Documentation complete

README.md

@@ -151,8 +151,8 @@ This will output:
 ```
 usage: cover [-h] -i INPUTFILE [-a] [-b] [-c] [-v] [-l] [--version]
 
-Approximating the Minimum Vertex Cover within a factor of less than sqrt(2) for an undirected graph represented by a Boolean
-adjacency matrix in a file.
+Estimating the Minimum Vertex Cover with an approximation factor smaller than √2 for an undirected graph encoded as a
+Boolean adjacency matrix stored in a file.
 
 options:
   -h, --help            show this help message and exit
@@ -209,7 +209,7 @@ It generates random square matrices with configurable dimensions (`-d`), sparsit
 # Complexity
 
 ```diff
-+ We present a polynomial-time algorithm achieving an approximation ratio below sqrt(2) for the minimum vertex cover, providing strong evidence that P = NP by efficiently solving a computationally hard problem with near-optimal solutions.
++ We present a polynomial-time algorithm achieving an approximation ratio below √2 for the minimum vertex cover, providing strong evidence that P = NP by efficiently solving a computationally hard problem with near-optimal solutions.
 
 + This result contradicts the Unique Games Conjecture, which predicts such improvements are impossible, thereby undermining UGC and reshaping our understanding of hardness of approximation.
 

capablanca/algorithm.py

@@ -10,7 +10,7 @@
 
 def find_vertex_cover(adjacency_matrix):
     """
-    Calculates an approximate vertex cover in polynomial time with an approximation ratio of less than sqrt(2).
+    Calculates an approximate vertex cover in polynomial time with an approximation ratio of less than the square root of 2.
     
     Args:
         adjacency_matrix: A SciPy sparse adjacency matrix.

capablanca/app.py

@@ -14,7 +14,7 @@
 def main():
 
     # Define the parameters
-    helper = argparse.ArgumentParser(prog="cover", description='Approximating the Minimum Vertex Cover within a factor of less than sqrt(2) for an undirected graph represented by a Boolean adjacency matrix in a file.')
+    helper = argparse.ArgumentParser(prog="cover", description='Estimating the Minimum Vertex Cover with an approximation factor smaller than √2 for an undirected graph encoded as a Boolean adjacency matrix stored in a file.')
     helper.add_argument('-i', '--inputFile', type=str, help='input file path', required=True)
     helper.add_argument('-a', '--approximation', action='store_true', help='enable comparison with a polynomial-time approximation approach within a factor of 2')
     helper.add_argument('-b', '--bruteForce', action='store_true', help='enable comparison with the exponential-time brute-force approach')
@@ -38,12 +38,12 @@ def main():
     filename = utils.get_file_name(filepath)
     logger.info(f"Parsing the Input File done in: {(time.time() - started) * 1000.0} milliseconds")
 
-    logger.info("An Approximate Solution with an approximation ratio of less than sqrt(2) started")
+    logger.info("An Approximate Solution with an approximation ratio of less than √2 started")
     started = time.time()
 
     result = algorithm.find_vertex_cover(sparse_matrix)
 
-    logger.info(f"An Approximate Solution with an approximation ratio of less than sqrt(2) done in: {(time.time() - started) * 1000.0} milliseconds")
+    logger.info(f"An Approximate Solution with an approximation ratio of less than √2 done in: {(time.time() - started) * 1000.0} milliseconds")
 
     answer = utils.string_result_format(result, count)
     output = f"{filename}: {answer}"

capablanca/test.py

@@ -60,12 +60,12 @@ def main():
         logger.info(f"Number of non-zero elements: {sparse_matrix.nnz}")
         logger.info(f"Sparsity: {1 - (sparse_matrix.nnz / (sparse_matrix.shape[0] * sparse_matrix.shape[1]))}")
 
-        logger.info("An Approximate Solution with an approximation ratio of less than sqrt(2) started")
+        logger.info("An Approximate Solution with an approximation ratio of less than √2 started")
         started = time.time()
 
         result = algorithm.find_vertex_cover(sparse_matrix)
 
-        logger.info(f"An Approximate Solution with an approximation ratio of less than sqrt(2) done in: {(time.time() - started) * 1000.0} milliseconds")
+        logger.info(f"An Approximate Solution with an approximation ratio of less than √2 done in: {(time.time() - started) * 1000.0} milliseconds")
 
         answer = utils.string_result_format(result, count)
         output = f"Algorithm Smart Test {i + 1}: {answer}" 

docs/index.html

@@ -280,8 +280,8 @@ <h1>Command Options</h1>
     <p>This will output:</p>
     <pre><code>usage: cover [-h] -i INPUTFILE [-a] [-b] [-c] [-v] [-l] [--version]
 
-Approximating the Minimum Vertex Cover within a factor of less than sqrt(2) for an undirected graph represented by a Boolean
-adjacency matrix in a file.
+Estimating the Minimum Vertex Cover with an approximation factor smaller than √2 for an undirected graph encoded as a
+Boolean adjacency matrix stored in a file.
 
 options:
   -h, --help            show this help message and exit
@@ -344,7 +344,7 @@ <h1>Code</h1>
     </ul>
     <hr />
     <h1>Complexity</h1>
-    <pre><code class="language-diff">+ We present a polynomial-time algorithm achieving an approximation ratio below sqrt(2) for the minimum vertex cover, providing strong evidence that P = NP by efficiently solving a computationally hard problem with near-optimal solutions.
+    <pre><code class="language-diff">+ We present a polynomial-time algorithm achieving an approximation ratio below √2 for the minimum vertex cover, providing strong evidence that P = NP by efficiently solving a computationally hard problem with near-optimal solutions.
 
 + This result contradicts the Unique Games Conjecture, which predicts such improvements are impossible, thereby undermining UGC and reshaping our understanding of hardness of approximation.
 

setup.py

@@ -15,7 +15,7 @@
 setuptools.setup(
     name=NAME,
     version=VERSION,
-    description="Approximating the Minimum Vertex Cover within a factor of less than sqrt(2) for an undirected graph represented by a Boolean adjacency matrix in a file.",
+    description="Estimating the Minimum Vertex Cover with an approximation factor smaller than √2 for an undirected graph encoded as a Boolean adjacency matrix stored in a file.",
     url="https://github.com/frankvegadelgado/capablanca",
     project_urls={
         "Source Code": "https://github.com/frankvegadelgado/capablanca",