Author: ignougroup

Problem Detail: Here is a definition from the functions section in my discrete math textbook (Discrete Mathematics and its Applications 7e, Rosen 2012): Let $f$ be a function from $A$ to $B$, and let $S$ be a subset of $A$. The Read More …

Problem Detail: This a homework question from Udi Manber’s book. Any hint would be nice 🙂 I must show that: $n(log_3(n))^5 = O(n^{1.2})$ I tried using Theorem 3.1 of book: $f(n)^c = O(a^{f(n)})$ (for $c > 0$, $a > 1$) Substituing: Read More …

Problem Detail: I know that Big O is used to bound worst case running time. So an algorithm with running time $O(n^5)$ means its running time in worse case is less than $n^5$ asymptotically. Similarly, one can say that for example Read More …

Problem Detail: Say that for a particular problem, e.g., the independent set problem, it has been shown that no polynomial-time algorithm exists to solve it. Could we get around this by finding an algorithm which approximates the solution to a certain Read More …

Problem Detail: I am concerned with the question of the asymptotic running time of the Ukkonen’s algorithm, perhaps the most popular algorithm for constructing suffix trees in linear (?) time. Here is a citation from the book “Algorithms on strings, trees Read More …

Problem Detail: I am making database on Disaster Management. There are four tables. DisasterEvent (eventid, name, glideID, status, description, date_occurred, date_ended, disaster_type) People(eventid, num_deaths, num_injuries, num_affected) Homes (eventid, num_homes_destroyed, num_homes_damaged, total_insured_loss, total_uninsured_loss) Place (place_id, city, state, country, postal_code) In my design, Read More …

Problem Detail: At the Wikipedia article on time complexity, only a PRAM example is given for polylogarithmic time. Let $T(n)$ denote the largest number of steps used by a machine to reach a final state on any input with size $n$ Read More …

Problem Detail: I can see how adding 2 unsigned four-bit values is $O(n)$. We just go from the rightmost digits to the leftmost digits and add the digits up sequentially. We can also perform multiplication in polynomial time ($O(n^2)$) via the Read More …

Problem Detail: I’m currently dealing with a problem for which I could show that an exact algorithm would imply a general algorithm for finding the real (but not complex) roots of an arbitrary univariate polynomial with real coefficients. Now, what exactly Read More …