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This overview explains how a frozen router,

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budgeted restart, and prefix conversion address costly exact computations.

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Protecting a catastrophic tail can help even when the
route still loses overall to the best fixed representation.

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Imagine a job with a three-unit prefix and five-unit suffix.

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A routing budget expires after the prefix.

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Some partial state exists, but the complete output has not been delivered.

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The next strategy determines whether that partial work can be used.

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A full restart discards the useful partial state and runs the whole job again.

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The total is the spent prefix plus the repeated prefix and suffix, giving eleven units.

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The initial work must remain in the complete-request ledger.

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If conversion costs two and preserves enough state to continue at the suffix,

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the total is ten.

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That is better than this restart schedule.

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It does not establish that conversion beats every strategy available from the beginning.

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It does not establish that conversion beats every strategy available from the beginning.

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C9 freezes a static decision tree.

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C10 starts one exact representation and restarts after a product budget.

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C11 converts the already-built prefix into a packed
representation so that prefix need not be recomputed.

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Use a conceptual work trace with prefix P and remaining work Q.

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Restart pays for P in the first representation
and then repeats it in the fallback.

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Conversion pays for P once, a conversion step, and Q.

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These accounting expressions describe
the routes, not measured elapsed times.

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A conversion may still cost more than
choosing the best fixed arm at the start.

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The retained C9-C11 routes preserved exact outputs
yet lost to the best fixed arm on their declared splits.

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C10's protection of a catastrophic tail is still a useful scoped result.

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It does not turn a losing median
or aggregate into a successful default policy.

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With conversion costing four, the converted route totals twelve and is

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worse than the eleven-unit restart.

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The benefit depends on the actual conversion cost and on how much

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completed work it preserves.

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A fixed strategy that simply completes the original job costs eight in this example.

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It beats both the cheaper conversion schedule and the restart.

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Improving one adaptive route relative to another does not prove that

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adaptation itself is profitable.

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These numbers explain accounting choices rather than recreating historical timings.

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The retained routing results must still be read under their exact job definitions, fixed

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controls, and aggregate and tail criteria.

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Separate tail protection from aggregate profitability.

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Separate tail protection from aggregate profitability.

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Charge restart or conversion work and
compare against the best fixed exact arm.