Related papers: Combinatorial decomposition approaches for efficie…
Floating-point arithmetic (FPA) is a mechanical representation of real arithmetic (RA), where each operation is replaced with a rounded counterpart. Various numerical properties can be verified by using SMT solvers that support the logic of…
We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…
In this paper, we propose a uniformly dithered 1-bit quantization scheme for high-dimensional statistical estimation. The scheme contains truncation, dithering, and quantization as typical steps. As canonical examples, the quantization…
A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to…
Here we present two novel contributions for achieving quantum advantage in solving difficult optimisation problems, both in theory and foreseeable practice. (1) We introduce the "Quantum Tree Generator", an approach to generate in…
In this paper, we focus on knapsack cones, a specific type of simplicial cones that arise naturally in the context of the knapsack problem $x_1 a_1 + \cdots + x_n a_n = a_0$. We present a novel combinatorial decomposition for these cones,…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
We study the d-dimensional hypercube knapsack problem where we are given a set of d-dimensional hypercubes with associated profits, and a knapsack which is a unit d-dimensional hypercube. The goal is to find an axis-aligned non-overlapping…
We (claim to) prove the extremely surprising fact that NP=RP. It is achieved by creating a Fully Polynomial-Time Randomized Approximation Scheme (FPRAS) for approximately counting the number of independent sets in bounded degree graphs,…
High-performance learned image compression codecs require flexible probability models to fit latent representations. Gaussian Mixture Models (GMMs) were proposed to satisfy this demand, but suffer from a significant runtime performance…
A distributed system consisting of a huge number of computational entities is prone to faults, because faults in a few nodes cause the entire system to fail. Consequently, fault tolerance of distributed systems is a critical issue.…
Fault-tolerant quantum computing typically requires the transpilation of arbitrary quantum circuits into a finite, universal gate set, such as Clifford+T. As a baseline, Diagonal approximation can be used for synthesizing single-qubit Pauli…
We study pseudo-polynomial time algorithms for the fundamental \emph{0-1 Knapsack} problem. Recent research interest has focused on its fine-grained complexity with respect to the number of items $n$ and the \emph{maximum item weight}…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
Let a polytope $P$ be defined by a system $A x \leq b$. We consider the problem of counting the number of integer points inside $P$, assuming that $P$ is $\Delta$-modular, where the polytope $P$ is called $\Delta$-modular if all the rank…
Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we…
Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to ma- nipulate and analyze such information. Even though datasets have grown in size, the K-means algorithm…
The quantum approximate optimisation ansatz (QAOA) is one of the flagship algorithms used to tackle combinatorial optimisation on graphs problems using a quantum computer, and is considered a strong candidate for early fault-tolerant…
0-1 knapsack is of fundamental importance in computer science, business, operations research, etc. In this paper, we present a deep learning technique-based method to solve large-scale 0-1 knapsack problems where the number of products…
We consider a generalization of the fundamental $k$-means clustering for data with incomplete or corrupted entries. When data objects are represented by points in $\mathbb{R}^d$, a data point is said to be incomplete when some of its…