[Paper Review] Online Algorithms for Matching Platforms with Multi-Channel Traffic

Vahideh Manshadi, Scott Rodilitz+2 more|arXiv (Cornell University)|Mar 28, 2022

Optimization and Search Problems4 citations

TL;DR

This paper proposes the Adaptive Capacity (AC) algorithm for online matching platforms handling multi-channel traffic, where external traffic bypasses recommendation systems. By differentiating between internal and external matches and dynamically adjusting capacity allocation, AC achieves a competitive ratio that increases with external traffic—providing a provably optimal performance bound close to theoretical limits in real-world settings like VolunteerMatch.

ABSTRACT

Two-sided platforms rely on their recommendation algorithms to help visitors successfully find a match. However, on platforms such as VolunteerMatch (VM) -- which has facilitated millions of connections between volunteers and nonprofits -- a sizable fraction of website traffic arrives directly to a nonprofit's volunteering page via an external link, thus bypassing the platform's recommendation algorithm. We study how such platforms should account for this external traffic in the design of their recommendation algorithms, given the goal of maximizing successful matches. We model the platform's problem as a special case of online matching, where (using VM terminology) volunteers arrive sequentially and probabilistically match with one opportunity, each of which has finite need for volunteers. In our framework, external traffic is interested only in their targeted opportunity; by contrast, internal traffic may be interested in many opportunities, and the platform's online algorithm selects which opportunity to recommend. In evaluating different algorithms, we parameterize the competitive ratio based on the amount of external traffic. After demonstrating the shortcomings of a commonly-used algorithm that is optimal in the absence of external traffic, we propose a new algorithm -- Adaptive Capacity (AC) -- which accounts for matches differently based on whether they originate from internal or external traffic. We provide a lower bound on AC's competitive ratio that is increasing in the amount of external traffic and that is close to (and, in some regimes, exactly matches) the parameterized upper bound we establish on the competitive ratio of any online algorithm. We complement our theoretical results with a numerical study motivated by VM data that demonstrates the strong performance of AC and furthers our understanding of the difference between AC and other commonly-used algorithms.

Motivation & Objective

• To address the challenge of maximizing successful matches on two-sided platforms when a significant portion of traffic arrives via external links, bypassing recommendation algorithms.
• To model the platform’s decision-making as an online matching problem with probabilistic arrivals and finite opportunity capacities.
• To refine competitive ratio analysis by parameterizing performance based on the fraction of external traffic.
• To design and analyze an algorithm that optimally allocates capacity between internal and external traffic to maximize total useful matches.
• To validate the algorithm’s performance using real data from VolunteerMatch and compare it to current industry practices.

Proposed method

• Formalizes the platform’s problem as an online matching model where volunteers arrive sequentially and are matched to opportunities with finite capacity.
• Introduces a parameterized competitive ratio that depends on the proportion of external traffic, refining standard competitive analysis for this setting.
• Proposes the Adaptive Capacity (AC) algorithm, which dynamically adjusts matching decisions based on traffic source—prioritizing under-subscribed opportunities for internal traffic and preserving external matches.
• Uses a primal-dual framework to derive a lower bound on AC’s competitive ratio, showing it increases with external traffic volume.
• Establishes a theoretical upper bound on the competitive ratio of any online algorithm, demonstrating that AC’s performance is nearly optimal.
• Employs numerical simulations based on VolunteerMatch data to compare AC with existing algorithms, validating its superiority in practice.

Experimental results

Research questions

• RQ1 How should a matching platform optimally allocate capacity when a fraction of traffic arrives externally, bypassing the recommendation system?
• RQ2 What is the theoretical performance limit of online algorithms in this multi-channel traffic setting, and how does it depend on the share of external traffic?
• RQ3 Can an algorithm be designed that adapts its matching strategy based on traffic source to improve overall match efficiency?
• RQ4 How does the performance of the proposed Adaptive Capacity (AC) algorithm compare to existing algorithms in real-world data scenarios?
• RQ5 What is the gap between the best possible competitive ratio and the actual performance of AC, and how does it vary with system parameters?

Key findings

• The AC algorithm achieves a competitive ratio that increases with the fraction of external traffic, demonstrating improved performance as external traffic grows.
• AC’s competitive ratio is bounded below by a function that closely matches the theoretical upper bound on the performance of any online algorithm, indicating near-optimality.
• The competitive ratio of AC is strictly greater than the standard lower bound of β (the expected fraction of useful matches in the optimal clairvoyant solution), showing it outperforms traditional algorithms in the presence of external traffic.
• Numerical studies using VolunteerMatch data show AC significantly outperforms current industry practices, especially in scenarios with high external traffic.
• The model reveals that external traffic can be leveraged strategically: by preserving external matches and redirecting internal traffic to under-subscribed opportunities, platforms can achieve higher overall match efficiency.
• The analysis shows that relying solely on internal traffic optimization—common in prior work—leads to suboptimal performance when external traffic is substantial.