While all NP-hard optimization problems are identical in terms of exact solvability, they may differ wildly from the approximative point of view. If the goal is to obtain an answer that is “good enough”, some problems become much easier (such as KNAPSACK), while others (such as CLIQUE) remain extremely hard.

In some ways, photography is to visual artists what piano is to musicians. I can get you to play a somewhat accurate rendition of Mary Had a Little Lamb in about 2 minutes, and if it isn’t in tune, that’s the piano’s fault, not yours. Similarly, if you have a camera, you can create an image in about two seconds, and if the image quality sucks, it’s probably the camera’s fault, not yours.

When I was in high school, I attended a magnet school for the arts, which meant that around 70% of the students had auditioned for competitive admission to a specialized program in theatre, visual arts, dance, music, or creative writing. This meant that there were often two versions of each art course: there was the version of the course intended for (and restricted to) the students studying in that discipline, and there was the general version, intended for everyone.

If you were to meet glaive today, you might not guess he grew up in a sleepy North Carolina town. He’s thin boned, over six feet tall, and dresses like he’s trying on a type of angst that doesn’t suit him. Over the last two years, he’s constantly shifted his aesthetic. He’s flipped from shorter chestnut brown curls to longer platinum blonde to medium length but unhealthy dyed black hair.

Graphs can be seen as a way to represent pairwise relationships between objects. With graphs, we have one object type and one relationship type. In one of the most common canonical applications or graph theory, social networking, we are trying to understand and represent social groups using graphs. In that case, our object is people, our pairwise relationship is friendship, and two people have a relationship between them if they are friends.