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Sparse Ising problems can be found in application areas such as logistics, condensed matter physics and training of deep Boltzmann networks, but can be very difficult to tackle with high efficiency and accuracy. This report presents new…
The crossing resolution of a non-planar drawing of a graph is the value of the minimum angle formed by any pair of crossing edges. Recent experiments have shown that the larger the crossing resolution is, the easier it is to read and…
The commercial and industrial demand for the solution of hard combinatorial optimization problems push forward the development of efficient solvers. One of them is the Ising machine which can solve combinatorial problems mapped to Ising…
We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut…
One of the challenges in optimization of high dimensional problems is finding appropriate solutions in a way that are as close as possible to the global optima. In this regard, one of the most common phenomena that occurs is the curse of…
We introduce a new heuristic algorithm for the problem of finding minimum size loop cutsets in multiply connected belief networks. We compare this algorithm to that proposed in [Suemmondt and Cooper, 1988]. We provide lower bounds on the…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
Achieving high-quality solutions faster than classical solvers on computationally hard problems is a challenge for quantum optimization to deliver utility. Using a superconducting quantum computer, we experimentally investigate the…
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…
Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative…
The study of large Condorcet domains (CD) has been a significant area of interest in voting theory. In this paper, our goal is to search for large CDs that are hitherto unknown. With a straightforward combinatorial definition, searching for…
Ising machines -- special-purpose hardware for heuristically solving Ising optimization problems -- based on probabilistic bits (p-bits) have been established as a promising alternative to heuristic optimization algorithms run on…
The Maximum Cut (Max-Cut) problem could be naturally expressed either in a Quadratic Unconstrained Binary Optimization (QUBO) formulation, or as an Ising model. It has long been known that the Maximum Independent Set (MIS) problem could…
Optimizing over separable quantum objects is challenging for two key reasons: determining separability is NP-hard, and the dimensionality of the problem grows exponentially with the number of qubits. We address both challenges by…
Ising solvers offer a promising physics-based approach to tackle the challenging class of combinatorial optimization problems. However, typical solvers operate in a quadratic energy space, having only pair-wise coupling elements which…
The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced…
Decades of exponential scaling in high performance computing (HPC) efficiency is coming to an end. Transistor based logic in complementary metal-oxide semiconductor (CMOS) technology is approaching physical limits beyond which further…
By Emerging huge databases and the need to efficient learning algorithms on these datasets, new problems have appeared and some methods have been proposed to solve these problems by selecting efficient features. Feature selection is a…
For over two decades, the G-set benchmark has remained a cornerstone challenge for combinatorial optimization solvers. Remarkably, it continues to yield new best-known solutions even to the present day. Here, we report a new best-known…
We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut…