Related papers: Concavity of reweighted Kikuchi approximation
In $k$-hypergraph matching, we are given a collection of sets of size at most $k$, each with an associated weight, and we seek a maximum-weight subcollection whose sets are pairwise disjoint. More generally, in $k$-hypergraph $b$-matching,…
We determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of…
Region extraction is necessary in a wide range of applications, from object detection in autonomous driving to analysis of subcellular morphology in cell biology. There exist two main approaches: convex hull extraction, for which exact and…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
This paper extends the classic theory of convex optimization to the minimization of functions that are equal to the negated logarithm of what we term as a sum-log-concave function, i.e., a sum of log-concave functions. In particular, we…
We study two-stage bipartite matching, in which the edges of a bipartite graph on vertices $(B_1 \cup B_2, I)$ are revealed in two batches. In stage one, a matching must be selected from among revealed edges $E \subseteq B_1 \times I$. In…
This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…
We propose a new approach to deriving quantitative mean field approximations for any probability measure $P$ on $\mathbb{R}^n$ with density proportional to $e^{f(x)}$, for $f$ strongly concave. We bound the mean field approximation for the…
The push-sum algorithm is probably the most important distributed averaging approach over directed graphs, which has been applied to various problems including distributed optimization. This paper establishes the explicit absolute…
In this paper we show that the weighted Bernstein-Walsh inequality in logarithmic potential theory is sharp up to some new universal constant, provided that the external field is given by a logarithmic potential. Our main tool for such…
Measurement-Based Quantum Computing (MBQC) is inherently well-suited for Distributed Quantum Computing (DQC): once a resource state is prepared and distributed across a network of quantum nodes, computation proceeds through local…
Given an edge-weighted (metric/general) complete graph with $n$ vertices, the maximum weight (metric/general) $k$-cycle/path packing problem is to find a set of $\frac{n}{k}$ vertex-disjoint $k$-cycles/paths such that the total weight is…
Image segmentation is critically important in almost all medical image analysis for automatic interpretations and processing. However, it is often challenging to perform image segmentation due to data imbalance between intra- and…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
We consider the fundamental problem of ReLU regression, where the goal is to output the best fitting ReLU with respect to square loss given access to draws from some unknown distribution. We give the first efficient, constant-factor…
In this paper, we present sufficient conditions ensuring that the sum of the image of quadratic functions and the nonnegative orthant is convex. The hidden convexity of the trust-region problem with linear inequality constraints is…
In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…
We study the fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…