KXCON23 | Matching Algorithms in q and kdb

Matching algorithms are used to find pairs of entities that satisfy certain criteria. They are used in a variety of applications, such as job matching, college admissions, and medical scheduling.

There are many different matching algorithms, each with its own strengths and weaknesses. Some of the most common matching algorithms include:

• Hungarian algorithm: The Hungarian algorithm is a greedy algorithm that finds a maximum weight matching in a bipartite graph. It is a simple and efficient algorithm, but it is not guaranteed to find the optimal solution.
• Gale-Shapley algorithm: The Gale-Shapley algorithm is a stable matching algorithm that finds a matching in which no two entities prefer each other to their current partners. It is a guaranteed to find an optimal solution, but it can be slower than the Hungarian algorithm.
• Deferred acceptance algorithm: The deferred acceptance algorithm is a stable matching algorithm that is similar to the Gale-Shapley algorithm. However, it is more efficient and can be used to find a matching in larger problems.

The q and kdb languages provide a number of functions for implementing matching algorithms. The match function can be used to find a matching between two lists of entities. The stable function can be used to find a stable matching between two lists of entities.

Here is an example of how to use the match function to find a matching between two lists of entities:

list1 = [1, 2, 3]
list2 = [4, 5, 6]

match(list1, list2)

This function will return a list of pairs of entities, where each pair consists of an entity from list1 and an entity from list2.

Here is an example of how to use the stable function to find a stable matching between two lists of entities:

list1 = [1, 2, 3]
list2 = [4, 5, 6]

stable(list1, list2)

This function will return a list of pairs of entities, where each pair consists of an entity from list1 and an entity from list2. The matching is guaranteed to be stable.

Matching algorithms are a powerful tool that can be used to solve a variety of problems. The q and kdb languages provide a number of functions for implementing matching algorithms, making it easy to use these algorithms to solve real-world problems.

In kdb+, which is a high-performance database system with a built-in programming language called q, you can implement various types of matching algorithms. Matching algorithms are essential in various fields such as finance, data analytics, and more. Here are some common matching algorithms and how they can be implemented in q:

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1. Exact Matching:
   • Description: This type of matching finds exact matches between elements in two datasets.
   • Example Code:
     t1: (1 2 3 4 5) / First dataset
     t2: (3 4 5 6 7) / Second dataset

     t1 inter t2 / Returns the intersection (3 4 5)


2. Fuzzy Matching:
   • Description: Fuzzy matching finds similar matches between elements using some kind of similarity or distance metric.
   • Example Code:
     // Levenshtein Distance (Edit Distance) Example
     lev: {+/1_&~(1+/:/:\:x)=/:/:/:y}

     x: "kdb+"
     y: ("qb+", "qd+", "db+", "kdb")

     lev[x] each y / Returns the Levenshtein distances for each comparison


3. Pattern Matching (Regular Expressions):
   • Description: This type of matching involves finding patterns in strings.
   • Example Code:
     // Example: Finding email addresses in a list of strings
     data: ("john@example.com", "jane.doe@gmail.com", "info@company.com", "notanemail")

     @[data; where each data like "*@*.*"; :; "MATCH"] / Replaces matching strings with "MATCH"


4. Range Matching:
   • Description: Range matching involves finding elements within a specified range.
   • Example Code:
     t: 1 2 3 4 5
     r: 2 3

     t where t within r / Returns elements within the range (2 3)


5. Nearest Neighbor Matching:
   • Description: This type of matching finds the closest match to a given element.
   • Example Code:
     // Example: Finding the nearest neighbor to 3 in a list of numbers
     t: 1 2 3 4 5
     n: 3

     t where abs t - n = min abs t - n / Returns 3


These are just a few examples of matching algorithms you can implement in q using kdb+. Depending on your specific use case and requirements, you might need to develop custom matching logic or use specialized libraries if available. Remember to consider performance implications, especially when dealing with large datasets.