Related papers: Boundary optimization for rough sets
This paper presents a detailed study of constrained quantization for both finite and infinite discrete probability distributions supported on subsets of the real line. Under specific geometric constraints - namely, a semicircular arc and…
In the last decade, various works have used statistics on relations to improve both the theory and practice of conjunctive query execution. Starting with the AGM bound which took advantage of relation sizes, later works incorporated…
Let $E$ be a bounded open subset of $\mathbb{R}^n$. We study the following questions: For i.i.d. samples $X_1, \dots, X_N$ drawn uniformly from $E$, what is the probability that $\cup_i \mathbf{B}(X_i, \delta)$, the union of $\delta$-balls…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
This paper studies lower bounds for fundamental optimization problems in the CONGEST model. We show that solving problems exactly in this model can be a hard task, by providing $\tilde{\Omega}(n^2)$ lower bounds for cornerstone problems,…
We develop an randomized approximation algorithm for the size of set union problem $\arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert$, which given a list of sets $A_1,...,A_m$ with approximate set size $m_i$ for $A_i$ with $m_i\in…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…
In this paper we relate the partition function to the max-statistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As…
We investigate optimization models for the purpose of computational redistricting. Our focus is on nonconvex objectives for estimating expected Black Representatives and Political Representation. The objectives are a composition of a ratio…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
Partitioning algorithms play a key role in many scientific and engineering disciplines. A partitioning algorithm divides a set into a number of disjoint subsets or partitions. Often, the quality of the resulted partitions is measured by the…
This paper introduces a class of mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the partitions…
We present conjectured candidates for the least perimeter partition of a disc into $N \le 10$ regions which take one of two possible areas. We assume that the optimal partition is connected, and therefore enumerate all three-connected…
Given a sequence of $N$ positive real numbers $\{a_1,a_2,..., a_N \}$, the number partitioning problem consists of partitioning them into two sets such that the absolute value of the difference of the sums of $a_j$ over the two sets is…
In this paper, we investigate an optimal design problem motivated by some issues arising in population dynamics. In a nutshell, we aim at determining the optimal shape of a region occupied by resources for maximizing the survival ability of…
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…
We provide a two-sided inequality for the alpha-optimal partition value of a measurable space according to n nonatomic finite measures. The result extends and often improves Legut (1988) since the bounds are obtained considering several…
Computing the partition function and the marginals of a global probability distribution are two important issues in any probabilistic inference problem. In a previous work, we presented sub-tree based upper and lower bounds on the partition…
The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…