Index: src/wp-includes/formatting.php
===================================================================
--- src/wp-includes/formatting.php	(revision 43572)
+++ src/wp-includes/formatting.php	(working copy)
@@ -1926,6 +1926,17 @@
 			// grave accent
 			'Ǜ' => 'U',
 			'ǜ' => 'u',
+			// Dialytika and tonos (Greek)
+			'Ϊ' => 'I',
+			'ϊ' => 'i',
+			'Ί' => 'I',
+			'ί' => 'i',
+			'ΐ' => 'i',
+			'Ϋ' => 'Y',
+			'ϋ' => 'u',
+			'Ύ' => 'Y',
+			'ύ' => 'u',
+			'ΰ' => 'u',
 		);
 
 		// Used for locale-specific rules
@@ -2264,6 +2275,9 @@
 				'%cc%80',
 				'%cc%84',
 				'%cc%8c',
+				// dialytika and tonos
+				'%ce%84',
+				'%ce%85',
 			),
 			'',
 			$title
Index: tests/phpunit/tests/formatting/RemoveAccents.php
===================================================================
--- tests/phpunit/tests/formatting/RemoveAccents.php	(revision 43572)
+++ tests/phpunit/tests/formatting/RemoveAccents.php	(working copy)
@@ -143,4 +143,11 @@
 
 		$this->assertEquals( 'Dd', remove_accents( 'Đđ' ) );
 	}
+
+	/**
+	 * @ticket 44793
+	 */
+	public function test_remove_greek_dialytika_and_tonos() {
+		$this->assertEquals( 'IiIiiYuYuu', remove_accents( 'ΪϊΊίΐΫϋΎύΰ' ) );
+	}
 }
Index: tests/phpunit/tests/formatting/SanitizeTitleWithDashes.php
===================================================================
--- tests/phpunit/tests/formatting/SanitizeTitleWithDashes.php	(revision 43572)
+++ tests/phpunit/tests/formatting/SanitizeTitleWithDashes.php	(working copy)
@@ -140,4 +140,11 @@
 		$this->assertEquals( 'aaaa', sanitize_title_with_dashes( 'ááa´aˊ', '', 'save' ) );
 	}
 
+	/**
+	 * @ticket 44793
+	 */
+	function test_replaces_dialytika_and_tonos() {
+		$this->assertEquals( 'ii', sanitize_title_with_dashes( '΅I΄I', '', 'save' ) );
+	}
+
 }