相关论文: The Distance Approach to Approximate Combinatorial…

Classical work on metric space based committee selection problem interprets distance as ``near is better''. In this work, motivated by real-life situations, we interpret distance as ``far is better''. Formally stated, we initiate the study…

Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…

We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…

This paper presents a new approach, based on polynomial optimization and the method of moments, to the problem of anomaly detection. The proposed technique only requires information about the statistical moments of the normal-state…

Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…

Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in…

Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a…

Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting lattice points inside a polytope. However, state-of-the-art algorithms for this problem…

We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is…

This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise…

We study an extension of the cardinality-constrained knapsack problem wherein each item has a concave piecewise linear utility structure (CCKP), which is motivated by applications such as resource management problems in monitoring and…

A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed…

We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…

We consider the problem of allocating samples to a finite set of discrete distributions in order to learn them uniformly well in terms of four common distance measures: $\ell_2^2$, $\ell_1$, $f$-divergence, and separation distance. To…

Since its introduction Boson Sampling has been the subject of intense study in the world of quantum computing. The task is to sample independently from the set of all $n \times n$ submatrices built from possibly repeated rows of a larger $m…

Given $n$ independent random variables $X_1, X_2, ..., X_n$ and an integer $C$, we study the fundamental problem of computing the probability that the sum $X=X_1+X_2+...+X_n$ is at most $C$. We assume that each random variable $X_i$ is…

It has been known that the distribution of the random distances between two uniformly distributed points within a convex polygon can be obtained based on its chord length distribution (CLD). In this report, we first verify the existing…

Several papers have achieved time $O(\sqrt n m)$ for cardinality matching, starting from first principles. This results in a long derivation. We simplify the task by employing well-known concepts for maximum weight matching. We use Edmonds'…

We give a constant factor polynomial time pseudo-approximation algorithm for min-sum clustering with or without outliers. The algorithm is allowed to exclude an arbitrarily small constant fraction of the points. For instance, we show how to…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…