Programming, problem solving, and algorithms

CPSC 203, 2025 W2

April 9, 2026

Strongly Connected Components

I ♥ National Parks

I have no skills. But I have a lot of ideas, and one of them involves taking photographs from the national parks and turning them into things that look like stained glass — algorithmically.

Pointillism

Voronoi cells as art. The original photo of UBC cherry blossoms, and a pointillist rendering using Voronoi regions.

Stained Glass?

Not quite. The regions are too rectangular — they don’t honor the color boundaries in the image the way stained glass would.

Stained Glass?

Still not quite. The Voronoi approach doesn’t know about the image content — it just divides space.

What we really want: equal sized, continuous, compact regions that honor boundaries.

Phone a Friend

 

“What you need are superpixels!”

Superpixels

Equal sized, continuous, compact regions that honor boundaries.

So I went to ask DAF for advice. He said two things. First: use superpixels. Superpixels are an image summary technique — groups of pixels clustered together in similar-sized regions that honor color boundaries. The simplest algorithm is exactly what you’d expect: k-means in 5D space (x, y, r, g, b) with a scale parameter.

Second: how will you know when you’ve done a good job?

Yay Python — skimage has the SLIC superpixels algorithm built in.

Phone a Friend

 

“How will you know if you’ve done a good job?”

Gerrymandering

Gerrymandering

NC — gerrymandered

NC — compact

Equal sized, continuous, compact regions?

The question “how will you know if you’ve done a good job?” brought me to gerrymandering — the redrawing of political boundaries to provide advantage to certain parties.

Gerrymandering = NOT equal sized, continuous, compact regions.

Canada Fixed It

In 1964 a law was passed requiring each province to form an independent panel to draw boundaries.

Source: Washington Post / WonkBlog. The lighter, larger regions in Canada vs. the fragmented mess in parts of the US. Canada’s independent redistricting commissions produce much more compact districts.

Which is fair?

Three ways to divide 50 people into 5 districts. 60% blue, 40% red population.

1. Perfect representation: 3 blue, 2 red districts — proportional
2. Compact but unfair (packing): 5 blue, 0 red — blue “wastes” votes
3. Neither compact nor fair (cracking): 2 blue, 3 red — red wins despite being the minority

The shape of the district determines the outcome.

Which is fair?

Three ways to divide 50 people into 5 districts. 60% blue, 40% red population.

1. Perfect representation: 3 blue, 2 red districts — proportional
2. Compact but unfair (packing): 5 blue, 0 red — blue “wastes” votes
3. Neither compact nor fair (cracking): 2 blue, 3 red — red wins despite being the minority

The shape of the district determines the outcome.

Which is fair?

Three ways to divide 50 people into 5 districts. 60% blue, 40% red population.

1. Perfect representation: 3 blue, 2 red districts — proportional
2. Compact but unfair (packing): 5 blue, 0 red — blue “wastes” votes
3. Neither compact nor fair (cracking): 2 blue, 3 red — red wins despite being the minority

The shape of the district determines the outcome.

How will you know if you’ve done a good job?

For each district, count wasted votes:

Observe:

• Any vote over 50% for the district winner is wasted.
• Any vote over 0% for the district loser is wasted.

Suggests a simple metric of quality!

For each district:

• Count votes over 50% for district winner
• Count votes for district loser
• Sum wasted votes for each party
• Find difference between two numbers as fraction of votes cast

Go district by district, counting how many votes the winner got above 50% — anything higher was a waste. Then count the loser’s votes, because all those went down the tubes. Add up all the waste by party statewide, then take the difference as a percentage of votes cast.

Want to minimize the gap!

Efficiency Gap

The Rabbit Hole

What should we do with the gap?

1. What would Nate Silver do?
2. What happens in the limit?
3. What happens in a multi-party system?
4. Is there an MLE for the gap?
5. Can I apply this within a clustering algorithm on pixels?

The key insight: a cost of misclassifying voters can be directly applied to pixels! Wasted pixels = pixels assigned to the wrong superpixel region.

And here’s the connection. My understanding of gerrymandering was increased by my personal quest for stained glass, and what I learned about gerrymandering will inform my future artistic decisions.

THIS HAPPENS ALL THE TIME, EVERYWHERE.

Strong Connectivity

→
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The Tiffany stained glass tree — the thing I originally wanted to make. And the Canadian Charter of Rights and Freedoms — the thing gerrymandering threatens.

These two images are connected through superpixels. And I only found that connection because I followed my curiosity from one domain into another.

Mutually beneficial. The connections go both ways — that’s what makes them strongly connected.

A Diversity Diversion

Diverse teams improve results:

• Cognitive Diversity and Speed: cognitively diverse teams solve problems up to 3x faster and consider 48% more solutions (HBR/SA).

• Reduced Groupthink and Bias: groups with diverse members are more likely to correct errors and avoid groupthink, making them more accurate in decisions (NLI).

• Innovation Boost: cognitive diversity can improve team innovation by 20% (JoAP).

Inherent diversity: characteristics we’re born with or into.

Acquired diversity: the breadth of our interests, experiences, and connections.

The field of CS demands constant innovation, and diverse teams are more innovative. That’s mostly argued in terms of inherent diversity. But this talk is about acquired diversity.

The part that makes this relevant: the connections between these problems arise from completely different problem domains. You all have diverse interests. The purpose of this talk is to convince you that they are deeply worthwhile — that they are NEVER a waste of time. You cannot predict the ways in which they will make you smarter.

A Diversity Diversion

Travel. Books and games. Food. Exercise. Music. Arts. Learn about other cultures. Build something. Plant a garden.

Sometimes the connections are with ideas, sometimes with people, sometimes with places.

It is this broad definition of diversity — diversity of connections — that I hope for you in your future.

We cannot predict which connections will be important — so build as many as you can.

Do things for beauty, for fun, or because you are afraid of them.

Gratitude

Thank you for being so bright and so fun to teach.

Thank you for all the ways you’re going to make the world a better place.