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This general form of problem is a facility location problem. The specific version you're asking about is a covering problem – you have a set of points (the houses) and you're trying to cover them with …

It appears that you have a periodic scheduling system on a single processor where task $i$ must run for $C_i$ seconds out of every $T_i$. If this is the case, then the requirement that $\tfrac{C_i}{T …

There's no possibility of an efficient algorithm here, unless you have more information about $T$. $T$ might only return true for one input and, in the worst case, you'd have to try all $2^n$ possibil …

This is just the assignment problem: you need to find a maximum-weight matching between the users and frequencies. The Hungarian algorithm solves this in time $O(n^3)$.

This is a knapsack problem. In the most basic version, you have a single resource (e.g., space in your knapsack) and you're trying to choose which items to put in it so you can carry the greatest valu …

Full details are in Robert L. Karg and James L. Thompson, A Heuristic Approach to Solving Traveling Salesman Problems (Management Science, 10(2):225–248, 1964). The PDF is available from JStor and In …

You need to formally define the computational problem. It appears that the input is "a programming language" and the output is the length of the shortest quine in that language. But how is the program …

Represent the events as a bipartite graphs: the vertices are the users and subjects and the edges are events (so there's an edge from user $x$ to subject $y$ if there's an event involving that user an …

It's called four-dimensional matching and it's NP-complete.

The problem of finding a longest simple cycle in a digraph is NP-hard, since the problem of finding a longest simple cycle in an undirected graph is a special case: you can consider an undirected grap …

Any recursive algorithm can be rewritten to use iteration. After all, a Turing machine knows nothing about recursion but can implement any algorithm. In principle, you can rewrite your recursive funct …

An optimization problem is an example of a function problem: i.e., one where the task is to map some input to some output. The class of function problems solvable in polynomial time is FP. … (Note that there is a class OptP but that's not the polynomial-time optimization problems. …

Let your vertex set be $\{v_1, \dots, v_n\}$. If $n\leq5$, just add all possible edges. Otherwise, create a new graph with vertices $\big\{v_{i,j}\mid i\in\{1, \dots, n\},\ j\in\{1, 2, 3, 4\}\big\}$ …

narek gives the polynomial-time algorithm. The more general problem is the facility location problem. This includes several problems but the basic idea is that you want to know where to build your res …

This answer will probably be quite annoying... To be explicit, your bin packing problem is: find a way of assigning items of size $s_1, \dots, s_k$, to the minimum number of bins such that no bin con …