Related papers: A PTAS for the Classical Ising Spin Glass Problem …
In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency oscillating transverse…
We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…
Pruhs and Woeginger prove the existence of FPTAS's for a general class of minimization and maximization subset selection problems. Without losing generality from the original framework, we prove how better asymptotic worst-case running…
We discuss generation of series expansions for Ising spin-glasses with a symmetric $\pm J$ (i.e. bimodal) distribution on d-dimensional hypercubic lattices using linked-cluster methods. Simplifications for the bimodal distribution allow us…
The Minimum Linear Arrangement problem (MLA) consists of finding a mapping $\pi$ from vertices of a graph to distinct integers that minimizes $\sum_{\{u,v\}\in E}|\pi(u) - \pi(v)|$. In that setting, vertices are often assumed to lie on a…
We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut…
This paper develops approximate message passing algorithms to optimize multi-species spherical spin glasses. We first show how to efficiently achieve the algorithmic threshold energy identified in our companion work, thus confirming that…
We show that there is no subexponential time algorithm for computing the exact solution of the maximum independent set problem in d-regular graphs unless ETH fails. We expand our method to show that it helps to provide lower bounds for…
The embedding is an essential step when calculating on the D-Wave machine. In this work we show the hardness of the embedding problem for both types of existing hardware, represented by the Chimera and the Pegasus graphs, containing…
We study theoretical runtime guarantees for a class of optimization problems that occur in a wide variety of inference problems. these problems are motivated by the lasso framework and have applications in machine learning and computer…
In this paper we study a scheduling problem arising from executing numerical simulations on HPC architectures. With a constant number of parallel machines, the objective is to minimize the makespan under memory constraints for the machines.…
Finding a shortest path in a graph is one of the most classic problems in algorithmic and graph theory. While we dispose of quite efficient algorithms for this ordinary problem (like the Dijkstra or Bellman-Ford algorithms), some slight…
We consider the Minimum Steiner Cut problem on undirected planar graphs with non-negative edge weights. This problem involves finding the minimum cut of the graph that separates a specified subset $X$ of vertices (terminals) into two parts.…
We consider extension variants of the classical graph problems Vertex Cover and Independent Set. Given a graph $G=(V,E)$ and a vertex set $U \subseteq V$, it is asked if there exists a minimal vertex cover (resp.\ maximal independent set)…
We present an $(1+\varepsilon)$-approximation algorithm with quasi-polynomial running time for computing the maximum weight independent set of polygons out of a given set of polygons in the plane (specifically, the running time is $n^{O(…
In their seminal work, Mustafa and Ray (2009) showed that a wide class of geometric set cover (SC) problems admit a PTAS via local search -- this is one of the most general approaches known for such problems. Their result applies if a…
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…
We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a…
In this paper, we propose a general framework to design {efficient} polynomial time approximation schemes (EPTAS) for fundamental stochastic combinatorial optimization problems. Given an error parameter $\epsilon>0$, such algorithmic…
For a metric graph $G=(V,E)$ and $R\subset V$, the internal Steiner minimum tree problem asks for a minimum weight Steiner tree spanning $R$ such that every vertex in $R$ is not a leaf. This note shows a simple polynomial-time…