Related papers: Exact Distance Oracles for Planar Graphs
In the {\em distributed all-pairs shortest paths} problem (APSP), every node in the weighted undirected distributed network (the CONGEST model) needs to know the distance from every other node using least number of communication rounds…
Similar subtrajectory search is a finer-grained operator that can better capture the similarities between one query trajectory and a portion of a data trajectory than the traditional similar trajectory search, which requires the two checked…
We consider approximate {\em path-reporting} distance oracles, distance labeling and labeled routing with extremely low space requirement, for general undirected graphs. For distance oracles, we show how to break the n\log n space bound of…
Given a clique-width $k$-expression of a graph $G$, we provide $2^{O(k)}\cdot n$ time algorithms for connectivity constraints on locally checkable properties such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected Vertex…
The notion of shortcut partition, introduced recently by Chang, Conroy, Le, Milenkovi\'c, Solomon, and Than [CCLMST23], is a new type of graph partition into low-diameter clusters. Roughly speaking, the shortcut partition guarantees that…
We give an algorithm which for an input planar graph $G$ of $n$ vertices and integer $k$, in $\min\{O(n\log^3n),O(nk^2)\}$ time either constructs a branch-decomposition of $G$ with width at most $(2+\delta)k$, $\delta>0$ is a constant, or a…
In this paper we provide a $\tilde{O}(m\sqrt{n})$ time algorithm that computes a $3$-multiplicative approximation of the girth of a $n$-node $m$-edge directed graph with non-negative edge lengths. This is the first algorithm which…
The directed graph reachability problem takes as input an $n$-vertex directed graph $G=(V,E)$, and two distinguished vertices $s$ and $t$. The problem is to determine whether there exists a path from $s$ to $t$ in $G$. This is a canonical…
Algebraic techniques have had an important impact on graph algorithms so far. Porting them, e.g., the matrix inverse, into the dynamic regime improved best-known bounds for various dynamic graph problems. In this paper, we develop new…
In this paper, we provide faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape…
Consider a pair of plane straight-line graphs, whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n log n)-time O(n)-space technique to preprocess such pair of graphs, that…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…
We present an optimal oracle for answering connectivity queries in undirected graphs in the presence of at most three vertex failures. Specifically, we show that we can process a graph $G$ in $O(n+m)$ time, in order to build a data…
In this paper we present new data structures for two extensively studied variants of the orthogonal range searching problem. First, we describe a data structure that supports two-dimensional orthogonal range minima queries in $O(n)$ space…
Sublinear time algorithms for approximating maximum matching size have long been studied. Much of the progress over the last two decades on this problem has been on the algorithmic side. For instance, an algorithm of Behnezhad [FOCS'21]…
We show that any embedding of a planar graph can be encoded succinctly while efficiently answering a number of topological queries near-optimally. More precisely, we build on a succinct representation that encodes an embedding of $m$ edges…
We present an $f$-fault tolerant distance oracle for an undirected weighted graph where each edge has an integral weight from $[1 \dots W]$. Given a set $F$ of $f$ edges, as well as a source node $s$ and a destination node $t$, our oracle…
Designing approximate all-pairs distance oracles in the fully dynamic setting is one of the central problems in dynamic graph algorithms. Despite extensive research on this topic, the first result breaking the $O(\sqrt{n})$ barrier on the…
In this paper we show that set-intersection is harder than distance oracle on sparse graphs. Given a collection of total size n which consists of m sets drawn from universe U, the set-intersection problem is to build a data structure which…