Problem Detail: Since, I don’t have strong algorithmic background my question may sound a litlle odd. Please correct me, if so. I have quite a large bitmap (~100 Million bits) (e.g. 100100101001010001001…010010). The bitmap is just an example, it doesn’t have Read More …
Author: ignougroup
[Solved]: Simplifying a nested sum
Problem Detail: I’m trying to analyze an algorithm of a function, I can express the function in term of summation, but I have no clues on how I could simplify this summation down to get the run-time in tern of big Read More …
[Solved]: Why is least fixed point (lfp) important in program analysis
Problem Detail: I am trying to get a big picture on the importance of least fixed point (lfp) in program analysis. For instance abstract interpretation seems to use the existence of lfp. Many research papers on program analysis also focus heavily Read More …
[Solved]: Reducing context-free languages with polynomial-time reductions
Problem Detail: So, let’s say we have two languages $L$ (which is any context-free language) and $M$ which is the basic CFL ${0^n1^n: ngeq 0}$. Can $L le_p M$ ? Why or why not? How do polynomial time reductions even work Read More …
[Solved]: Data structure for range-value-sum
Problem Detail: I have to be able to perform insert, delete, range-value-sum, and range-2-max-values with a data structure. Range-value-sum(xl,xr): with a range [xl,xr] (for a range query), it reports the sum of values of all elements whose keys are in the Read More …
[Solved]: Simple Pushdown Automaton
Problem Detail: I’m currently learning about PDAs and their power when constructing them from Context-Free Grammars, however I’m still unsure of how to properly construct a CFG, and then a PDA from that CFG. In the book, Formal Languages, Automata, and Read More …
[Solved]: Are there some real-world optimization problems with very cheap objective functions?
Problem Detail: Many real world optimization tasks (especially black box optimization) have objective functions, which are quite expensive to evaluate. For example to find the optimal shape of an airplane wing, a computer model of the wing needs to be constructed Read More …
[Solved]: How many possible assignments does a CNF sentence have?
Problem Detail: I’m having some trouble understanding the following: When we look at satisfiability problems in conjunctive normal form, an underconstrained problem is one with relatively few clauses constraining the variables. For eg. here is a randomly generated 3-CNF sentence with Read More …
[Solved]: Is it more effective to vote for a woman?
Problem Detail: A certain political party wants to encourage women to participate in their primary elections, so they decide, that the 4th position is reserved for a woman. That is, if there is no woman in the top 4 positions, then Read More …
[Solved]: Partition points in a plane with a straigth line
Problem Detail: Given are a 2D plane and a array of points in this plane, with every point having an integer value assigned. Is there an algorithm which, when given a ratio a/b, divides the plane with a straight line, so Read More …
