Adaptive Caching Algorithms with Optimality Guarantees for NDN Networks Stratis Ioannidis and Edmund Yeh
A Caching Network Nodes in the network store content items (e.g., files, file chunks) 1 Adaptive Caching Networks w. Optimality Guarantees
A Caching Network ? Nodes generate requests for content items 2 Adaptive Caching Networks w. Optimality Guarantees
A Caching Network ? Requests are routed towards a content source 3 Adaptive Caching Networks w. Optimality Guarantees
A Caching Network Responses routed over reverse path 4 Adaptive Caching Networks w. Optimality Guarantees
A Caching Network ? Nodes have caches with finite capacities 5 Adaptive Caching Networks w. Optimality Guarantees
A Caching Network ? Nodes have caches with finite capacities 6 Adaptive Caching Networks w. Optimality Guarantees
A Caching Network ? Requests terminate early upon a cache hit 7 Adaptive Caching Networks w. Optimality Guarantees
Example: Named Data Networks Webserver ? cache-enabled routers User 8 Adaptive Caching Networks w. Optimality Guarantees
Optimal Content Allocation Q : How should items be allocated to caches so that routing costs are minimized ? 9 Adaptive Caching Networks w. Optimality Guarantees
Optimal Content Allocation Challenge: Caching algorithm should be adaptive , and distributed. 10 Adaptive Caching Networks w. Optimality Guarantees
[Cohen and Shenker 2002] A Simple Algorithm: Path-Replication [Jacobson et al. 2009] ? Distributed Adaptive Popular! Cache item on every node in the reverse path Evict using a simple policy, e.g., LRU, LFU, FIFO etc. 11 Adaptive Caching Networks w. Optimality Guarantees
But… Path Replication combined with traditional eviction policies (LRU, LFU, FIFO, etc.) is arbitrarily suboptimal. 12 Adaptive Caching Networks w. Optimality Guarantees
Path Replication + LRU is Arbitrarily Suboptimal Cost when caching : Cost of PR+LRU: When M is large, PR+LRU is arbitrarily suboptimal! True for any strategy (LRU,LFU,FIFO,RR) requests per sec that ignores upstream costs ? ? 13 Adaptive Caching Networks w. Optimality Guarantees
Our Contributions Formal statement of offline problem NP-Hard [Shanmugam et al. IT 2013] Path Replication +LRU, LFU, FIFO, etc. is arbitrarily suboptimal Distributed , adaptive algorithm, within a constant approximation from optimal offline allocation Path Replication+novel eviction policy Great performance under 20+ network topologies 14 Adaptive Caching Networks w. Optimality Guarantees
Overview Problem Formulation Distributed Adaptive Algorithms Evaluation 15 Adaptive Caching Networks w. Optimality Guarantees
Overview Problem Formulation Distributed Adaptive Algorithms Evaluation 16 Adaptive Caching Networks w. Optimality Guarantees
Model: Network Network represented as a directed , bi-directional graph 17 Adaptive Caching Networks w. Optimality Guarantees
Model: Edge Costs Edge costs: 5 Each edge has a cost/weight 18 Adaptive Caching Networks w. Optimality Guarantees
Model: Node Caches Edge costs: Node capacities: Node has a cache with capacity 19 Adaptive Caching Networks w. Optimality Guarantees
Model: Cache Contents Edge costs: Node capacities: Items stored and requested form the item catalog 20 Adaptive Caching Networks w. Optimality Guarantees
Model: Cache Contents Edge costs: Node capacities: For and , let if stores o.w. Then, for all , 21 Adaptive Caching Networks w. Optimality Guarantees
Model: Designated Sources Edge costs: Node capacities: , for all For each and , there exists a set of nodes (the designated sources of ) that permanently store . I.e., if then 22 Adaptive Caching Networks w. Optimality Guarantees
Model: Demand Edge costs: Node capacities: , for all ? Requests are always satisfied! A request is a pair such that: is an item in is a simple path in such that . 23 Adaptive Caching Networks w. Optimality Guarantees
Model: Demand Edge costs: Node capacities: , for all : demand Request rates: ? Demand : set of all requests Request arrival process is Poisson with rate 24 Adaptive Caching Networks w. Optimality Guarantees
