DEX Aggregators

Last modified: June 13, 2026

DEX Aggregators

A DEX aggregator is a blockchain-based routing service that monitors prices and available liquidity across multiple decentralized exchanges and determines how a trade should be executed in order to obtain the best possible outcome. In particular, an aggregator may split a single order across several AMMs rather than route the full order to a single pool. This is often advantageous because the price impact of a trade depends on pool depth, so distributing the trade across multiple venues can improve the effective execution price.

To illustrate this mechanism, consider the following simplified problem. Suppose that a trader wants to sell a total amount $T$ of token $X$ across two different constant-product pools in order to receive as much token $Y$ as possible. For $j \in \{1,2\}$ , let

x_j,\; y_j

denote the reserves of tokens $X$ and $Y$ in pool $j$ , respectively, and let

\phi_j\in[0,1)

be the trading fee of pool $j$ . Define, for convenience,

\lambda_j := 1-\phi_j.

Suppose that the trader sends an amount $u\in[0,T]$ of token $X$ to pool 1 and the remaining amount $T-u$ to pool 2. Then, by the fee-adjusted constant-product formula, the amount of token $Y$ received from pool 1 is

\Delta y_1(u)=\frac{y_1\lambda_1 u}{x_1+\lambda_1 u},

while the amount received from pool 2 is

\Delta y_2(u)=\frac{y_2\lambda_2 (T-u)}{x_2+\lambda_2 (T-u)}.

Hence, the total output of token $Y$ is

F(u)=\frac{y_1\lambda_1 u}{x_1+\lambda_1 u} + \frac{y_2\lambda_2 (T-u)}{x_2+\lambda_2 (T-u)}, \qquad u\in[0,T].

Therefore, the optimal routing problem reduces to maximizing $F$ over the interval $[0,T]$ .

It is convenient to rewrite $F$ as

F(u)= y_1-\frac{x_1y_1}{x_1+\lambda_1u} + y_2-\frac{x_2y_2}{x_2+\lambda_2(T-u)}.

Differentiating, we obtain

F'(u)= \frac{x_1y_1\lambda_1}{(x_1+\lambda_1u)^2} - \frac{x_2y_2\lambda_2}{(x_2+\lambda_2(T-u))^2}.

Since the denominator is always positive on $[0,T]$ , the sign of $F'(u)$ is the same as the sign of

g(u) := x_1y_1\lambda_1\bigl(x_2+\lambda_2(T-u)\bigr)^2 - x_2y_2\lambda_2\bigl(x_1+\lambda_1u\bigr)^2.

Thus, to locate the maximizer of $F$ , it is sufficient to study the zeros and sign changes of the quadratic polynomial $g$ .

Example 2.8

Consider two CTN/USDC constant-product pools with the following reserves and fees:

	Pool 1	Pool 2
CTN reserve	7,000	9,000
USDC reserve	24,500,000	28,350,000
Fee	0.3%	0.3%

Suppose that a trader wants to sell a total amount

T=1500

of CTN across the two pools in order to maximize the amount of USDC received.

Since both pools charge the same fee, we have

\lambda_1=\lambda_2=0.997.

Therefore, the objective function is

F(u)= \frac{24{,}500{,}000\cdot 0.997\,u}{7000+0.997\,u} + \frac{28{,}350{,}000\cdot 0.997\,(1500-u)}{9000+0.997\,(1500-u)}, \qquad u\in[0,1500].

Its derivative has the same sign as

g(u)= 7000\cdot 24{,}500{,}000\cdot 0.997\bigl(9000+0.997(1500-u)\bigr)^2 - 9000\cdot 28{,}350{,}000\cdot 0.997\bigl(7000+0.997u\bigr)^2.

Expanding this expression, we obtain

g(u)= -83{,}148{,}852{,}850\,u^2 + 7{,}150{,}540{,}330{,}500{,}000\,u + 6{,}389{,}321{,}722{,}875{,}000{,}000.

Applying the quadratic formula, the roots of $g$ are

u_1 \approx -86881.3085, \qquad u_2 \approx 884.4477.

Since the leading coefficient of $g$ is negative, it follows that $g(u)$ is positive on the interval $(u_1,u_2)$ and negative on $(-\infty,u_1)\cup(u_2,\infty)$ . Because $u_2\in[0,1500]$ , we conclude that $F$ is strictly increasing on $[0,u_2]$ and strictly decreasing on $[u_2,1500]$ . Hence, the unique maximizer on $[0,1500]$ is

u^\star \approx 884.4477.

Therefore, the optimal routing is:

send

884.4477 \text{ CTN}

to pool 1,

send

1500-884.4477 = 615.5523 \text{ CTN}

to pool 2.

The corresponding outputs are

\Delta y_1(u^\star)\approx 2{,}740{,}995.2719 \text{ USDC},

and

\Delta y_2(u^\star)\approx 1{,}809{,}765.8129 \text{ USDC}.

Thus, the maximum total output is

F(u^\star)\approx 4{,}550{,}761.0848 \text{ USDC}.

For comparison, if the entire trade were executed only in pool 1, the trader would receive

F(1500)\approx 4{,}312{,}842.0929 \text{ USDC},

whereas if the entire trade were executed only in pool 2, the trader would receive

F(0)\approx 4{,}039{,}581.2491 \text{ USDC}.

Hence, splitting the order optimally across both pools yields a substantially better execution than routing the whole trade to either single pool.

This example makes clear why DEX aggregators are valuable. In order to identify the optimal split, one must know the current state of each pool and perform a nontrivial optimization. Aggregators automate this entire procedure and thereby allow users to obtain better prices without carrying out these computations manually.