# All Questions

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### Removing all but a few cycles in a graph

Let problem $S$ be defined as Given undirected graph $G$ and a set of cycles $C_1,C_2, \ldots, C_n$ in G, find minimum number of vertices that need to be deleted to remove all cycles in the ...
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472 views

### Visualizing Unique Games

How would you design a picture to illustrate the unique games conjecture? This is for a "Current Events" presentation on unique games at the next AMS Joint Meeting and for the booklet that will be ...
• 4,902
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### Using Kolmogorov complexity to establish proof complexity lower bounds?

The motivation for this question is the fact that most n-bit strings are incompressible. Intuitively, we can propose by analogy that most proofs for Tautologies are incompressible to polynomial size. ...
4k views

### Semantic vs. Syntactic Complexity Classes

In his "Computational Complexity" book, Papadimitriou writes: RP is in some sense a new and unusual kind of complexity class. Not any polynomially bounded nondeterministic Turing machine can be the ...
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### Optimal greedy algorithms for NP-hard problems

Greed, for lack of a better word, is good. One of the first algorithmic paradigms taught in introductory algorithms course is the greedy approach. Greedy approach results in simple and intuitive ...
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### NP-hard problems on trees

Several optimization problems that are known to be NP-hard on general graphs are trivially solvable in polynomial time (some even in linear time) when the input graph is a tree. Examples include ...
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1k views

### NP-complete variants of undecidable problems?

Examples of bounded $NP$-complete variants of undecidable sets: Bounded Halting problem={ $(M, x, 1^t)$| NTM machine $M$ halts and accepts $x$ within $t$ steps} Bounded Tiling={ $(T, 1^t)$| there is ...
703 views

### Hardness Guarantees for AES

Many public-key cryptosystems have some kind of provable security. For example, the Rabin cryptosystem is provably as hard as factoring. I wonder whether such kind of provable security exists for ...
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### What videos should everybody watch?

Stanford University now has a Youtube channel, with free access to HD video of full courses on everything from dynamical systems to quantum entanglement. More conferences and workshops are ...
1 vote
16k views

### What is the k-SAT problem? [closed]

First of all I am of course aware of the wikipedia article: http://en.wikipedia.org/wiki/Boolean_satisfiability_problem However I still do not understand exactly what the problem is. To demonstrate ...
• 145
966 views

### Graph Theory Fun Problem

Show that in any graph $G$ with min-degree $k$ ($k \geq 1$ duh!) you can find as its subgraph any tree on $k+1$ vertices. I have not been able to solve the question so far. However, I would like if ...
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### What papers should everyone read?

This question is (inspired by)/(shamefully stolen from) a similar question at MathOverflow, but I expect the answers here will be quite different. We all have favorite papers in our own respective ...
873 views

### Universal Turing Machines in "Computational Complexity" by Papadimitriou

The first part of this question has been solved (see comments). In the book "computational complexity" by Papadimitriou, a Universal Turing Machine is given. But this machine is not concrete, in the ...
1k views

### Projective Plane of Order 12

Objective: Settle the conjecture that there is no projective plane of order 12. In 1989, using computer search on a Cray, Lam proved that no projective plane of order 10 exists. Now that God's ...
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351 views

### How can I model this usage scenario mathematically?

I want to create a fairly simple mathematical model that describes usage patterns and performance trade-offs in a system. The system behaves as follows: clients periodically issue multi-cast packets ...
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### How do I formally describe a rooted, directed, acyclic graph?

I need a formalism to describe the following requirements: I have a graph comprised of nodes and transitions between nodes Nodes maybe one of three types, all are sub-classes of a base abstract node ...
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### Introduction to spectral graph theory

What are the basic references? Are there any good, high-level surveys of SGT and its applications to CS in general and machine learning more specifically?
440 views

### Is this problem mappable to 3SAT or is it weaker than 3SAT?

Consider a variant of a satisifiability problem. Given n dimensions (n >= 3, n < 10,000 think of n as large but finite) The range of each dimension is either an interval over the integers or an ...
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530 views