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We introduce a generic technique to obtain linear relaxations of semidefinite programs with provable guarantees based on the commutativity of the constraint and the objective matrices. We study conditions under which the optimal value of…
Circuits are fundamental objects in linear programming and oriented matroid theory, representing the elementary difference vectors of a polyhedron between points in its affine space. A recent concept introduced by Ekbatani, Natura, and…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
We introduce a novel variant of cutting production planning problems named Integrated Cutting and Packing Heterogeneous Precast Beams Multiperiod Production Planning (ICP-HPBMPP). We propose an integer linear programming model for the…
We study a colourful generalization of the linear programming feasibility problem, comparing the algorithms introduced by Barany and Onn with new methods. We perform benchmarking on generic and ill-conditioned problems, as well as as…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
A linear programming (LP) based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses,…
Large language models are increasingly deployed in settings where reliability matters, yet output-level uncertainty signals such as token probabilities, entropy, and self-consistency can become brittle under calibration--deployment…
We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programming relaxation of the problem has no fractional solutions, then the cavity or belief propagation…
In many practical applications the underlying graph must be as equitable colored as possible. A coloring is called equitable if the number of vertices colored with each color differs by at most one, and the least number of colors for which…
This paper investigates various approaches using Large Language Models (LLMs) to identify gaps and misconceptions in students' self-explanations of specific instructional material, in our case explanations of code examples. This research is…
The integration of large language models (LLMs) into automated algorithm design has shown promising potential. A prevalent approach embeds LLMs within search routines to iteratively generate and refine candidate algorithms. However, most…
Although large language models (LLMs) have transformed AI, they still make mistakes and can explore unproductive reasoning paths. Self-correction capability is essential for deploying LLMs in safety-critical applications. We uncover a…
Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the…
To gain a comprehensive view of what the LHC tells us about physics beyond the Standard Model (BSM), it is crucial that different BSM-sensitive analyses can be combined. But in general, search analyses are not statistically orthogonal, so…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
In the 1970's, Lov\'asz built a bridge between graphs and alternating matrix spaces, in the context of perfect matchings (FCT 1979). A similar connection between bipartite graphs and matrix spaces plays a key role in the recent resolutions…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Linear Complementarity Problems (LCPs) with sufficient matrices form an important subclass of LCPs, and it remains a significant open question whether problems in this class can be solved in polynomial time. Kojima, Megiddo, Noma, and…
The Quadratic Assignment Problem (QAP) is an important discrete optimization instance that encompasses many well-known combinatorial optimization problems, and has applications in a wide range of areas such as logistics and computer vision.…