Competitive Transaction Admission in PCNs: Online Knapsack with Positive and Negative Items

TL;DR

This paper introduces an optimal online algorithm for maximizing transaction acceptance in payment channel networks by modeling it as a new online knapsack problem with positive and negative items.

Contribution

It presents a deterministic online algorithm with proven $O(\log B)$-competitiveness for the online knapsack variant in PCNs, matching the lower bound and improving throughput.

Findings

The algorithm is $O(\log B)$-competitive.

Lower bound of $\Omega(\log B)$ for any randomized algorithm.

The model handles arbitrary, sequential transactions in PCNs.

Abstract

Payment channel networks (PCNs) are a promising approach to making cryptocurrency transactions faster and more scalable. At their core, PCNs bypass the blockchain by routing transactions through intermediary channels. However, a channel can forward a transaction only if it has the necessary funds: the problem of keeping the channels balanced is a current bottleneck for the PCN's transaction throughput. This paper considers the problem of maximizing the number of transactions accepted by a channel in a PCN. Previous works either considered the associated optimization problem with all transactions known in advance or developed heuristics tested on particular transaction datasets. This work, however, considers the problem in its purely online form where the transactions are arbitrary and revealed one after the other. We show that the problem can be modeled as a new online knapsack variant where the items (transaction proposals) can be either positive or negative depending on the direction of the transaction. The main contribution of this paper is a deterministic online algorithm that is $O(\log B)$-competitive, where $B$ is the knapsack capacity (maximum allowed channel balance). We complement this result with an asymptotically matching lower bound of $\Omega(\log B)$ which holds for any randomized algorithm, demonstrating our algorithm's optimality.