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Algorithms

36 items

RESEARCHarXiv CS.LG·4/30/2026

A Randomized PDE Energy driven Iterative Framework for Efficient and Stable PDE Solutions

This work introduces a PDE energy-driven iterative framework for solving partial differential equations efficiently and stably, without relying on traditional matrix-based discretizations or costly data-driven neural network training. It evolves random initial fields through physically constrained diffusion iterations and Gaussian smoothing, strictly enforcing boundary conditions, and demonstrates stable convergence on Poisson, Heat, and viscous Burgers equations.

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RESEARCHarXiv CS.AI·5/6/2026

Computing Thiele Rules on Interval Elections and their Generalizations

The paper addresses the computational complexity of Thiele rules in approval-based committee voting, a topic of significant interest in social choice theory. It resolves an open question regarding the voter interval domain, showing that an existing linear program approach still yields optimal solutions despite the matrix not being totally unimodular.

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RESEARCHarXiv CS.AI·4/22/2026

On Solving the Multiple Variable Gapped Longest Common Subsequence Problem

This paper tackles the Variable Gapped Longest Common Subsequence (VGLCS) problem, a generalization of LCS with flexible gap constraints, relevant to molecular sequence comparison and time-series analysis. It proposes a root-based state graph search framework combined with an iterative beam search strategy to manage combinatorial explosion and find high-quality solutions.

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