Problem Detail: When using Ford-Fulkerson to find max-flow between s and t, the exact choice of flow-graph depends on which paths are found. However, if you then use the left-over residual graph to produce a min-cut (by flood-filling outward from s Read More …
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[Solved]: Proving a specific language is regular
Problem Detail: In my computability class we were given a practice final to go over and I’m really struggling with one of the questions on it. Prove the following statement: If $L_1$ is a regular language, then so is $L_2 = Read More …
[Solved]: Can finding a witness be NP-hard even if we already know there is one?
Problem Detail: The common examples of NP-hard problems (clique, 3-SAT, vertex cover, etc.) are of the type where we don’t know whether the answer is “yes” or “no” beforehand. Suppose that we have a problem in which the we know the Read More …
[Solved]: $L(M) = L$ where $M$ is a $TM$ that moves only to the right side so $L$ is regular
Problem Detail: Suppose that $L(M) = L$ where $M$ is a $TM$ that moves only to the right side. I need to Show that $L$ is regular. I’d relly like some help, I tried to think of any way to prove Read More …
[Solved]: Counting trees (order matters)
Problem Detail: As a follow up to this question (the number of rooted binary trees of size n), how many possible binary trees can you have if the nodes are now labeled, so that abc is different than bac cab etc Read More …
[Solved]: Testing Polygon for Monotonicity
Problem Detail: It’s well known that Monotone polygon plays a crucial role in Polygon triangulation. Definiton: monotone polygon – a polygon $P$ in the plane is called monotone with respect to a straight line $L$, if every line orthogonal to $L$ Read More …
[Solved]: Difference between symbolic execution and reachability analysis
Problem Detail: Now I am confused about symbolic execution (SE) and reachability analysis (RA). As I know, SE uses symbols to execute some code to reach each branch with branch conditions. And RA can be used to find the reachability of Read More …
[Solved]: Little’s law and average time on a system with a switch
Problem Detail: We have a switch with $2$ lines of input and $2$ output. Each line is $10 Mbps$. The size of packets is fixed and is $1KB$. The $1^{st}$ line of input is active (transferring packets) $40%$ of the time, Read More …
[Solved]: Sorted-greedy for Load Balancing Problem
Problem Detail: In load balancing problem we have $m$ machines and $n$ jobs, each taking processing time $t_j$. Total processing time on the machine $i$ is $T_i =sum_{jin A(i)}{t_j}$, where $A(i)$ is the set of jobs assigned to machine $i$. Goal Read More …
[Solved]: From Whence the Randomization in Randomized Quicksort
Problem Detail: Cormen talks briefly about the advantages of picking a random pivot in quicksort. However as pointed out here(4th to the last paragraph): Using a random number generator to choose the positions is relatively expensive So how is picking a Read More …
