Prefix Tree Search Skipping Identical Subtrees
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Solution Overview
Problem
String matching operations in Electronic Design Automation (EDA) tools, particularly in prefix trees with hierarchical names, are inefficient due to the need to traverse all tree structures, leading to long computation times when searching for design elements that match user-defined regular expressions.
Innovation Solution
The algorithm skips identical subtrees that have already been searched without finding matches by utilizing a prefix equivalence check, reducing the search space and improving efficiency through Depth-First Search and techniques like Brzozowski derivatives or Nondeterministic Finite Automatons.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the algorithm traverses all tree structures to search for matching objects, then completeness of search is ensured, but computation time becomes excessively long
Solution Approach 1:
The algorithm performs preliminary actions by pre-computing and storing canonical forms of module names and their prefix equivalence relationships before the actual search begins. This preliminary preparation allows the search algorithm to quickly identify and skip identical subtrees during execution, significantly reducing computation time while maintaining search completeness through the use of depth-first search with proper backtracking.
2Reliability
If the algorithm searches every subtree in the prefix tree, then all potential matches are found, but redundant searches in identical subtrees increase computation cost
Solution Approach 1:
The algorithm uses the concept of copying by creating a canonical representation of each module name and storing it in a lookup structure. When encountering a subtree, the algorithm checks if its prefix matches a previously seen prefix with the same canonical form. If so, it skips searching that subtree since it would be redundant. This copying approach maintains match completeness while dramatically improving search efficiency by eliminating duplicate work.
Solution Approach 2:
The algorithm changes the parameter of search by introducing a new dimension to the search space: the canonical form of module names. By transforming the search problem from simply traversing tree nodes to traversing nodes while comparing their canonical forms, the algorithm identifies equivalent subtrees and skips redundant searches. This parameter transformation enables efficient search while maintaining completeness.
3Duration of action of moving object
If the algorithm uses depth-first search to traverse the tree, then search depth is controlled, but identical subtrees are searched multiple times increasing time complexity
Solution Approach 1:
The algorithm implements feedback by continuously monitoring the canonical forms of module names encountered during depth-first search and using this information to make intelligent decisions about which subtrees to skip. The feedback mechanism stores results of previous searches and uses them to guide future search decisions, allowing the algorithm to maintain controlled search depth while avoiding redundant work in identical subtrees through efficient use of the feedback information.
Data Source
AI summary
A search for a regular expression in a tree hierarchy, includes, in part, searching for a match to the regular expression in a first subtree defined by a first node name, recording information about the first subtree if there is no match, determining whether a second subtree defined by a second node name is identical to the first node, skipping search of the second subtree if the second subtree is determined to be identical and prefix equivalent, with respect to the regular expression, to the first subtree. The second subtree is determined to be prefix equivalent to the first subtree when for any string s, a first prefix defined by a concatenation of the first node name and the string s results in a match if and only if a second prefix defined by a concatenation of the second node name and the string s results in a match.