The intuition is that a transaction with more locks is more likely to block other transactions in the system. However, this approach does not account for the popularity of objects in the system. In other words, a transaction might be holding many locks but on unpopular objects, which are unlikely to be requested by other transactions.

简而言之就是一个通过最多的locks决定那个transaction最先，缺点是这个txn locks不一定是热点数据。

An improvement over the previous criterion is to only count those locks that have at least one transaction waiting on them.
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The issue with this criterion is that it treats all blocked transactions as the same, even if they contribute unequally to the overall contention.

通过使用最多等待作为判断标准，解决前一种算法存在的问题。缺点是没有区分block的txn，而txn造成的contention不是相同的。

A more sophisticated criterion is the depth of a transaction’s dependency subgraph. For a transaction t, this is defined as the subgraph of the dependency graph comprised of all vertices that can reach t (and all edges between such vertices). The depth of t’s dependency subgraph is characterized by the number of transactions on the longest path in the subgraph that ends in t. 

DDF使用了dependency graph的深度来决定那个txn最先运行，就有可能让更对的dependency graph的“深度”更加浅的尽快得到运行，减少contention。但是缺点是没有考虑到深度很深的，但是之间contention很少的情况，比如就是一条比较长的链结构的case。

Consider two transactions t1 and t2 in the system. If there is a path from t1 to t2 in the dependency graph, we say that t1 is dependent on t2 (i.e., t1 depends on t2’s completion/abortion for at least one of its required locks). We define the dependency set of t, denoted by g(t), as the set of all transactions that are dependent on t (i.e., the set of transactions in t’s dependency subgraph). Our LDSF algorithm uses the size of the dependency sets of different transactions to decide which one(s) to schedule first. For example, in Figure 4, there are five transactions in the dependency set of transaction t1 (including t1 itself) while there are four transactions in t2’s dependency set. Thus, in a situation where both t1 and t2 have requested an exclusive lock on object o1, LDSF grants the lock to t1 (instead of t2) as soon as o1 becomes available.