I think you can try to use some Python’s libraries dedicated to scientific computing or datascience such as numpy or pandas and use HDF5 files to store/retrieve your data using h5py.

For example, your first lines could be replaced by:

import numpy as np
edge = np.asarray(edge) # edge as numpy array of shape (n, 10)
pair_max = edge.max(axis=0)
pair_min = edge.min(axis=0)
pair = np.stack([pair_min, pair_max], axis=-1)

You can use np.isin to check if an element is in another array.

As a rule of thumb, try to avoid for loops and string conversion (and intermediary I/O operations if not needed), and replace them with vectorized operations.

Otherwise I’m afraid that you’ll have to switch to more performant langages such as C/C++, etc.

I benchmarked using golang

package main

import (
  "fmt"
  "strings"
  "sync"
  "time"
 )

 const numWorkers = 12 // Number of goroutines (workers) to run

 func main() {
  // Define the number of records (2 billion)
  // numRecords := 2_000_000_000
  numRecords := 100_000_000

  // Start benchmark
  simulateAndBenchmark(numRecords)
 }

 // Worker function to process a batch of records
 func worker(id int, jobs <-chan int, wg *sync.WaitGroup, targetPair, replacement string) {
  defer wg.Done()

  for job := range jobs {
    // Simulate a record with the target pair
    record := fmt.Sprintf("Record %d: %s some other data", job, targetPair)

    // Check if the record contains the target pair
    if strings.Contains(record, targetPair) {
        // Replace the target pair with underscores
        record = strings.ReplaceAll(record, targetPair, replacement)
    }

    // For demonstration purposes, we won't print the record, but you could process it here
    // fmt.Printf("Worker %d processed record %dn", id, job)
    }
  }

func simulateAndBenchmark(numRecords int) {
  // Start timer
  start := time.Now()

  // Target string to replace
  targetPair := "(1, 2)"
  replacement := strings.Repeat("_", len(targetPair))

  // Channel to distribute jobs
  jobs := make(chan int, numWorkers)

  // WaitGroup to synchronize all workers
  var wg sync.WaitGroup

  // Start the worker pool
  for i := 1; i <= numWorkers; i++ {
    wg.Add(1)
    go worker(i, jobs, &wg, targetPair, replacement)
  }

  // Send jobs (records) to workers
  for i := 0; i < numRecords; i++ {
    jobs <- i
  }

  // Close the jobs channel to signal no more work
  close(jobs)

  // Wait for all workers to finish
  wg.Wait()

  // Record the time taken
  elapsed := time.Since(start)
  fmt.Printf("Processed %d records in %s using %d workersn", numRecords, elapsed, numWorkers)
}

On average the process takes about 34 minutes on a 16GB 3200 MT/s RAM with
CPU

11th Gen Intel(R) Core(TM) i5-1135G7 @ 2.40GHz

Base speed: 2.42 GHz
Sockets:    1
Cores:  4
Logical processors: 8
Virtualisation: Enabled
L1 cache:   320 KB
L2 cache:   5.0 MB
L3 cache:   8.0 MB

Utilisation 11%
Speed   2.32 GHz
Up time 0:22:05:24
Processes   359
Threads 4952
Handles 291775

For the results are as follows for different workers and different ranges

 Processed 1000000 records in 724.045ms using 8 workers 
 Processed 1000000 records in 446.1339ms using 12 workers   
 Processed 10000000 records in 4.6425266s using 12 workers 
 Processed 100000000 records in 52.8540714s using 12 workers
 Processed 2000000000 records in 32m42.0265975s using 8 workers 

But it would be even faster in C++ since it offers direct memory access.
I would perfer you using a better GPU and memory to make things even faster. The tests above are from a mere laptop with a basic GPU.