MIT 6.006 Introduction to Algorithms, Fall 2011 View the complete course: ocw.mit.edu/6-006F11 Instructor: Srini Devadas License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms More courses at ocw.mit.edu
Everyone please stop saying the lecture is worthless. This lecture is a Primer for shortest path algorithms. Understanding negative weights, negative loops was pretty important. Also learning about all different problems like exponential number of vertices. Surely if you had gone through the topic already might be useless to you, so you can skip it. But if you are going through shortest path algos for the first time, its a good lecture.
Right. Without this one, subsequent lectures are hard to grasp at least regarding the notations. I concur that this one is a good and necessary primer.
This professor's lecture is so structured! He really stresses the important things. So easy to get the big picture, but also gives you the often-overlooked details (e.g., it's not the neg. weight edges, but the *cycles* that are a problem; Dijkstra is essentially *linear*)
If each edge represents a multiplier, and you want to minimize the product of the multipliers along a path; that is equivalent to minimizing the sum of the logarithms of those multipliers. Logarithms have a range from -inf to +inf, and so include both negative, zero, and positive values. One commonly cited example is where the multipliers represent currency conversion rates; where each vertex represents one currency, and edges represent conversion rates between currencies.
neg weights? 28:55 - What about graphs being represented as electric circuits? Some branches have passive components like resistors that cause a potential drop and some branches have active components like batteries that cause a potential gain. Intersections or splits in the circuit are vertices. The connections between splits are edges and the weights are the voltage gain (+ve) or drop (-ve) of that connection.
thats an interesting obeservation! ..... but how would we use the different paths/ because in electrical circuits, current (I) is gonna flow in all the branches, i mean we cant tell it to use only a certain path. So, can you think of any way it could be used? but good analogy nonetheless.
Isn’t there a mistake at 48:20? How can you relax the edge from v4 to v5 to then have d(v5) be 12? That would mean v4 can be reached in 12, and v5 can also be reached in 12? That can’t be correct...? Really great lecture otherwise, quite surprised at all the negative comments on here...
29:36 you will see Victor giving a example about negative weight. We would know more about MIT TA work. That is so different in my college. I don't even know who is my TA in the entire of my college.
yeah, jotted that down and got really confused later. if there are |E| edges, the number of possible unique weights is |E|... and E=O(V^2), so yeah, i think he meant to say roughly V^2 possible weights.
how about circuits where there are multiple paths w/ positive or negative voltage differentials for a motivation? if so, I can send you my address for a cushion... ;)
I know it's too late i guess. but can anyone explain why does the asymptotic relation between edges and vertices is v^2? don't know if i said it correctly as well just didn't get that point.
In a complete graph, the number of edges is V choose 2 (The total number of ways by which we can pair two vertices), which equals V*(V-1)/2. This is of order V^2. Hence, E = O(V^2)
Number of possible edges between n vertices is nC2 i.e the number of ways to pick 2 vertices from a given set of n vertices. Unless I screwed up, replacing r=2 in the equation for nC2 should derive into (V^2 - 1)/2 which is O(V^2).
I think it is because every Vertex can have atmost V Edges(Unless we are talking about Multi Graph). So you have V Vertex with each having V Edges, so overall edges are V^2
why are cycles even a thing? if they add positive path length you'd obviously never take them, if they add negative path length you'd obviously go around around them forever so surely it makes no sense to even have a graph with cycles when asking the question 'what's the shortest path'.. without adding extra criteria like 'without retracing the same edge' or 'without visiting the same node more than x times'
i don't understand the hate both teacher are best and you haters are nothing more than a keyboard warrior how did you get the audacity to hate people providing free education
Assume two vertices v1 and v2. The total number of possible edges would be 4 which is 2^2 ( 2= total number of vertices). All possible edges v1 -> v2, v2 -> v1, v1->v1, v2->v2. They all add up to 4. But this is only correct if the graph is directed. If undirected, I think it should be v(v-1)/2.
it's about how many (u,v) pairs can be formed. Directed edges would yield nP2 edges given the graph is simple (u cannot be equal to v) and nC2 edges for undirected as (u,v) and (v,u) would only be counted once
Erik is the boss. I love his intuitive explanations. He gets straight to the ideas in a really down-to-earth way: "Dynamic programming is really just careful brute force". If you get DP, you realise how other teachers make it out to be much more complicated than it is.
why would anyone imagine the weight defined for an edge WOULD affect the calculation speed of an algorithm? that'd be like thinking the 'weight' of an object would affect the time it took to sort it. 'this is a really heavy object so it takes longer to add it to the list' wot no 'this is a really long path so it takes longer to calculate its length' WOT NO WHY WOULD YOU THINK THAT :V
I like the other professor a little better I feel like his lectures are more random and less structured...I felt like this professor was just teaching by the book...But they're are both great sup lectures
No, the professor explains how E’s asymptotic upper bound is V^2(imagine each vertex containing an edge to every other vertex) therefore V * E = V * V^2 = V^3 (asymptotic upper bound)
I can feel the pain. The reason why sometimes he is not delivering the lectures is probably the fact that Dr. Devadas is not a mathematician like Erik.
Negative takes so much work with squares and cubes. People don’t want what appears to be infinities of work. They want a genesis of general and fast tracked work.
You get to appreciate the quality of a lecture after watching something like this. Where's Eric??? I think this guy forgot whats' the point of lectures, so he just rambles.
