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Constrained Topological Sorting with bounded number of chains

In general, constrained topological sorting is NP-hard. Now we add another constraint to it, such that take any k+1 nodes and there will be at least one pair ...
181 views

NP-completeness of a specific topological sorting problem

Consider $(V, E)$ be a DAG, and $p_1, \dots, p_n$ be its topological sorting (i.e. such permutation $p$ of $V$ that $\forall(x, y) \in E.\ p^{-1}(x) < p^{-1}(y)$). Let's call the goodness of $p$ a ...
884 views

Minimum cost topological ordering

We are given a $n$ vertex directed graph $G=(V,E)$ and also given a cost function $c:V\times [n]\to \mathbb{R}$. Consider a topological ordering of the vertices, $v_1,\ldots,v_n$, the cost of the ...
1k views

Is feedback vertex set problem is solvable in polynomial time for 3-degree bounded graphs?

Feedback Vertex Set is NP-complete for general graphs. It is known to be NP-complete for degree-8 bounded graphs due to a reduction from vertex cover. The Wikipedia article says that it is poly-time ...
1k views

Are there any public synchronous discussion forums (slack, discord, etc.) for TCS

I'm a 2nd year masters student studying theoretical CS (algorithms to be precise). I would like to know if there are any public synchronous discussion groups (slack, discord, etc.) for TCS. CSTheory ...
42k views

What would a very simple quantum program look like?

In light of the announcement of the world's first programmable quantum photonic chip, I was wondering just what software for a computer that uses quantum entanglement would be like. One of the first ...
103 views

Why can MIP be restricted to just two provers?

In several places I see it referred to that the MIP class can be assumed to be two interactive provers that don't communicate with each other, rather than any polynomial number of provers. Why are ...
93 views

172 views

A boolean function $f: \{0,1\}^n \rightarrow \{0,1\}$ is chosen at random from all $2^{2^n}$ such $f$. What do the Fourier coefficients look like?

As in the title. I'm not sure where to start here. My guess is that in expectation at least a constant fraction are non zero, and as a result there would exist some "large" coefs. and some "small" ...
3k views

What tools do you use to give presentations?

I was wondering what tools that people in this field (theoretical computer science) use to create presentations. Since a great deal of computer science is not just writing papers but also giving ...
94 views

An integer programming on maximum number of triangles

Consider three distinct sets $A, B, C$ of $N$ elements respectively. For each pair of sets, say $A,B$, we introduce an variable for each combination of values $a,b$ as $x_{ab}$. Similarly, we ...
66 views

Hardness of vertex colouring on hypergraphs with $O(\log n)$ edges

I'm interested to know whether there has been any work done on the problem in the title. For the problem to be meaningful, we would naturally need that the hyperedges must have large ($\omega(1)$) ...
289 views

Proof that Entanglement Cannot Increase the Capacity of a Noiseless Classical Channel

I am aware that quantum entanglement cannot increase the asymptotic capacity of a noiseless classical channel. However, can anyone provide some type of reference in the literature that contains a ...
113 views

Languages whose Parikh image is recognizable

Let $\Sigma$ be some alphabet, and $p : \Sigma^* \to \mathbb N_0^{|\Sigma|}$ the Parikh map. A formal language $L \subseteq \Sigma^*$ is called a slip-language, if $p(L)$ is a semilinear set. By ...
64 views

How can I find dependent rounding procedures with the desirable properties?

I'm seeking for materials on dependent rounding. However, what I've found are two papers: Gandhi, R., Khuller, S., Parthasarathy, S., Srinivasan, A., 2006. Dependent rounding and its applications to ...
1k views

I come from mathematics and, for whatever reason, am trying to publish in theoretical computer science. I'm still trying to understand the role of conference proceedings, and I have two specific ...
101 views

Network design with reachability pattern

We are given two sets of terminals $A$ and $B$. For each $a\in A$, we are also given $R_a\subseteq B$. Let $|A|+|B|=n$. We want to find a directed acyclic graph $G$ where $A$ and $B$ are subsets of ...
470 views

Constraints on sliding windows

Let $L\subseteq \Sigma^*$ be a language of finite words and $n>0$ some integer. I would like to know if anything is known on the time and space complexity with respect to $n$ to check for ...
58 views

We know that X3C is NP-complete with |X|=3q and |C|=m. Is this problem still remains NP-complete if |C|<2q? [closed]

Exact-Cover-by-3Sets (X3C) is NP-complete. If the number of classes i.e. |C|<2q then whether this is version of X3C is NP-complete or not?
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125 views

Defining finite sets inductively in a proof assistant?

To represent finite sets within coq, we either use something like ListSet, which are just definitions on top of list, or we ...
135 views

How to efficiently find a loop between two nodes in a directed graph?

Given two nodes in a directed graph, how can I find a loop (if exists) that pass these two nodes? The loop cannot pass a node more than once. And if there isn't such a loop, how to efficiently ...
235 views

Is there an assumption that implies $P=ZPP$ which is not known to imply $P=BPP$?

There are assumptions that are known to imply that $P = BPP$. For example, if there exists a function in $E = DTIME(2^{O(n)})$ that has circuit complexity $2^{\Omega(n)}$, then $P = BPP$ [1]. Clearly, ...
79 views

NP-Hard or PTIME?

I am working on my research problem that essentially boils down to the following question. Consider an $N \times N$ matrix. There is a man at given a starting point $(x,y)$. In each unit of time, the ...
5k views

Oracle Construction for Grover's Algorithm

In Mike and Ike's "Quantum Computation and Quantum Information", Grover's algorithm is explained in great detail. However, in the book, and in all explanations I have found online for Grover's ...
116 views