There is a difference about understanding LOB dynamics and using an algorithmic solution to capture these dynamics.

How LOB evolves. We understood now long ago (see Jeremy Large's papers) that a Markov chain on "pictures" of the LOB would be an interesting model. After few years of modeling LOB dynamics with Hawkes processes (see for instance Emmanuel Bacry and co-authors' paper), and thanks to the interesting push by Rama Cont and Adrien de Larrard, we came to the idea that heterogenous Poisson process to model each event (insert, cancel, market) was really good. Especially if the intensities of these processes are functions of the state of the orderbook (i.e. of the "pictures" I referred too). See the Queue Reactive Model. This incorportaes the predicting power of orderbook imbalence.

How to compress the dynamics. I do believe that intensities are a good way to keep track of the dynamics. It is only if you want to associate the best next action (between insert/cancel/stay/market) that somehow a decision tree, i.e. a binary tree. Can be useful. But I would suggest to rely on reinforcement learning (see the examples of this paper) to choose the branches of your tree.

[EDIT] If your goal is to implement a matching engine, this is another story. It is something I had to do to debug or backtest trading algorithms. I would say that in theory you just need something that is equivalent to a quicksearch logic, and yes read-black tree is a solution that for. The important point is not to redo the search each time you want to insert an order in your list of price levels, since it is already sorted. Most programming language already have a solution that for (in python, why not simply use a dictionary), but if you want to do it from scratch because you are really concerned by the implementation speed, then it could be a good idea to start to search at the mid-price (and not at the lowest or highest price), because you have more order insertions and updates around the mid.

There is a difference about understanding LOB dynamics and using an algorithmic solution to capture these dynamics.

How LOB evolves. We understood now long ago (see Jeremy Large's papers) that a Markov chain on "pictures" of the LOB would be an interesting model. After few years of modeling LOB dynamics with Hawkes processes (see for instance Emmanuel Bacry and co-authors' paper), and thanks to the interesting push by Rama Cont and Adrien de Larrard, we came to the idea that heterogenous Poisson process to model each event (insert, cancel, market) was really good. Especially if the intensities of these processes are functions of the state of the orderbook (i.e. of the "pictures" I referred too). See the Queue Reactive Model. This incorportaes the predicting power of orderbook imbalence.

How to compress the dynamics. I do believe that intensities are a good way to keep track of the dynamics. It is only if you want to associate the best next action (between insert/cancel/stay/market) that somehow a decision tree, i.e. a binary tree. Can be useful. But I would suggest to rely on reinforcement learning (see the examples of this paper) to choose the branches of your tree.

[EDIT] If your goal is to implement a matching engine, this is another story. It is something I had to do to debug or backtest trading algorithms. I would say that in theory you just need something that is equivalent to a quicksearch logic, and yes red-black tree is a solution that for. The important point is not to redo the search each time you want to insert an order in your list of price levels, since it is already sorted. Most programming language already have a solution that for (in python, why not simply use a dictionary), but if you want to do it from scratch because you are really concerned by the implementation speed, then it could be a good idea to start to search at the mid-price (and not at the lowest or highest price), because you have more order insertions and updates around the mid.

There is a difference about understanding LOB dynamics and using an algorithmic solution to capture these dynamics.

How LOB evolves. We understood now long ago (see Jeremy Large's papers) that a Markov chain on "pictures" of the LOB would be an interesting model. After few years of modeling LOB dynamics with Hawkes processes (see for instance Emmanuel Bacry and co-authors' paper), and thanks to the interesting push by Rama Cont and Adrien de Larrard, we came to the idea that heterogenous Poisson process to model each event (insert, cancel, market) was really good. Especially if the intensities of these processes are functions of the state of the orderbook (i.e. of the "pictures" I referred too). See the Queue Reactive Model. This incorportaes the predicting power of orderbook imbalence.

How to compress the dynamics. I do believe that intensities are a good way to keep track of the dynamics. It is only if you want to associate the best next action (between insert/cancel/stay/market) that somehow a decision tree, i.e. a binary tree. Can be useful. But I would suggest to rely on reinforcement learning (see the examples of this paper) to choose the branches of your tree.

There is a difference about understanding LOB dynamics and using an algorithmic solution to capture these dynamics.

How LOB evolves. We understood now long ago (see Jeremy Large's papers) that a Markov chain on "pictures" of the LOB would be an interesting model. After few years of modeling LOB dynamics with Hawkes processes (see for instance Emmanuel Bacry and co-authors' paper), and thanks to the interesting push by Rama Cont and Adrien de Larrard, we came to the idea that heterogenous Poisson process to model each event (insert, cancel, market) was really good. Especially if the intensities of these processes are functions of the state of the orderbook (i.e. of the "pictures" I referred too). See the Queue Reactive Model. This incorportaes the predicting power of orderbook imbalence.

How to compress the dynamics. I do believe that intensities are a good way to keep track of the dynamics. It is only if you want to associate the best next action (between insert/cancel/stay/market) that somehow a decision tree, i.e. a binary tree. Can be useful. But I would suggest to rely on reinforcement learning (see the examples of this paper) to choose the branches of your tree.

[EDIT] If your goal is to implement a matching engine, this is another story. It is something I had to do to debug or backtest trading algorithms. I would say that in theory you just need something that is equivalent to a quicksearch logic, and yes read-black tree is a solution that for. The important point is not to redo the search each time you want to insert an order in your list of price levels, since it is already sorted. Most programming language already have a solution that for (in python, why not simply use a dictionary), but if you want to do it from scratch because you are really concerned by the implementation speed, then it could be a good idea to start to search at the mid-price (and not at the lowest or highest price), because you have more order insertions and updates around the mid.