Max-Heaps For Batching Optimization

Blockchain networks require an efficient way to manage and prioritize transactions. Miners need to select transactions that maximize their rewards, typically prioritizing those with the highest fee-to-size ratio. To streamline this process, we implement a Max-Heap-based transaction pool that dynamically manages and selects high-priority transactions.

Why Use a Max-Heap?

A Max-Heap is a binary tree-based data structure where the highest-priority element is always at the root. This makes it potentially ideal for selecting the most valuable transaction efficiently.

Key Advantages:

• Efficient Prioritization: Transactions with the highest fee-to-size ratio are processed first.

• Fast Extraction: The highest-priority transaction can be retrieved in O(1) time.

• Dynamic Ordering: When a new transaction arrives, it is placed appropriately in the heap with an O(log n) operation.

Implementation

Let's break down the core components of our transaction pool.

Transaction Class

In our design, each transaction has three main attributes: fee, size, and priority. The priority which is calculated as fee / size to ensure miners prioritize transactions that yield the highest reward per byte.

class Transaction:

    def_init__(self, fee, size):

        self.fee = fee  # Transaction fee

        self.size = size  # Transaction size in bytes

        self.priority = self.fee / self.size  # Priority score
    
    def __repr__(self):

        return f"Transaction(priority={self.priority:.3f}, fee={self.fee}, size={self.size})"

This assumption of calculating priority holds a solid foundation of our design.

Max-Heap Transaction Pool

We construct a simple implementation of Max-Heap class that efficiently maintains transaction order using heap operations.

class MaxHeap:

    def __init__(self):

        self.heap = []  # Array to store transactions

        self.current_size = 0  # Number of transactions

    def _heapify_up(self, i):

        parent = (i - 1) // 2

        if i > 0 and self.heap[i][0] > self.heap[parent][0]:

            self.heap[i], self.heap[parent] = self.heap[parent], self.heap[i]
            self._heapify_up(parent)

    def _heapify_down(self, i):

        left_child, right_child = 2*i + 1, 2*i + 2
        largest = i
        
        if left_child < len(self.heap) and self.heap[left_child][0] > self.heap[largest][0]:

            largest = left_child

        if right_child < len(self.heap) and self.heap[right_child][0] > self.heap[largest][0]:

            largest = right_child

        if largest != i:

            self.heap[i], self.heap[largest] = self.heap[largest], self.heap[i]

            self._heapify_down(largest)

    def insert(self, transaction):

        self.heap.append((transaction.priority, transaction.fee, transaction.size))

        self._heapify_up(len(self.heap) - 1)
        self.current_size += 1

    def extract_next_transaction(self):
        if not self.heap:
            return None

        if len(self.heap) == 1:
            self.current_size -= 1
            return self.heap.pop()
        
        max_transaction = self.heap[0]

        self.heap[0] = self.heap[-1]
        self.heap.pop()

        self.current_size -= 1

        self._heapify_down(0)

        return max_transaction

This heap operations are key concepts to maximizing priority in our design.

Simulating Transaction Arrivals

To effectively test our design to an adequate level, we simulate incoming transactions using a Poisson distribution, essentially mimicking real-world traffic.

import numpy as np

def broadcast(arrival_rate, total_duration):

    transactions = []

    for t in range(total_duration):

        num = np.random.poisson(arrival_rate)

        for _ in range(num):

            fee = np.random.randint(10, 100)

            size = np.random.randint(100, 1000)

            transactions.append(Transaction(fee, size))

    return transactions

Parallel Transaction Insertion

To optimize performance, transactions are inserted using multithreading with a locking mechanism to prevent drawbacks such as race conditions.

from concurrent.futures import ThreadPoolExecutor\

from threading import Lock

def parallel_execution(transaction_pool, transactions):

    lock = Lock()

    def safe_insert(transaction):

        with lock:

            transaction_pool.insert(transaction)

    with ThreadPoolExecutor() as executor:

        executor.map(safe_insert, transactions)

Pruning Low-Priority Transactions

To keep the transaction pool efficient, we periodically remove transactions below a priority threshold.

def prune_transactions(transaction_pool, threshold):

    transaction_pool.heap = [txn for txn in transaction_pool.heap if txn[0] >= threshold]

    for i in range(len(transaction_pool.heap)):\

        transaction_pool._heapify_down(i)

Running the Simulation

Finally, we tie everything together by running a test scenario.

arrival_rate = 10

duration = int(input("Enter simulation duration: "))
thresh = 0.1

transactions = broadcast(arrival_rate, duration)

transaction_pool = MaxHeap()

prune_transactions(transaction_pool, thresh)

parallel_execution(transaction_pool, transactions)

print(f"Total Transactions Inserted: {len(transaction_pool.heap)}")

latest_transaction = transaction_pool.extract_next_transaction()
print("Max Transaction Extracted:", latest_transaction)

Conclusion

Using a Max-Heap for transaction selection provides an efficient and scalable solution for blockchain transaction pools. This method ensures that the highest-value transactions are processed first while allowing concurrent execution. Further enhancements to this include dynamic pruning thresholds based on network congestion and adaptive transaction prioritization to maximize efficiency.