Related papers: Spanner for the $0/1/\infty$ weighted region probl…
The approximate single-source shortest-path problem is as follows: given a graph with nonnegative edge weights and a designated source vertex $s$, return estimates of the distances from~$s$ to each other vertex such that the estimate falls…
In the \emph {barrier resilience} problem (introduced by Kumar {\em et al.}, Wireless Networks 2007), we are given a collection of regions of the plane, acting as obstacles, and we would like to remove the minimum number of regions so that…
A distributed network is modeled by a graph having $n$ nodes (processors) and diameter $D$. We study the time complexity of approximating {\em weighted} (undirected) shortest paths on distributed networks with a $O(\log n)$ {\em bandwidth…
Given an edge-weighted graph $G$ and $\epsilon>0$, a $(1+\epsilon)$-spanner is a spanning subgraph $G'$ whose shortest path distances approximate those of $G$ within a $(1+\epsilon)$ factor. If $G$ is from certain minor-closed graph…
We consider the classical makespan minimization scheduling problem where $n$ jobs must be scheduled on $m$ identical machines. Using weighted random sampling, we developed two sublinear time approximation schemes: one for the case where $n$…
We present a randomized algorithm for the single-source shortest paths (SSSP) problem on directed graphs with arbitrary real-valued edge weights that runs in $n^{2+o(1)}$ time with high probability. This result yields the first almost…
In undirected graphs with real non-negative weights, we give a new randomized algorithm for the single-source shortest path (SSSP) problem with running time $O(m\sqrt{\log n \cdot \log\log n})$ in the comparison-addition model. This is the…
We devise a data structure that can answer shortest path queries for two query points in a polygonal domain $P$ on $n$ vertices. For any $\varepsilon > 0$, the space complexity of the data structure is $O(n^{10+\varepsilon })$ and queries…
A \emph{spanner} of a graph $G$ is a subgraph $H$ that approximately preserves shortest path distances in $G$. Spanners are commonly applied to compress computation on metric spaces corresponding to weighted input graphs. Classic spanner…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
Near-additive (aka $(1+\epsilon,\beta)$-) emulators and spanners are a fundamental graph-algorithmic construct, with numerous applications for computing approximate shortest paths and related problems in distributed, streaming and dynamic…
We present a new efficient localized algorithm to construct, for any given quasi-unit disk graph G=(V,E) and any e > 0, a (1+e)-spanner for G of maximum degree O(1) and total weight O(w(MST)), where w(MST) denotes the weight of a minimum…
We present the first polynomial time approximation algorithm for computing shortest paths in weighted three-dimensional domains. Given a polyhedral domain $\D$, consisting of $n$ tetrahedra with positive weights, and a real number…
Let $G$ be a unit disk graph in the plane defined by $n$ disks whose positions are known. For the case when $G$ is unweighted, we give a simple algorithm to compute a shortest path tree from a given source in $O(n\log n)$ time. For the case…
Given a set P of n points in the plane, the unit-disk graph G_{r}(P) with respect to a parameter r is an undirected graph whose vertex set is P such that an edge connects two points p, q \in P if the Euclidean distance between p and q is at…
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…
Given a set S of n points, a weight function w to associate a non-negative weight to each point in S, a positive integer k \ge 1, and a real number \epsilon > 0, we present algorithms for computing a spanner network G(S, E) for the metric…
Given a set $S$ of $n$ points, a weight function $w$ to associate a non-negative weight to each point in $S$, a positive integer $k \ge 1$, and a real number $\epsilon > 0$, we devise the following algorithms to compute a $k$-vertex…
Miller et al. \cite{MPVX15} devised a distributed\footnote{They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in \cite{MPVX15}.} algorithm in the CONGEST model, that given a parameter $k =…
Understanding the structure of minor-free metrics, namely shortest path metrics obtained over a weighted graph excluding a fixed minor, has been an important research direction since the fundamental work of Robertson and Seymour. A…