Advances in Computational Complexity and Algorithm Design

The field of computational complexity and algorithm design is witnessing significant developments, driven by innovative approaches to understanding the intricacies of complex systems and the pursuit of efficient solutions. Researchers are making strides in resolving long-standing open problems, such as the complexity dichotomy of Holant problems and the sorting of sumsets, by leveraging geometric perspectives, sparse incomparability lemmas, and novel algorithmic techniques. Furthermore, there is a growing interest in axiomatizing intelligence and designing objective-driven dynamical stochastic fields, which has the potential to revolutionize our understanding of intelligent systems and their applications. Noteworthy papers include: the Holant* Dichotomy on Domain Size 3, which provides an explicit tractability criterion for Holant problems on domain size 3. The paper on An Explicit and Efficient O(n^2)-Time Algorithm for Sorting Sumsets presents the first explicit comparison-based algorithm for sorting sumsets in optimal O(n^2) time and comparisons.

Sources

Dichotomy for orderings?

Holant* Dichotomy on Domain Size 3: A Geometric Perspective

Toward the Axiomatization of Intelligence: Structure, Time, and Existence

A Framework for Objective-Driven Dynamical Stochastic Fields

An Explicit and Efficient $O(n^2)$-Time Algorithm for Sorting Sumsets

Sorting as Gradient Flow on the Permutohedron

Drainability and Fillability of Polyominoes in Diverse Models of Global Control

Breaking the Sorting Barrier for Directed Single-Source Shortest Paths

Simple Universally Optimal Dijkstra

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