Parameterized Complexity of Caching in Networks

TL;DR

This paper conducts a detailed parameterized complexity analysis of the network caching problem, identifying conditions that determine when the problem is computationally tractable, thus advancing theoretical understanding beyond its known NP-hardness.

Contribution

It provides the first comprehensive parameterized complexity analysis of network caching, establishing bounds that delineate tractable and intractable cases.

Findings

Identifies parameter regimes where caching is tractable.

Establishes algorithmic lower bounds for caching complexity.

Provides upper bounds indicating efficient algorithms in certain cases.

Abstract

The fundamental caching problem in networks asks to find an allocation of contents to a network of caches with the aim of maximizing the cache hit rate. Despite the problem's importance to a variety of research areas -- including not only content delivery, but also edge intelligence and inference -- and the extensive body of work on empirical aspects of caching, very little is known about the exact boundaries of tractability for the problem beyond its general NP-hardness. We close this gap by performing a comprehensive complexity-theoretic analysis of the problem through the lens of the parameterized complexity paradigm, which is designed to provide more precise statements regarding algorithmic tractability than classical complexity. Our results include algorithmic lower and upper bounds which together establish the conditions under which the caching problem becomes tractable.