Algorithms for iceberg orders seem to assume that the trader wants all the partial orders to be subject to a price limit. Do any of the available algorithms allow an iceberg order's partial orders to be entirely at the market price?
Yes, depending on what you needs. Pure VWAP and TWAP algos kinda are exactly that. There is such a thing as "volume participation" algos - i.e. you say "I'd like to be 10% of volume for the rest of the day up to X units in total". There are also various liquidity seeking algos which will wait for passive liquidity to arrive and cross in small clips.
Thanks. The acronyms got me headed in the right direction to see how feasible such algos would be. Seems like the ones IB has are more designed for leisurely accumulation of shares at some non-critical time that is specified well before hand. That wouldn't be convenient for discretionary indicator-driven trades, but maybe it would be workable.
You would prefer LMT instead of MKT for those sizes. That would add liquidity and gain rebates from the exchange.