CSCE 235

Handout 13: Sets: Searching the World

February 11, 2004

Assume that you are an expert in database management. You are given the following database. Your responsibilities include writing a program that allow users to query the database by specifying the country name, the capital name, the country’s area, the country’s population, and the continent of the country. For example, the users should be able to ask for “Give me the countries on the continent of North America that each has more than 200,000,000 people.” Or, “Give me the countries whose capital shares the same name as the name of the country.” “Give me the countries on the Oceania continent.” “Give me the countries with fewer than 10,000,000 people in its population.” “Give me the countries with an area larger than 100,000 sq mi yet with a population fewer than 200,000,000 people.”

Country	Capital	Area	Population	Continent
Algeria	Algiers	919,595 sq mi	30,774,000	Africa
Angola	Luanda	481,354 sq mi	12,479,000	Africa
Indonesia	Jakarta	741,101 sq mi	211,806,000	Asia
China	Beijing	3,705,820 sq mi	1,254,062,000	Asia
U.S.A.	Washington, D.C.	3,717,796 sq mi	270,933,000	North America
Canada	Ottawa	3,849,670 sq mi	30,589,000	North America
Brazil	Brasilia	3,286,488 sq mi	167,988,000	South America
Argentina	Buenos Aires	1,068,302 sq mi	36,568,000	South America
United Kingdom	London	94,248 sq mi	59,364,000	Europe
France	Paris	210,026 sq mi	59,067,000	Europe
Australia	Canberra	2,966,153 sq mi	18,981,000	Oceania
New Zealand	Wellington	103,883 sq mi	3,817,000	Oceania
India	New Delhi	1,269,346 sq mi	986,611,000	Asia
Turkey	Ankara	300,948 sq mi	65,869,000	Asia
Belgium	Brussels	11,783 sq mi	10,225,000	Europe
Belarus	Minsk	80,154 sq mi	10,167,000	Europe
Russia	Moscow	6,592,692 sq mi	146,519,000	Europe
Denmark	Copenhagen	16,638 sq mi	5,325,000	Europe
Italy	Rome	116,324 sq mi	57,717,000	Europe
Netherlands	Amsterdam	16,023 sq mi	15,799,000	Europe
Malaysia	Kuala Lumpur	127,317 sq mi	22,710,000	Asia
Singapore	Singapore	239 sq mi	3,999,000	Asia
Cameroon	Yaounde	183,569 sq mi	15,456,000	Africa
Egypt	Cairo	386,662 sq mi	66,924,000	Africa
Senegal	Dakar	75,955 sq mi	9,240,000	Africa
Cuba	Havana	42,804 sq mi	11,178,000	North America
Peru	Lima	496,225 sq mi	26,624,000	South America
Chile	Santiago	292,135 sq mi	15,018,000	South America
Mexico	Mexico City	756,066 sq mi	99,734,000	North America

Let us use what we learn about sets to accomplish the above queries.

Take “Give me the countries on the continent of North America that each has more than 200,000,000 people.” First, we define the set NA = { x: x is a country on the continent of North America }, and P200M = { x : x is a country with more than 200,000,000 people }. To obtain the results for the query, we simply intersect the two sets: .

Take “Give me the countries with an area larger than 100,000 sq mi yet with a population fewer than or equal to 200,000,000 people.” How do we define this? First, suppose that A100K = { x : x is a country with an area larger than 100,000 sq. mi }, and we can use the same definition of P200M above. To obtain the results for the query, we simply do a difference of the two sets: . What about ? What does this difference say? Be very careful about this. In the latter set, it gives you “all countries that each has a population greater than 200,000,000 people but each has an are smaller than 100,000 sq mi.” So, be very careful on how you form this set.

Now, given the above examples, is it possible for you to find a unique combination of sets for each country listed in the above table? For example, can you find a unique combination of sets for Mexico such that if you type in the query using the combination, Mexico is the only result returned; or the only member of the set? Of course we could do something like this: T = { x : x is a country with 99,734,000 people }. However, this approach would be too specific and useless to truly differentiate Mexico from other countries. In data mining, we look for the simplest and the most general way of defining uniqueness. So, what about this: Suppose that A3M = { x : x is a country with an area larger than 3,000,000 sq. mi } and the definition of NA holds. Then, we could retrieve Mexico by .

Ultimately, in the area of data mining, we see each definition of a set as a rule. The key is to have as fewest rules as possible to describe the entire database—where each country, in our example, can be queried and retrieved by combining these rules.