Related papers: On the Hardness of Average-case k-SUM
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size k is planted in a random G(n, 1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best…
We develop new tools in the theory of nonlinear random matrices and apply them to study the performance of the Sum of Squares (SoS) hierarchy on average-case problems. The SoS hierarchy is a powerful optimization technique that has achieved…
The $K$-medoids problem is a challenging combinatorial clustering task, widely used in data analysis applications. While numerous algorithms have been proposed to solve this problem, none of these are able to obtain an exact (globally…
Let D be a database of N objects where each object has m fields. The objects are given in m sorted lists (where the ith list is sorted according to the ith field). Our goal is to find the top k objects according to a monotone aggregation…
In this work we consider the problem of fitting Random Utility Models (RUMs) to user choices. Given the winner distributions of the subsets of size $k$ of a universe, we obtain a polynomial-time algorithm that finds the RUM that best…
Data summarization tasks are often modeled as $k$-clustering problems, where the goal is to choose $k$ data points, called cluster centers, that best represent the dataset by minimizing a clustering objective. A popular objective is to…
In data summarization we want to choose $k$ prototypes in order to summarize a data set. We study a setting where the data set comprises several demographic groups and we are restricted to choose $k_i$ prototypes belonging to group $i$. A…
We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…
We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least $k$ length substrings. First, we show an $O(mn)$ time algorithm for the problem which gives a…
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…
Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
The $k$-cut problem asks, given a connected graph $G$ and a positive integer $k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$ connected components. We give the first polynomial-time algorithm with approximation…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…
$k$-means++ is an important algorithm for choosing initial cluster centers for the $k$-means clustering algorithm. In this work, we present a new algorithm that can solve the $k$-means++ problem with nearly optimal running time. Given $n$…
The Subset Sum problem is a classical NP-complete problem with a long-standing $O^*(2^{n/2})$ deterministic bound due to Horowitz and Sahni. We present results at two distinct levels of generality. First (instance-sensitive bound), we…
The input to the $k$-median for lines problem is a set $L$ of $n$ lines in $\mathbb{R}^d$, and the goal is to compute a set of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum of squared distances over every line in $L$ and its…
We study the parameterized complexity of algorithmic problems whose input is an integer set $A$ in terms of the doubling constant $C := |A + A|/|A|$, a fundamental measure of additive structure. We present evidence that this new…
The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature,…