Pair Trading – Trade two stocks which naturally track each other an example could be Coke and Pepsi, make money when they fall out of line on the idea that they will have to revert back to tracking each other. This is a common mean revision strategy used by hedge funds and might not exactly fit high-frequency trading however it still fall under algorithmic trading.

Volume-Weighted Average Price  – VWAP is used to execute large orders at a better average price. It is the ratio of the value traded to the total volume traded over a time period

Time-Weighted Average Price – TWAP like VWAP is another sophisticated strategy for buying or selling large blocks of shares without affecting the price.

Percentage of Volume – POV is used where the traders want to define the percentage, trading intervals and price when there is a need to trade in large blocks of stock without affecting price.

Iceberg and Sniffer – Are algorithms used to detect and react to other traders trying to hide large block trades using the above algorithms.

Flash Orders – Markets expose their order books in advance to algorithms subscribed to receive flash orders. This creates a two-tired market for most passive investors where algorithms can front run them. A flash order received to sell a stock at a price allows algorithms to clear their own deal books of that stock at a higher price.

A lot of HF algorithms and the minimum latency network infrastructure is to ensure that you can collect the liquidity-rebate that markets pay to ensure a highly liquid environment. When a lot of actors are rushing in to provide this liquidity you have to be the fastest and  smartest to catch the rebate.

While VWAP, TWAP, POV are technicals they are also benchmarks that algorithms use while making their trading decisions. For example in theory
 if the price of a buy trade is lower than the VWAP, it is a good trade and its
not a good trade if the price is higher than the VWAP. It is obviously way more complicated than this and today algo. trading firms probably use vastly more complex derivatives of these mentioned strategies.

These below links will help with understanding more:

Volume-weighted average price…

Competitive Algorithms for VWAP and Limit Order Trading…

Time-weighted average price…

An Overview of the Algorithmic Trading Process…

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