Related papers: Approximate Distance Oracles for Planar Graphs wit…

Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ such that the diameter of the resulting graph is minimized. Previously (in ICALP 2015) the problem was solved in…

We present new quantum algorithms for Triangle Finding improving its best previously known quantum query complexities for both dense and spare instances.For dense graphs on $n$ vertices, we get a query complexity of $O(n^{5/4})$ without any…

We combine ideas from distance sensitivity oracles (DSOs) and fixed-parameter tractability (FPT) to design sensitivity oracles for FPT graph problems. An oracle with sensitivity $f$ for an FPT problem $\Pi$ on a graph $G$ with parameter $k$…

Given a set of pairwise disjoint polygonal obstacles in the plane, finding an obstacle-avoiding Euclidean shortest path between two points is a classical problem in computational geometry and has been studied extensively. Previously,…

In the pairwise weighted spanner problem, the input consists of an $n$-vertex-directed graph, where each edge is assigned a cost and a length. Given $k$ vertex pairs and a distance constraint for each pair, the goal is to find a…

Given a graph $G$ and a set of terminals $T$, a \emph{distance emulator} of $G$ is another graph $H$ (not necessarily a subgraph of $G$) containing $T$, such that all the pairwise distances in $G$ between vertices of $T$ are preserved in…

Plotkin, Rao, and Smith (SODA'97) showed that any graph with $m$ edges and $n$ vertices that excludes $K_h$ as a depth $O(\ell\log n)$-minor has a separator of size $O(n/\ell + \ell h^2\log n)$ and that such a separator can be found in…

The Fr\'echet distance is a commonly used similarity measure between curves. It is known how to compute the continuous Fr\'echet distance between two polylines with $m$ and $n$ vertices in $\mathbb{R}^d$ in $O(mn (\log \log n)^2)$ time;…

We design a space-efficient algorithm for performing depth-first search traversal(DFS) of a graph in $O(m+n\log^* n)$ time using $O(n)$ bits of space. While a normal DFS algorithm results in a DFS-tree (in case the graph is connected), our…

We consider preprocessing a set $S$ of $n$ points in convex position in the plane into a data structure supporting queries of the following form: given a point $q$ and a directed line $\ell$ in the plane, report the point of $S$ that is…

In fault-tolerant distance labeling we wish to assign short labels to the vertices of a graph $G$ such that from the labels of any three vertices $u,v,f$ we can infer the $u$-to-$v$ distance in the graph $G\setminus \{f\}$. We show that any…

We consider the problem of computing the diameter of a unicycle graph (i.e., a graph with a unique cycle). We present an O(n) time algorithm for the problem, where n is the number of vertices of the graph. This improves the previous best…

Let $V$ be a set of $n$ points in the plane. The unit-disk graph $G = (V, E)$ has vertex set $V$ and an edge $e_{uv} \in E$ between vertices $u, v \in V$ if the Euclidean distance between $u$ and $v$ is at most 1. The weight of each edge…

For any $\epsilon \in (0,1)$, a $(1+\epsilon)$-approximate range mode query asks for the position of an element whose frequency in the query range is at most a factor $(1+\epsilon)$ smaller than the true mode. For this problem, we design an…

The Fr\'echet distance is a popular distance measure between trajectories or curves in space, or between walks in graphs. We study computing the Fr\'echet distance between walks in the $d$-dimensional grid graphs, i.e. $\mathbb{Z}^d$ where…

A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit…

Consider the following generalization of the classic binary search problem: A searcher is required to find a hidden target vertex $x$ in a graph $G$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$.…

Let G be an edge-weighted hypergraph on n vertices, m edges of size \le s, where the edges have real weights in an interval [1,W]. We show that if we can approximate a maximum weight matching in G within factor alpha in time T(n,m,W) then…

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…

Given a graph $G$ and two vertices $s$ and $t$ in it, {\em graph reachability} is the problem of checking whether there exists a path from $s$ to $t$ in $G$. We show that reachability in directed layered planar graphs can be decided in…