Combination Networks with End-user-caches: Novel Achievable and Converse\n Bounds under Uncoded Cache Placement
Bibliographic record
Abstract
Caching is an efficient way to reduce network traffic congestion during peak\nhours by storing some content at the users' local caches. For the shared-link\nnetwork with end-user-caches, Maddah-Ali and Niesen proposed a two-phase coded\ncaching strategy. In practice, users may communicate with the server through\nintermediate relays. This paper studies the tradeoff between the memory size\n$M$ and the network load $R$ for networks where a server with $N$ files is\nconnected to $H$ relays (without caches), which in turn are connected to $K$\nusers equipped with caches of $M$ files. When each user is connected to a\ndifferent subset of $r$ relays, i.e., $K = \\binom{H}{r}$, the system is\nreferred to as a {\\it combination network with end-user-caches}.\n In this work, converse bounds are derived for the practically motivated case\nof {\\it uncoded} cache contents, that is, bits of the various files are\ndirectly pushed into the user caches without any coding. In this case, once the\ncache contents and the user demands are known, the problem reduces to a general\nindex coding problem.This paper shows that relying on a well-known "acyclic\nindex coding converse bound" results in converse bounds that are not tight for\ncombination networks with end-user-caches. A novel converse bound that\nleverages the network topology is proposed, which is the tightest converse\nbound known to date. As a result of independent interest, an inequality that\ngeneralizes the well-known sub-modularity of entropy is derived. Several novel\ncaching schemes are proposed, based on the Maddah-Ali and Niesen cache\nplacement. The proposed schemes are proved: (i) to be (order) optimal for some\n$(N,M,H,r)$ parameters regimes under the constraint of uncoded cache placement,\nand (ii) to outperform the state-of-the-art schemes in numerical evaluations.\n
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.027 |
| Meta-epidemiology (narrow) | 0.004 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.006 | 0.009 |
| Open science | 0.004 | 0.008 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".