arXiv subjects

Marcus Ritt

Publications and source records attributed to Marcus Ritt.

6 recordsLinked to original sources

arXiv2026

A Quantum-Inspired Approach to MaxCut Based on Sparse Walsh/Pauli-Correlation Encoding

We present a quantum-inspired Walsh/PCE solver for MaxCut based on sparse Pauli-correlation encodings. Instead of assigning one qubit or one variable to each graph vertex directly, the method represents relaxed binary variables through expectation values of diagonal Pauli/Walsh observables. These correlators are computed classically from sparse Walsh autocorrelations, producing a compact differentiable relaxation of the MaxCut objective. We evaluate the method on selected Gset instances, G1, G6, G12, and G18, and compare it with random search and tabu search over 10 independent seeds. The proposed model uses $801$ active parameters, corresponding to only $0.306\%$ of the full Walsh space over $18$ qubits. After a final bitflip local search, Walsh/PCE achieves approximation ratios of $0.99033 \pm 0.00226$ on G1, $0.95647 \pm 0.01604$ on G6, $0.96007 \pm 0.00951$ on G12, and $0.92964 \pm 0.02202$ on G18, outperforming both baselines on all tested instances. The method also yields the lowest average runtime in all cases. These results suggest that sparse Walsh/PCE representations provide an efficient quantum-inspired route for MaxCut and may be further extended to hardware-based estimation of Pauli/Walsh correlators.

cs.ET↗

arXiv2026

Wildfire Suppression: Complexity, Models, and Instances

Wildfires cause major losses worldwide, and the frequency of fire-weather conditions is likely to increase in many regions. We study the allocation of suppression resources over time on a graph-based representation of a landscape to slow down fire propagation. Our contributions are theoretical and methodological. First, we prove strong NP-completeness on planar graphs for this problem and two related variants, and on full weighted directed grids for two of the three problems. We also show that this problem remains strongly NP-complete when all resources are released simultaneously. Second, we propose a new mixed-integer programming (MIP) formulation that obtains state-of-the-art results, showing that MIP is a competitive approach contrary to earlier findings. Third, showing that existing benchmarks lack realism and difficulty, we introduce a physics-grounded instance generator based on Rothermel's surface fire spread model. We use these diverse instances to benchmark the literature, identifying the specific conditions where each algorithm succeeds or fails.

cs.CE↗

arXiv2013

Exact and Heuristic Methods for the Assembly Line Worker Assignment and Balancing Problem

In traditional assembly lines, it is reasonable to assume that task execution times are the same for each worker. However, in sheltered work centres for disabled this assumption is not valid: some workers may execute some tasks considerably slower or even be incapable of executing them. Worker heterogeneity leads to a problem called the assembly line worker assignment and balancing problem (ALWABP). For a fixed number of workers the problem is to maximize the production rate of an assembly line by assigning workers to stations and tasks to workers, while satisfying precedence constraints between the tasks. This paper introduces new heuristic and exact methods to solve this problem. We present a new MIP model, propose a novel heuristic algorithm based on beam search, as well as a task-oriented branch-and-bound procedure which uses new reduction rules and lower bounds for solving the problem. Extensive computational tests on a large set of instances show that these methods are effective and improve over existing ones.

cs.AI↗

arXiv2011

Improved integer programming models for simple assembly line balancing and related problems

We propose a stronger formulation of the precedence constraints and the station limits for the simple assembly line balancing problem. The linear relaxation of the improved integer program theoretically dominates all previous formulations using impulse variables, and produces solutions of significantly better quality in practice. The improved formulation can be used to strengthen related problems with similar restrictions. We demonstrate their effectiveness on the U-shaped assembly line balancing problem and on the bin packing problem with precedence constraints.

cs.DM↗

arXiv2010

Motion planning with pull moves

It is well known that Sokoban is PSPACE-complete (Culberson 1998) and several of its variants are NP-hard (Demaine et al. 2003). In this paper we prove the NP-hardness of some variants of Sokoban where the warehouse keeper can only pull boxes.

cs.CC↗

arXiv2010

Simple heuristics for the assembly line worker assignment and balancing problem

We propose simple heuristics for the assembly line worker assignment and balancing problem. This problem typically occurs in assembly lines in sheltered work centers for the disabled. Different from the classical simple assembly line balancing problem, the task execution times vary according to the assigned worker. We develop a constructive heuristic framework based on task and worker priority rules defining the order in which the tasks and workers should be assigned to the workstations. We present a number of such rules and compare their performance across three possible uses: as a stand-alone method, as an initial solution generator for meta-heuristics, and as a decoder for a hybrid genetic algorithm. Our results show that the heuristics are fast, they obtain good results as a stand-alone method and are efficient when used as a initial solution generator or as a solution decoder within more elaborate approaches.

cs.DS↗