Related papers: A Quantum Time-Space Tradeoff for Directed $st$-Co…
In the Directed Steiner Network problem we are given an arc-weighted digraph $G$, a set of terminals $T \subseteq V(G)$, and an (unweighted) directed request graph $R$ with $V(R)=T$. Our task is to output a subgraph $G' \subseteq G$ of the…
We consider space efficient implementations of some classical applications of DFS including the problem of testing biconnectivity and $2$-edge connectivity, finding cut vertices and cut edges, computing chain decomposition and…
To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a…
This paper focuses on showing time-message trade-offs in distributed algorithms for fundamental problems such as leader election, broadcast, spanning tree (ST), minimum spanning tree (MST), minimum cut, and many graph verification problems.…
In the k-edge connected directed Steiner tree (k-DST) problem, we are given a directed graph G on n vertices with edge-costs, a root vertex r, a set of h terminals T and an integer k. The goal is to find a min-cost subgraph H of G that…
Coordination of dynamical routes can alleviate traffic congestion and is essential for the coming era of autonomous self-driving cars. However, dynamical route coordination is difficult and many existing routing protocols are either static…
A directed graph $D$ is semicomplete if for every pair $x,y$ of vertices of $D,$ there is at least one arc between $x$ and $y.$ \viol{Thus, a tournament is a semicomplete digraph.} In the Directed Component Order Connectivity (DCOC)…
We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity.…
Accurate traffic prediction is a challenging task in intelligent transportation systems because of the complex spatio-temporal dependencies in transportation networks. Many existing works utilize sophisticated temporal modeling approaches…
The clock synchronization problem is to determine the time difference $\Delta$ between two spatially separated clocks. When message delivery times between the two clocks are uncertain, $O(2^{2n})$ classical messages must be exchanged…
Traffic forecasting is essential to intelligent transportation systems, which is challenging due to the complicated spatial and temporal dependencies within a road network. Existing works usually learn spatial and temporal dependencies…
Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science: Given a directed graph $G=(V, E)$ with edge costs $c \in \mathbb{R}_{\geq 0}^E$, a root $r \in V$ and $k$ terminals $K\subseteq…
We give a deterministic $\tilde{O}(\log n)$-space algorithm for approximately solving linear systems given by Laplacians of undirected graphs, and consequently also approximating hitting times, commute times, and escape probabilities for…
Time-Dependent Constrained Path Optimization (TD-CPO) takes the following input: (i) time-dependent (TD) road network, (ii) source ($s$), (iii) destination ($d$), (iv) departure time ($t$) and, (v) budget ($\mathcal{B}$). In TD graph, each…
We present a deterministic fully-dynamic data structure for maintaining information about the cut-vertices in a graph; i.e. the vertices whose removal would disconnect the graph. Our data structure supports insertion and deletion of edges,…
We give new deterministic bounds for fully-dynamic graph connectivity. Our data structure supports updates (edge insertions/deletions) in $O(\log^2n/\log\log n)$ amortized time and connectivity queries in $O(\log n/\log\log n)$ worst-case…
Let $S$ be a planar $n$-point set. A triangulation for $S$ is a maximal plane straight-line graph with vertex set $S$. The Voronoi diagram for $S$ is the subdivision of the plane into cells such that all points in a cell have the same…
This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space. The fully dynamic graph connectivity problem is the following: given a graph on a fixed set of n nodes, process an online…
We revisit once more the problem of designing an oracle for answering connectivity queries in undirected graphs in the presence of vertex failures. Specifically, given an undirected graph $G$ with $n$ vertices and $m$ edges and an integer…
One of the most fundamental graph problems is finding a shortest path from a source to a target node. While in its basic forms the problem has been studied extensively and efficient algorithms are known, it becomes significantly harder as…