What are arrival price-based trading algorithm?

The arrival price is the midpoint between the bid/ask prices at the time the order was placed.

The goal is to execute the entire order at the arrival price or better, which is more difficult for larger orders/less liquid stocks.

VWAP is one type of algorithm that can be used but there are others. The arrival price serves as a benchmark.

However the broker, unless she is explicitly told what levels to buy at or what prompted the desire to buy, does not know when or why the decision was made. Her best guess is that the current price at the time the order is received is what prompted the decision and thus her decision price is the arrival price. There is no common definition of this price, but the broker normally uses the last traded price or the "mid price" - equal to the average of the current bid and ask prices being quoted at the time the order was received.

Brokerage firms specialize in developing algorithmic strategies, and providing them to the institutional investment community, that aid in the quest to minimise slippage from benchmarks such as implementation shortfall, volume-weighted average price or time-weighted average price. Alpha Profiling is an example of an algorithmic method of minimising implementation shortfall.

Source: Implementation shortfall (Wikipedia)