K PackCache: Adaptive Cost Caching

• K PackCache is a caching problem that involves bundling multiple correlated data items to minimize overall system costs, including transfer and cache rental fees.
• The adaptive algorithm uses correlation matrix analysis, clique construction, and dynamic pack management to serve batch user requests efficiently.
• Empirical results demonstrate significant cost reductions—up to 63% savings—and competitive performance compared to traditional pairwise caching methods.

The K PackCache problem addresses the efficient caching, bundling, and retrieval of multiple correlated data items in modern content delivery networks, with the explicit objective of minimizing total system cost consisting of transfer and memory rental components. Conceptually, the problem generalizes previous “pairwise packing” caching schemes to support arbitrary-size bundles (packs) of data items, selected and served dynamically based on content correlations and user access patterns. This framework is particularly relevant for cloud and CDN environments, where user requests are often temporally and contextually linked, and where naive caching of individual content items leads to redundancy and elevated operational costs.

1. Problem Formulation and Motivation

The K PackCache problem arises from the recognition that requests in real content distribution systems frequently involve multiple co-accessed items. Existing caching strategies typically serve requests individually or in fixed-size pairs, overlooking opportunities for greater cost savings achievable via larger packs. The paper “Adaptive K-PackCache: Cost-Centric Data Caching in Cloud” (Sarkar et al., 14 Sep 2025) develops the K PackCache problem rigorously from the CDN operator’s perspective, seeking to minimize the total cost $C$:

$C = \sum_{r_i \in R} (C_T^{(r_i)} + C_P^{(r_i)})$

where $C_T^{(r_i)}$ is the transfer cost for serving request $r_i$, and $C_P^{(r_i)}$ is the cache rental cost for storing the packed items. The transfer cost is modeled as a base cost plus a linearly increasing term with the number of packed items, and the caching cost depends on both the amount of data and its storage duration. Overpacking (bundling weakly correlated or unused items) leads to unnecessary cache rental expense, whereas underpacking misses transfer cost savings available when correlated items are jointly served.

The overarching motivation is to minimize redundant data transfers and exploit frequently occurring content correlations to reduce cost and enhance real-world caching efficiency.

2. Algorithmic Framework: Adaptive K-PackCache (AKPC)

The AKPC algorithm provides an online, adaptive approach for solving the K PackCache problem. It continuously analyzes recent request traces to identify strong correlations between items and dynamically forms, splits, and merges “cliques”—variable-size groups whose members are frequently co-accessed.

• Correlation Matrix Analysis: Access logs are used to construct a normalized correlation matrix. Binary thresholding (at a tunable parameter $\theta$) produces an adjacency graph; nodes are items and edges denote strong co-access signals.
• Clique Construction: Disjoint cliques are extracted from the binary correlation graph. These cliques serve as candidate packs; each group may contain up to a user-specified maximum size $\omega$.
• Clique Splitting and Approximate Merging: Oversized cliques are split along weakest co-utilization links, while smaller cliques can be approximately merged if their induced subgraph has density above a threshold $\gamma$, enabling packing even when not all possible edges exist.
• Batch Request Handling: When a request for several items arrives, the algorithm references cached cliques for each requested item and serves the request using the associated clique, ensuring maximal transfer cost savings.
• Cache Maintenance: Expiration times and reference counts for cached packs are updated in real time, ensuring cache space is only devoted to packs with ongoing utility.

The AKPC system operates with background modules for clique generation and foreground modules for real-time request serving and cache maintenance.

3. Cost Model and Tradeoffs

The cost minimization in the K PackCache problem balances two opposing pressures: transfer discounts achievable with larger packs, and cache rental costs incurred for storing unneeded data.

• Transfer Cost ($C_T$): For an unpacked request,

$C_T^{(r_i)} = |D_i|\cdot \lambda$

For a packed request,

$$C_T^{(r_i)} = (1 + (|D_i| - 1)\cdot \alpha)\cdot \lambda$$

where $|D_i|$ is the size of the pack, $\lambda$ is the base transfer cost, and $\alpha$ ($0 < \alpha \leq 1$) is the discount factor for packed transfers.

• Caching Cost ($C_P$):

$C_P^{(r_i)} = |D_i| \cdot \mu \cdot \Delta t$

with $\mu$ as the per-item per-time cache rental cost and $\Delta t$ the caching duration.

Excessive packing (“overpacking”) raises $C_P$ due to increased cache footprint, while conservative (“underpacking”) strategies may fail to exploit available transfer discounts, raising $C_T$. AKPC’s adaptive clique construction aims to resolve this tension by focusing on packs with high empirical co-access and splitting weakly linked groups.

4. Performance Analysis and Guarantees

AKPC’s performance is assessed both theoretically and empirically.

• Competitive Ratio: The formal bound is

$$\text{Competitive Ratio} = \frac{2 + (\omega - 1)\alpha \mathcal{L}S}{1 + (\mathcal{L}S - 1)\alpha}$$

where $\omega$ is the maximal clique size, $\alpha$ is the packing discount factor, and $\mathcal{L}S$ is number of uncached items in the request. This guarantee bounds AKPC’s cost within a constant factor of the optimal offline algorithm.

• Empirical Results: On Netflix and Spotify traces, AKPC reduces total cost by up to 63% and 55% respectively over online baselines (pairwise-only packing or no packing) and achieves performance within 15% and 13% of the offline optimum.

These metrics validate that AKPC successfully exploits higher-order content correlations and dynamic batch arrivals, and that its online decisions approximate offline achievable cost.

5. Comparative Evaluation

A range of competitive baselines are considered:

• No Packing: Each item served individually, yielding maximal cost due to redundant transfers and cache rentals.
• 2-Packing (PackCache, DP_Greedy): Items are bundled in pairs; this captures some savings but fails to exploit higher-order content correlations.
• AKPC (K-packing): Bundles arbitrary-size packs, yielding much greater cost reductions as correlation order increases.

Even simplified versions of AKPC (without clique splitting/merging modules) outperform existing 2-packing baselines. The full algorithm, with adaptive splitting/merging, delivers best measured performance.

6. Scalability and System Implementation

The AKPC system scales effectively:

• Background clique generation modules update packs in subsecond time even for large item sets (e.g., 10K items).
• Foreground modules service batch and concurrent requests in real time (low latency).
• Experiments indicate that system cost grows sublinearly as concurrent user/request volume rises, owing to the focus on high-frequency packs and adaptive cache expiry mechanisms.

AKPC is robust to batch arrivals and multi-request concurrency per edge server, reflecting complex conditions encountered in real CDN deployments.

7. Theoretical and Practical Implications

The K PackCache framework, as implemented by AKPC, generalizes and subsumes previous caching models by enabling cost-effective, dynamic, and scalable packed caching. Its competitive guarantee and significant empirical savings position it as a reference point for future research. The modular clique approach—dynamic formation, splitting, and relaxed merging—offers a stable path for balancing cache footprint, transfer cost discounts, and system adaptability in settings with strong content correlation and unpredictably batched user accesses.

A plausible implication is the general adoption of dynamic K-packing in edge caching and cloud data architectures as the underlying demand patterns become more highly correlated and batch-based.

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This synthesis draws entirely on detailed findings from “Adaptive K-PackCache: Cost-Centric Data Caching in Cloud” (Sarkar et al., 14 Sep 2025) and frames the K PackCache problem as a principal cost-minimization challenge in modern data caching architectures, aligning methodologies, algorithms, performance metrics, and practical deployment dimensions.