How to find all editions from a master edition NFT in Solana

Question

I'm trying to get all the editions that come from a master edition NFT. According to the docs there is a PDA that links the edition back to the master edition but I can't find this relationship programatically with the Metaplex/Solana sdk.

My current solution is to parse all the transactions of the master edition and filter through looking for editions created:

import {JsonMetadata, Metadata, Metaplex, TaskStatus} from "@metaplex-foundation/js";
import {Connection, PublicKey, ConfirmedSignatureInfo} from "@solana/web3.js";
import * as fs from "fs";

const RPC_URL = 'https://...';
const MASTER_EDITION_ADDRESS = '';

(async () => {
    const connection = new Connection(RPC_URL);
    const metaplex = new Metaplex(connection);

    const start = new Date().toISOString()

    // Paginate transactions from Master Edition

    const signatures: { signature: string; }[] = []
    let before: string | undefined = undefined;
    while (true) {
        const sigs: ConfirmedSignatureInfo[] = await metaplex.connection.getSignaturesForAddress(
            new PublicKey(MASTER_EDITION_ADDRESS),
            {
                before: before
            },
            'finalized'
        )
        if (!sigs.length) break
        signatures.push(...sigs)
        before = sigs[sigs.length - 1].signature
    }

    // Parse Transactions and find new edition mints

    const hashlist: string[] = []
    for (let i = 0; i < signatures.length; i++) {
        console.log(`${i}/${signatures.length}`);
        await metaplex.connection.getParsedTransaction(signatures[i].signature).then(tx => {
            if (!tx) return

            if (JSON.stringify(tx).toLowerCase().includes('error')) return

            if (JSON.stringify(tx).includes('Mint New Edition from Master Edition')) {
                console.log(JSON.stringify(tx, null, 4))
                hashlist.push(tx.transaction.message.accountKeys[1].pubkey.toString());
            }
        });
    }

    console.log('found:', hashlist.length, 'items')
})()

However this becomes exponentially slow once the transactions are at a certain size. Is there a fast and reliable way to do this.

Assumptions:

1. The first creator is not unique to this collection as its not a Candy Machine
2. The update authority is not unique as it could be used by other collections too