Problem Detail: Suppose we have $N$ fixed points (set $S$ with $|S|=N$) on the plane and $m$ agents with fixed, known initial positions ($m<N$) outside $S$. We should transfer the agents so that in our final configuration they are all positioned Read More …
Category: Uncategorized
[Solved]: Normalizing edge weights and the effect on Dijkstra’s algorithm
Problem Detail: If I had a graph $G$ with some negative edge weights, clearly Dijkstra’s algorithm does not definitely halt, since it might get caught in a negative cycle (shedding infinite weight). However, would finding the minimum weight (most negative weight) Read More …
[Solved]: Is Directed Graph a Graph?
Problem Detail: I came across an issue with the definition of a (directed) graph in Sipser’s Introduction to the theory of computation, 2nd Ed. On pp.10, An undirected graph, or simply a graph, is a set of points with lines connecting Read More …
[Solved]: Rules regarding Chomsky Normal Form (CNF) grammars
Problem Detail: I’m writing a context-free grammar that I hope will be in Chomsky Normal Form, and I have two questions: Can I use a single variable (a non-terminal) on the left-hand side of multiple rules? Can I use a single Read More …
[Solved]: From the LR(1) parsing table, can we deduce that it is also an LALR and SLR table?
Problem Detail: There is this question I read somewhere but could not answer myself. Assume I have an LR(1) Parsing table. Is there any way that just by looking at it and its items, can I deduce that it is also Read More …
[Solved]: Reduction between $Sigma^*$ and $emptyset$
Problem Detail: Throughout the subject of reductions, I was wondering: If we take $L_1 = Sigma^* $ and $L_2 = emptyset$, is $L_1 leq L_2$? is $L_2 leq L_1$? What I mean is, Is there some sort of reduction between any Read More …
[Solved]: Why is the running time of edit distance with memoization $O(mn)$?
Problem Detail: I understand without memoization it is going to be $O(3^{max,{m,n}})$ because every call results in extra three calls: thus we end up having a call tree with three children for each node, with height $max,{m,n}$, m and n being Read More …
[Solved]: Maximum I/O Data Transfer if DMA is used
Problem Detail: I was reading lecture notes of Universiti Malaysia Perlis when I am came across following question: A computer consists of a CPU and an I/O device $D$ connected to main memory $M$ via a shared bus with a data Read More …
[Solved]: The equivalence relations cover problem (in graph theory)
Problem Detail: An equivalence relation on a finite vertex set can be represented by an undirected graph that is a disjoint union of cliques. The vertex set represents the elements and an edge represents that two elements are equivalent. If I Read More …
[Solved]: Why is the orthogonal line segment intersection algorithm $O(nlog n+R)$ instead of $O(nlog n + Rn)$?
Problem Detail: In the same lecture notes without providing many details it says that the complexity of the algorithm which uses a balanced search tree is $O(nlog n+R)$ where $R$ is the total amount of intersections. However I don’t understand Read More …
