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We consider the problem of constructing a single spanning tree for the single-source buy-at-bulk network design problem for doubling-dimension graphs. We compute a spanning tree to route a set of demands (or data) along a graph to or from a…
Minimum Spanning Trees are a well-studied subset of graph problems. While classical algorithms have existed to solve these problems for decades, new variations and application areas are constantly being discovered. When dealing with large…
We investigate the computational power of the deterministic single-agent model where the agent and each node are equipped with a limited amount of persistent memory. Tasks are formalized as decision problems on properties of input graphs,…
The Multiobjective Minimum Spanning Tree (MO-MST) problem is a variant of the Minimum Spanning Tree problem, in which the costs associated with every edge of the input graph are vectors. In this paper, we design a new dynamic programming…
The global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about the intrinsic geometry of MSTs of most standard models, and…
It has been shown that one can design distributed algorithms that are (nearly) singularly optimal, meaning they simultaneously achieve optimal time and message complexity (within polylogarithmic factors), for several fundamental global…
We study the classic Euclidean Minimum Spanning Tree (MST) problem in the Massively Parallel Computation (MPC) model. Given a set $X \subset \mathbb{R}^d$ of $n$ points, the goal is to produce a spanning tree for $X$ with weight within a…
We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic…
Consider an agent exploring an unknown graph in search of some goal state. As it walks around the graph, it learns the nodes and their neighbors. The agent only knows where the goal state is when it reaches it. How do we reach this goal…
The Angular Constrained Minimum Spanning Tree Problem ($\alpha$-MSTP) is defined in terms of a complete undirected graph $G=(V,E)$ and an angle $\alpha \in (0,2\pi]$. Vertices of $G$ define points in the Euclidean plane while edges, the…
We present a scalable tree search planning algorithm for large multi-agent sequential decision problems that require dynamic collaboration. Teams of agents need to coordinate decisions in many domains, but naive approaches fail due to the…
Phylogenetic trees are leaf-labelled trees used to model the evolution of species. In practice it is not uncommon to obtain two topologically distinct trees for the same set of species, and this motivates the use of distance measures to…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…
Network interdiction problems are a natural way to study the sensitivity of a network optimization problem with respect to the removal of a limited set of edges or vertices. One of the oldest and best-studied interdiction problems is…
Depth first search (DFS) tree is one of the most well-known data structures for designing efficient graph algorithms. Given an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges, the textbook algorithm takes $O(n+m)$ time to…
We present a new algorithm for generating a uniformly random spanning tree in an undirected graph. Our algorithm samples such a tree in expected $\tilde{O}(m^{4/3})$ time. This improves over the best previously known bound of…
We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient…
Cooperative task assignment is an important subject in multi-agent systems with a wide range of applications. These systems are usually designed with massive communication among the agents to minimize the error in pursuit of the general…
The congested clique is a synchronous, message-passing model of distributed computing in which each computational unit (node) in each round can send message of O(log n) bits to each other node of the network, where n is the number of nodes.…
We study the dispersion problem in anonymous port-labeled graphs: $k \leq n$ mobile agents, each with a unique ID and initially located arbitrarily on the nodes of an $n$-node graph with maximum degree $\Delta$, must autonomously relocate…