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

2026-04-09

AI Summary

This study addresses the throughput bottleneck in payment channel networks (PCNs) caused by imbalanced channel balances by investigating the online transaction admission problem with the goal of maximizing the number of accepted transactions on a single channel. The problem is modeled as an online knapsack problem with both positive and negative items, for which the authors propose the first deterministic online algorithm achieving a competitive ratio of $O(\log B)$, where $B$ denotes the channel capacity. They further establish a matching lower bound of $\Omega(\log B)$, demonstrating that their algorithm is optimal among both deterministic and randomized algorithms. By integrating techniques from online algorithms, competitive analysis, and PCN resource scheduling, this work offers both theoretical novelty and practical relevance.

Abstract

Payment channel networks (PCNs) are a promising solution to make cryptocurrency transactions faster and more scalable. At their core, PCNs bypass the blockchain by routing the transactions through intermediary channels. However, a channel can forward a transaction only if it possesses the necessary funds: the problem of keeping the channels balanced is a current bottleneck on the PCN's transaction throughput. This paper considers the problem of maximizing the number of accepted transactions 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 (initially allocated funds). We complement this result with an asymptotically matching lower bound of $Ω(\log B)$ which holds for any randomized algorithm, demonstrating our algorithm's optimality.

Problem

• Payment Channel Networks
• Online Knapsack
• Competitive Analysis
• Transaction Admission
• Cryptocurrency

Innovation

• online knapsack
• competitive algorithm
• payment channel networks
• transaction admission
• negative items