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The Bin Packing Problem (BPP) is a well-established combinatorial optimization (CO) problem. Since it has many applications in our daily life, e.g. logistics and resource allocation, people are seeking efficient bin packing algorithms. On…
We develop a novel mathematical programming approximation framework to tackle the stochastic knapsack problem. In this problem, the decision maker considers items for which either weights or values, or both, are random. The aim is to select…
Quantum annealing may provide advantages over simulated annealing on solving some problems such as Kth order binary optimization problem. No feasible architecture exists to implement the high-order optimization problem (K > 2) on current…
This paper presents several new tractability results for planning based on macros. We describe an algorithm that optimally solves planning problems in a class that we call inverted tree reducible, and is provably tractable for several…
We computationally resolve an open problem concerning the expressibility of $4 \times 4$ full-rank matrices as Hadamard products of two rank-2 matrices. Through exhaustive search over $\mathbb{F}_2$, we identify 5,304 counterexamples among…
Given items of different sizes and a fixed bin capacity, the bin-packing problem is to pack these items into the minimum number of bins such that the sum of the item sizes in each bin does not exceed the capacity. We define a new variant,…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We show enough evidence that a structured version of Adiabatic Quantum Computation (AQC) is efficient for most satisfiability problems. More precisely, when the success probability is fixed beforehand, the computational resources grow…
Real-world object manipulation has been commonly challenged by physical uncertainties and perception limitations. Being an effective strategy, while caging configuration-based manipulation frameworks have successfully provided robust…
In the field of algorithms and data structures analysis and design, most of the researchers focus only on the space/time trade-off, and little attention has been paid to energy consumption. Moreover, most of the efforts in the field of…
Bin Packing problems have been widely studied because of their broad applications in different domains. Known as a set of NP-hard problems, they have different vari- ations and many heuristics have been proposed for obtaining approximate…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical…
We show that the existence of a computationally efficient calibration algorithm, with a low weak calibration rate, would imply the existence of an efficient algorithm for computing approximate Nash equilibria - thus implying the unlikely…
The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources.…
Recent trends of technology have explored a numerous applications of cloud services, which require a significant amount of energy. In the present scenario, most of the energy sources are limited and have a greenhouse effect on the…
Packing and vehicle routing problems play an important role in the area of supply chain management. In this paper, we introduce a non-linear knapsack problem that occurs when packing items along a fixed route and taking into account travel…
Experimental groups are now fabricating quantum processors powerful enough to execute small instances of quantum algorithms and definitively demonstrate quantum error correction that extends the lifetime of quantum data, adding urgency to…
The paper studies quantum complexity, tractability, and strong tractability for high dimensional multivariate approximation. We study a space of functions important in many applications. A function space is weighted if certain variables are…
This work presents an empirical analysis of exact algorithms for the unbounded knapsack problem, which includes seven algorithms from the literature, two commercial solvers, and more than ten thousand instances. The terminating step-off, a…
It is now well established that there is no lower bound for the energy dissipated during a computation. The relevance of the zero-energy limit is unclear, however, because it entails computations that are unreliable or infinitely slow, or…