Da Qi Chen

Carnegie Mellon University | CMU · Department of Mathematical Sciences

Vaccines have proven to be extremely effective in preventing the spread of COVID-19 and potentially ending the pandemic. Lack of access caused many people not getting vaccinated early, so states such as Virginia deployed mobile vaccination sites in order to distribute vaccines across the state. Here we study the problem of deciding where these faci...

Evacuation planning is a crucial part of disaster management. However, joint optimization of its two essential components, routing and scheduling, with objectives such as minimizing average evacuation time or evacuation completion time, is a computationally hard problem. To approach it, we present MIP-LNS, a scalable optimization method that utiliz...

As the demand for electric vehicles continues to surge worldwide, it becomes increasingly imperative for the government to plan and anticipate its practical impact on society. In particular, any city/state needs to guarantee sufficient and proper placement of charging stations to service all current/future electric vehicle adopters. Furthermore, it...

Evacuation planning is a crucial part of disaster management where the goal is to relocate people to safety and minimize casualties. Every evacuation plan has two essential components: routing and scheduling. However, joint optimization of these two components with objectives such as minimizing average evacuation time or evacuation completion time,...

We consider the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We introduce and study a general downgrading variant of the interdiction problem where the capacity of an arc is a function of the subset of its endpoints that are d...

The minimum spanning tree of a graph is a well-studied structure that is the basis of countless graph theoretic and optimization problem. We study the minimum spanning tree (MST) perturbation problem where the goal is to spend a fixed budget to increase the weight of edges in order to increase the weight of the MST as much as possible. Two popular...

We consider an information dissemination problem where the root of an undirected graph constantly updates its information and we wish to keep everyone in the graph as freshly informed about the root as possible. Our synchronous information spreading model uses telephone calls at each time step, in which any node can call at most one neighbor, thus...

Generalized Turán problems have been a central topic of study in extremal combinatorics throughout the last few decades. One such problem, maximizing the number of cliques of a fixed order in a graph with fixed number of vertices and bounded maximum degree, was recently completely resolved by Chase. Kirsch and Radcliffe raised a natural variant of...

This paper considers an edge minimization problem in saturated bipartite graphs. An n by n bipartite graph G is H-saturated if G does not contain a subgraph isomorphic to H but adding any missing edge to G creates a copy of H. More than half a century ago, Wessel and Bollobas independently solved the problem of minimizing the number of edges in K(s...

This paper considers an edge minimization problem in saturated bipartite graphs. An $n$ by $n$ bipartite graph $G$ is $H$-saturated if $G$ does not contain a subgraph isomorphic to $H$ but adding any missing edge to $G$ creates a copy of $H$. More than half a century ago, Wessel and Bollob\'as independently solved the problem of minimizing the numb...

Generalized Tur\'an problems have been a central topic of study in extremal combinatorics throughout the last few decades. One such problem, maximizing the number of cliques of size $t$ in a graph of a fixed order that does not contain any path of a given length, was recently considered and asymptotically solved by Luo. We fully resolve this proble...

Generalized Tur\'an problems have been a central topic of study in extremal combinatorics throughout the last few decades. One such problem, maximizing the number of cliques of a fixed order in a graph with fixed number of vertices and bounded maximum degree, was recently completely resolved by Chase. Kirsch and Radcliffe raised a natural variant o...

We study the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We show hardness of obtaining strictly unicriterion approximations for this basic vertex interdiction problem. We also introduce and study a general downgrading variant...