Model: Routing Costs & Caching Gain Edge costs: Node capacities: , for all : demand 6 Request rates: 3 4 5 Request ? ? Worst case routing cost: 25 Adaptive Caching Networks w. Optimality Guarantees
Model: Routing Costs & Caching Gain Edge costs: Node capacities: , for all : demand 6 Request rates: 3 4 5 Request ? ? Worst case routing cost: Cost due to intermediate caching: 26 Adaptive Caching Networks w. Optimality Guarantees
Model: Routing Costs & Caching Gain Edge costs: Node capacities: , for all : demand 6 Request rates: 3 4 5 Request ? ? Worst case routing cost: Cost due to intermediate caching: Caching Gain: 27 Adaptive Caching Networks w. Optimality Guarantees
Caching Gain Maximization Edge costs: Node capacities: 6 , for all 3 4 5 : demand Request rates: ? ? Caching Gain: The global allocation strategy is the binary matrix 28 Adaptive Caching Networks w. Optimality Guarantees
Caching Gain Maximization Edge costs: Node capacities: 6 , for all 3 4 5 : demand Request rates: ? ? Caching Gain: Maximize: Subject to: , for all , for all and , for all and 29 Adaptive Caching Networks w. Optimality Guarantees
Offline Problem Maximize: Subject to: , for all , for all and , for all and Shanmugam, Golrezaei, Dimakis, Molisch, and Caire. Femtocaching: Wireless Content Delivery Through Distributed Caching Helpers . IT, 2013 NP-hard Submodula r objective, matroid constraints Greedy algorithm gives ½-approximation ratio 1-1/e ratio can be achieved through pipage rounding method [Ageev and Sviridenko, J. of Comb. Opt., 2004] 30 Adaptive Caching Networks w. Optimality Guarantees
Pipage Rounding [Ageev & Sviridenko 2004] Maximize: Subject to: , for all , for all and , for all and 31 Adaptive Caching Networks w. Optimality Guarantees
Pipage Rounding [Ageev & Sviridenko 2004] Maximize: Subject to: for all Expected CG , for all and Satisfied in , for all and expectation Think: All are independent Bernoulli random variables . 32 Adaptive Caching Networks w. Optimality Guarantees
Pipage Rounding [Ageev & Sviridenko 2004] Maximize: Subject to: for all , for all and , for all and Key idea: There exists a concave function such that 33 Adaptive Caching Networks w. Optimality Guarantees
Pipage Rounding [Ageev & Sviridenko 2004] Maximize: Subject to: for all , for all and , for all and Key idea: There exists a concave function such that Algorithm Sketch : Maximize ; round solution to obtain discrete solution . 34 Adaptive Caching Networks w. Optimality Guarantees
Overview Problem Formulation Distributed Adaptive Algorithms Evaluation 35 Adaptive Caching Networks w. Optimality Guarantees
Projected Gradient Ascent Time is divided into slots 36 Adaptive Caching Networks w. Optimality Guarantees
Projected Gradient Ascent 0.5 0.9 0.6 Each node keeps track of its own marginal distribution 37 Adaptive Caching Networks w. Optimality Guarantees
Projected Gradient Ascent 0.5 0.9 0.6 During a slot, estimates by collecting measurements through passing packets . 38 Adaptive Caching Networks w. Optimality Guarantees
Projected Gradient Ascent 0.5 0.6 0.9 0.7 0.6 0.7 At the conclusion of the -th slot, updates its marginals through: 39 Adaptive Caching Networks w. Optimality Guarantees
Projected Gradient Ascent 0.6 0.7 0.7 After updating , node places random items in its cache, independently of other nodes , so that: , for all 40 Adaptive Caching Networks w. Optimality Guarantees
Gradient Estimation 0.5 0.9 0.6 6 4 3 5 How can estimate in a distributed fashion? 41 Adaptive Caching Networks w. Optimality Guarantees
Gradient Estimation 0.5 0.9 0.6 6 4 3 5 ? When request is generated, create a new control message 42 Adaptive Caching Networks w. Optimality Guarantees
Gradient Estimation 0.5 0.5 0.9 0.9 0.6 0.6 0.6 6 0.2 0.7 4 3 5 ? Forward control message over path until: 43 Adaptive Caching Networks w. Optimality Guarantees
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