On the complexity of optimal routing and content caching in heterogeneous networks

Abstract

We investigate the problem of optimal request routing and content caching in a heterogeneous network supporting in-network content caching with the goal of minimizing average content access delay. Here, content can either be accessed directly from a back-end server (where content resides permanently) or be obtained from one of multiple in-network caches. To access a piece of content, a user must decide whether to route its request to a cache or to the back-end server. Additionally, caches must decide which content to cache. We investigate the problem complexity of two problem formulations, where the direct path to the back-end server is modeled as i) a congestionsensitive or ii) a congestion-insensitive path, reflecting whether or not the delay of the uncached path to the back-end server depends on the user request load, respectively. We show that the problem is NP-complete in both cases. We prove that under the congestion-insensitive model the problem can be solved optimally in polynomial time if each piece of content is requested by only one user, or when there are at most two caches in the network. We also identify a structural property of the user-cache graph that potentially makes the problem NP-complete. For the congestionsensitive model, we prove that the problem remains NP-complete even if there is only one cache in the network and each content is requested by only one user. We show that approximate solutions can be found for both models within a (1 − 1/e) factor of the optimal solution, and demonstrate a greedy algorithm that is found to be within 1% of optimal for small problem sizes. Through trace-driven simulations we evaluate the performance of our greedy algorithms, which show up to a 50% reduction in average delay over solutions based on LRU content caching.

Distributed Algorithms for Content Caching in Mobile Backhaul Networks

“…It is important to note that DFG differs from the distributed global greedy (DGG) algorithm used in [5], [11]. DGG chooses in every iteration the fictitious item (i, o) that maximizes the cost saving, and thus has computational complexity O(|N | 2 max i K i |O| log(|N ||O|)).…”

“…The authors in [5] give insights in the structure of the optimal placement in a regular two level hierarchical network, and they develop a greedy distributed 2-approximation algorithm. The authors in [11] consider a hybrid network with in-network caching and they propose a (1 − 1/e)-approximation greedy algorithm. A more generic cost model was considered in [7], where the authors develop a 10-approximation algorithm by rounding the optimal solution of the LP-relaxation of the problem.…”

“…[17] proposed a set of centralized, polynomial time algorithms with approximation guarantees, for the joint problem of request routing and content replication under strict bandwidth constraints at the storage sites. In contrast to [16], [5], [11], [7], [17], in our work we developed two distributed algorithms for computing a content placement based on limited information on the content demands and on the network topology, that can be used to solve large problem instances with prohibitive space complexity.…”

Exploiting Caching and Multicast for 5G Wireless Networks

“…For a given anticipated content demand, the caching problem asks for determining in which caches to store each content file. This becomes more challenging in HCNs where users are covered by multiple base stations and hence content can be delivered to requesters through multiple network paths [17]- [20]. Also, the caching problem differs when multicast is employed to serve concurrent requests for the same content file.…”

“…Since the SBS backhaul links are usually of low-capacity, e.g., often facilitated by the consumers' home networks such as Digital Subscriber Line (DSL) [24], they cannot be used to download content on demand to serve users. Instead, they are only used to periodically refresh the content stored in the caches [17]- [20]. In contrast, the backhaul link of the MBS is of sufficient capacity to download the content requested by users.…”