Related papers: Approximating observables is as hard as counting
Many problems in real life can be converted to combinatorial optimization problems (COPs) on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some…
A central theme in sublinear graph algorithms is the relationship between counting and sampling: can the ability to approximately count a combinatorial structure be leveraged to sample it nearly uniformly at essentially the same cost? We…
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…
The graph similarity problem, also known as approximate graph isomorphism or graph matching problem, has been extensively studied in the machine learning community, but has not received much attention in the algorithms community: Given two…
Given a graph $G$, a non-negative integer $k$, and a weight function that maps each vertex in $G$ to a positive real number, the \emph{Maximum Weighted Budgeted Independent Set (MWBIS) problem} is about finding a maximum weighted…
We prove the tightest-known upper bounds on the sample complexity of multi-group learning. Our algorithm extends the one-inclusion graph prediction strategy using a generalization of bipartite $b$-matching. In the group-realizable setting,…
In bipartite incidence graph sampling, the target study units may be formed as connected population elements, which are distinct to the units of sampling and there may exist generally more than one way by which a given study unit can be…
State minimization of combinatorial filters is a fundamental problem that arises, for example, in building cheap, resource-efficient robots. But exact minimization is known to be NP-hard. This paper conducts a more nuanced analysis of this…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
A dominating set of a graph $G=(V,E)$ is a subset of vertices $S\subseteq V$ such that every vertex $v\in V\setminus S$ has at least one neighbor in set $S$. The corresponding optimization problem is known to be NP-hard. The best known…
One of the most important recent developments in the complexity of approximate counting is the classification of the complexity of approximating the partition functions of antiferromagnetic 2-spin systems on bounded-degree graphs. This…
How to measure the complexity of a finite set of vectors embedded in a multidimensional space? This is a non-trivial question which can be approached in many different ways. Here we suggest a set of data complexity measures using universal…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
Group testing, a problem with diverse applications across multiple disciplines, traditionally assumes independence across nodes' states. Recent research, however, focuses on real-world scenarios that often involve correlations among nodes,…
Computing the densest subgraph is a primitive graph operation with critical applications in detecting communities, events, and anomalies in biological, social, Web, and financial networks. In this paper, we study the novel problem of Most…
A theorem of Ding, Oporowski, Oxley, and Vertigan implies that any sufficiently large twin-free graph contains a large matching, a co-matching, or a half-graph as a semi-induced subgraph. The sizes of these unavoidable patterns are measured…
Local graph partitioning is a key graph mining tool that allows researchers to identify small groups of interrelated nodes (e.g. people) and their connective edges (e.g. interactions). Because local graph partitioning is primarily focused…
The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging…
We study the minimization of fixed-degree polynomials over the simplex. This problem is well-known to be NP-hard, as it contains the maximum stable set problem in graph theory as a special case. In this paper, we consider a rational…
In this paper we investigate the colorful components framework, motivated by applications emerging from comparative genomics. The general goal is to remove a collection of edges from an undirected vertex-colored graph $G$ such that in the…