf{G}(n,p)$…
Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
The computation of a peeling order in a randomly generated hypergraph is the most time-consuming step in a number of constructions, such as perfect hashing schemes, random $r$-SAT solvers, error-correcting codes, and approximate set…
We investigate the two problems of computing the union join graph as well as computing the subset graph for acyclic hypergraphs and their subclasses. In the union join graph $G$ of an acyclic hypergraph $H$, each vertex of $G$ represents a…
Motivated by the development of computer theory, the sorting algorithm is emerging in an endless stream. Inspired by decrease and conquer method, we propose a brand new sorting algorithmUltimately Heapsort. The algorithm consists of two…
Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…
The problem of sparsifying a graph or a hypergraph while approximately preserving its cut structure has been extensively studied and has many applications. In a seminal work, Bencz\'ur and Karger (1996) showed that given any $n$-vertex…
We give an algorithm that decides whether the bipartite crossing number of a given graph is at most $k$. The running time of the algorithm is upper bounded by $2^{O(k)} + n^{O(1)}$, where $n$ is the number of vertices of the input graph,…