Path Finding Algorithms - Part I

Introduction

In the world of trading and finance, particularly in cryptocurrency and decentralized finance (DeFi), one of the critical challenges is finding the most optimal way to convert one asset to another. This process, known as asset conversion, involves the identification of a sequence of trading pairs, exchanges, and paths that can facilitate the exchange of a starting asset (e.g., USD) to a target asset (e.g., EUR) through a series of intermediate conversions (e.g., USD → BTC → ETH → EUR). The efficiency of this conversion process is crucial for traders and liquidity providers, as it directly impacts transaction costs, speed, and overall profitability.

The core problem we face in this context is path finding for asset conversion. This problem requires identifying not just any path but the optimal path, considering factors such as transaction fees, slippage, liquidity, execution speed, and volatility. This document details the problem statement, breaking down the key challenges and considerations involved in solving this problem.

Problem Breakdown

1. Asset Conversion

Asset conversion refers to the process of exchanging one asset for another through a series of trading pairs. For example, converting USD to EUR might require several intermediate steps involving cryptocurrencies such as BTC or ETH, depending on available liquidity and trading pairs on different exchanges.

Example:

  • USD → BTC → EUR: Convert USD to BTC, then BTC to EUR.

  • USD → ETH → BTC → EUR: Convert USD to ETH, then ETH to BTC, and finally BTC to EUR.

The goal is to find the most efficient path from the starting asset to the target asset.

2. Path Finding in Financial Markets

Path finding is a classic computer science problem, often used to navigate graphs where nodes represent states (in our case, assets or trading pairs) and edges represent transitions between states (the trades between pairs). In the context of asset conversion, this problem is typically represented as a weighted graph:

  • Nodes: Assets (e.g., USD, BTC, ETH, EUR)

  • Edges: Available trades or conversions between assets (e.g., USD/BTC, BTC/ETH)

The goal is to find the most cost-effective route, considering edge weights, which represent costs, fees, slippage, or any other conversion cost.

3. Key Challenges in Asset Conversion Path Finding

a. Transaction Costs

Every conversion between assets incurs a fee, typically a percentage of the transaction volume, but sometimes it includes fixed costs. These fees are usually different across exchanges and depend on the liquidity of the pair. The path-finding algorithm must minimize these fees to maximize the overall profit.

b. Slippage

Slippage occurs when the price at which a trade is executed differs from the expected price due to changes in market conditions or low liquidity. It can significantly impact the cost of a conversion, especially in volatile markets or for large trades. A good path-finding algorithm should account for potential slippage when evaluating paths.

c. Liquidity

Liquidity refers to the availability of sufficient assets to complete the trade at a given price without significantly impacting the market. Paths that pass through low-liquidity pairs may experience greater slippage or higher execution times, which can increase the total cost. Hence, liquidity considerations are crucial when determining the optimal path.

d. Execution Speed

In a fast-moving market, delays in executing trades can lead to suboptimal prices, thus increasing costs. Execution speed depends on both the market conditions and the network latency of the exchange or protocol. The path-finding solution should consider the expected execution speed of different routes.

e. Volatility

Volatility is the rate at which the price of an asset fluctuates over time. High volatility can increase the risk of price changes during the conversion process, potentially leading to higher costs or even losses. For example, converting through highly volatile assets might lead to significant fluctuations in value, affecting the end conversion rate.

f. Order Book Depth

The order book depth reflects the number of buy and sell orders available for a given asset pair. Paths with shallow order books are more prone to slippage and are less suitable for large trades. Thus, deeper order books are preferable when selecting a path for conversion, as they provide more liquidity and stability.

4. Categories of Costs Involved

To optimize asset conversion, it’s important to break down costs into different categories. These categories help identify what variables influence the path and how to model them:

  • Fixed Costs:

    • Transaction Fees: Set by exchanges for each trade, these are often either a fixed percentage or a flat fee.

    • Withdrawal/Deposit Fees: Fees associated with moving assets between exchanges.

  • Market Costs:

    • Slippage: The difference between the expected price and the actual execution price due to order book liquidity.

    • Spread: The difference between the highest bid price and the lowest ask price in the order book, which can add cost to the conversion.

    • Liquidity-Driven Price Impact: Larger trades tend to "eat through" the order book, causing the trade price to worsen as it progresses.

  • Performance-Based Costs:

    • Execution Time/Speed: The time it takes to execute the trade, which can be influenced by market activity, network congestion, and latency.

    • Volatility Risk: The risk that the price will fluctuate between trades, leading to higher costs or unfavorable conversion rates.

  • Historical Factors:

    • Market Trends: Past data showing historical slippage, volatility, or liquidity trends, which can be used to make informed predictions about costs.

    • Latency Metrics: Network and exchange latency based on past execution times, affecting how quickly trades can be executed.

5. The Need for Optimal Path-Finding Algorithms

Given the dynamic nature of markets, finding the best conversion path isn’t simply a shortest-path problem but a cost-optimization problem. A good path-finding algorithm must evaluate multiple factors (fees, slippage, execution speed, liquidity) to find the most optimal conversion route.

Example:

Converting USD to EUR might have several routes, such as:

  • USD → BTC → EUR (low fees, but high slippage)

  • USD → ETH → EUR (high fees, but fast execution)

  • USD → USDT → BTC → EUR (moderate fees, high liquidity)

Each route has its own trade-offs in terms of cost, speed, and reliability, and the goal is to balance these factors based on the user’s needs and the current market conditions.

6. Trade-offs in Path Selection

When considering the optimal path for asset conversion, different trade-offs need to be evaluated:

  • Lower Fees vs. Higher Liquidity: A low-fee path might have lower liquidity, resulting in more slippage.

  • Fast Execution vs. Slower, More Reliable Conversions: Some paths may execute faster, but slower paths might provide more reliable prices or reduced volatility risk.

  • Simple vs. Complex Paths: A direct path might be simpler and quicker but might incur higher fees, while a more complex multi-hop path could reduce costs at the expense of increased execution risk.

Conclusion

The path-finding problem for asset conversion is complex, involving multiple dynamic factors that influence the cost and feasibility of conversion routes. Traders, liquidity providers, and exchanges all benefit from solutions that can quickly and accurately identify the most efficient paths for conversion, optimizing for costs, speed, and risk. By leveraging advanced algorithms, it is possible to automate this process and create significant value in a fast-moving market.

In subsequent documents, we will explore various algorithms (DFS, BFS, A*, etc.) and techniques for optimizing path selection, and how they can be applied to solve the asset conversion problem effectively.

NextPath Finding Algorithms - Part II