相关论文: From Independence to Expansion and Back Again

In a recent paper with Thomas Hoffmann-Ostenhof, we proved that the number of critical points in the boundary set of a k-minimal partition tends to infinity as k tends to infinity. In this note, we show that this number increases linearly…

We consider the problem of chasing convex functions, where functions arrive over time. The player takes actions after seeing the function, and the goal is to achieve a small function cost for these actions, as well as a small cost for…

We construct several pairwise-incomparable bounds on the projective dimensions of edge ideals. Our bounds use combinatorial properties of the associated graphs; in particular we draw heavily from the topic of dominating sets. Through…

For a graph $G$, its $k$-th power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$ of each other. The $k$-independence number $\alpha_k(G)$ is defined as the independence number of $G^k$. By using…

To get estimators that work within a certain error bound with high probability, a common strategy is to design one that works with constant probability, and then boost the probability using independent repetitions. Important examples of…

For a graph $G$, its $k$-th graph power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$. We consider the problem of deriving upper bounds on the Shannon capacity of graph powers by using spectral…

When designing an algorithm, one cares about arithmetic/computational complexity, but data movement (I/O) complexity plays an increasingly important role that highly impacts performance and energy consumption. For a given algorithm and a…

How data is represented and operationalized is critical for building computational solutions that are both effective and efficient. A common approach is to represent data objects as binary vectors, denoted \textit{hash codes}, which require…

This work addresses the well-known Maximum Independent Set problem in the context of hypergraphs. While this problem has been extensively studied on graphs, we focus on its strong extension to hypergraphs, where edges may connect any number…

We introduce a new concept, which we call partition expanders. The basic idea is to study quantitative properties of graphs in a slightly different way than it is in the standard definition of expanders. While in the definition of expanders…

We introduce methods to count and enumerate all maximal independent, all maximum independent sets, and all independent sets in threshold graphs and k-threshold graphs. Within threshold graphs and k-threshold graphs independent sets…

The independent set reconfiguration problem asks whether one can transform one given independent set of a graph into another, by changing vertices one by one in such a way the intermediate sets remain independent. Extremal problems on…

Traditionally, reconfiguration problems ask the question whether a given solution of an optimization problem can be transformed to a target solution in a sequence of small steps that preserve feasibility of the intermediate solutions. In…

Expander graphs, due to their mixing properties, are useful in many algorithms and combinatorial constructions. One can produce an expander graph with high probability by taking a random graph (e.g., the union of $d$ random bijections for a…

We consider a generic algorithmic paradigm that we call progressive exploration, which can be used to develop simple and efficient parameterized graph algorithms. We identify two model-theoretic properties that lead to efficient progressive…

Spectral independence is a recently-developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal $O(n \log n)$ sampling algorithms on bounded-degree graphs…

We investigate the complexity consequences of adding pointer arithmetic to separation logic. Specifically, we study extensions of the points-to fragment of symbolic-heap separation logic with various forms of Presburger arithmetic…

In the Independent Set Reconfiguration problem under the Token Addition/Removal rule, given a graph $G$ and two independent sets $I$ and $J$ of $G$, we want to transform $I$ into $J$ by adding and removing vertices, such that all the sets…

The independence gap of a graph was introduced by Ekim et al. (2018) as a measure of how far a graph is from being well-covered. It is defined as the difference between the maximum and minimum size of a maximal independent set. We…

The problem of extending partial geometric graph representations such as plane graphs has received considerable attention in recent years. In particular, given a graph $G$, a connected subgraph $H$ of $G$ and a drawing $\mathcal{H}$ of $H$,…