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We propose and develop a novel framework for analyzing permutation-based combinatorial optimization problems, which could eventually be extended to other types of problems. Our approach is based on the decomposition of the objective…
For some weighted $NP$-complete problems, checking whether a proposed solution is optimal is a non-trivial task. Such is the case for the celebrated traveling salesman problem, or the spin-glass problem in 3 dimensions. In this letter, we…
Combinatorial optimization problems are crucial in industry. However, many COPs are NP-hard, causing the search space to grow exponentially with problem size and rendering large-scale instances computationally intractable. Conventional…
Ising Machines are emerging hardware architectures that efficiently solve NP-Hard combinatorial optimization problems. Generally, combinatorial problems are transformed into quadratic unconstrained binary optimization (QUBO) form, but this…
We propose a method to obtain an improved Hamiltonian (action) for the Ising universality class in three dimensions. The improved Hamiltonian has suppressed leading corrections to scaling. It is obtained by tuning models with two coupling…
This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for…
We derive an exact path integral formulation for the partition function for the Ising model using a mapping between spins and poles of a Laurent expansion for a field on the complex plane. The advantage in using this formulation for the…
We show that certain ways of solving some combinatorial optimization problems can be understood as using query planes to divide the space of problem instances into polyhedra that could fit into those that characterize the problem's various…
The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a…
Spin models are widely studied in the natural sciences, from investigating magnetic materials in condensed matter physics to studying neural networks. Previous work has demonstrated that there exist simple classical spin models that are…
We give a detailed theoretical derivation of the quantum master equation for the coherent Ising machine. This is a quantum computational network with feedback, that solves NP hard combinatoric problems, including the traveling salesman…
The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…
The monography considers the problem of constructing a Hamiltonian cycle in a complete graph. A rule for constructing a Hamiltonian cycle based on isometric cycles of a graph is established. An algorithm for constructing a Hamiltonian cycle…
We study three classical graph problems - Hamiltonian path, minimum spanning tree, and minimum perfect matching on geometric graphs induced by bichromatic (red and blue) points. These problems have been widely studied for points in the…
In this paper, we study the problem of finding the global minima of a given function. Specifically, we consider complicated functions with numerous local minima, as is often the case for real-world data mining losses. We do so by applying a…
The equivalence between the natural minimization of energy in a dynamical system and the minimization of an objective function characterizing a combinatorial optimization problem offers a promising approach to designing dynamical…
Efficiently optimizing Nondeterministic Polynomial time (NP) problems in polynomial time has profound implications in many domains. CMOS oscillator networks have been shown to be effective and efficient in approximating certain NP-hard…
We propose a new approach for solving combinatorial optimization problem by utilizing the mechanism of chases and escapes, which has a long history in mathematics. In addition to the well-used steepest descent and neighboring search, we…
We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical…
We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…