general questions about selecting a best element from some set of available alternatives.

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1
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0answers
58 views

Sync time between two points

Suppose we have two points, A and B, each point has its own clock. We are able to send messages between ...
2
votes
0answers
46 views

How hard is it to compute an approximately optimal non-greedy CART tree?

The question itself is closer to the bottom of this post, and is formulated without any rerefence to the term "CART". Motivation: In traditional CART (Classification and Regression Trees), one ...
5
votes
0answers
167 views

Permutation optimization problem

Here is the problem as posed by Jerrum: "The computational complexity of the following problem is investigated: Given a permutation group specified as a set of generators, and a single target ...
1
vote
1answer
311 views

finding “hubs” in a graph

consider the problem: given a graph and a number of vertices $n$ less than the vertices in the graph, and a distance $d$. find a set of $n$ vertices such that all vertices of the graph are within $d$ ...
3
votes
1answer
397 views

Subset of a bipartite graph with maximal number of minimal unmatched vertices

Given a bipartite graph $G = (U \sqcup V, E)$ with sets of vertices $U$ and $V$ and edge set $E \subseteq U \times V$, a matching $M$ is a subset of $E$ whose edges have no common vertices: for all ...
0
votes
0answers
299 views

dynamic algorithms for the subset-sum problem hold for vectors?

I have a vector (er, array) that is the sum of a number of other known vectors. I would like to reverse the process and find the specific known vectors that were summed to make the final vector. The ...
2
votes
0answers
85 views

KKT-like conditions for values close to optimal solution

The KKT conditions are necessary and sufficient conditions for problems where we maximize over a convex function subject to linear inequality and equality constraints. That is $x^*$ is an optimal ...
3
votes
1answer
418 views

Is it NP-Complete to determine if a quadratic program (QP) has multiple solutions?

If this is known, can someone point me to a proof? Edit: A QP is essentially a LP with a quadratic objective. That is, it looks like: minimize $\frac{1}{2} x^T Q x + c^T x$ s.t. $Ax \leq b$ It's ...
2
votes
0answers
106 views

Tiling a rectangle with weighted cells (min-max problem)

Given a sparse matrix $A[1..n, 1..n]$ containing cells with integer value of either $0$ or $1$, partition it in $J$ non-overlapping axis-parallel 2D rectangles, such that each $1$-cell is covered by ...
-5
votes
1answer
250 views

Attacking TSP via small nonintersecting circuits

Consider the problem of finding smaller "non-intersecting" circuits or paths in graphs embedded in the euclidean plane (visiting all vertices) in the sense of geometric intersections of edges plotted ...
3
votes
1answer
88 views

Questions about Farhi's pre-Adiabatic paper

I have been going through Eddie Farhi's 6-pages long pre-Adiabatic paper, An Analog Analogue of a Digital Quantum Computation. I guess I understand most of the math and physics but I am struggling ...
1
vote
0answers
30 views

Nonlinear optimization using parallel input/output

I have a system that accepts a vector and returns a function value. The goal is to change the elements of the vector such that the function value is minimized using a derivative-free solver, eg. using ...
3
votes
0answers
105 views

Symmetry of optimal solutions to discrete optimization problems

Given a graph, say one wants to find the clique number, independence number, chromatic number, vertex cover number etc., one knows that a solution exists. However if the solution space has more than ...
11
votes
2answers
373 views

Linear time algorithm for finding shifted max

Assume that we are given an array $A[1..n]$ containing nonnegative integers (not necessarily distinct). Let $B$ be $A$ sorted in the nonincreasing order. We want to compute $$m = \max_{i\in [n]} ...
3
votes
1answer
103 views

Approximation algorithms for multicut for special classes of graphs

The multicut problem is the following. Given a graph $G=(V,E)$ with edge costs $c_e$ for edge $e$ and a set of $k$ terminal pairs $\{(s_1,t_1),\ldots,(s_k,t_k)\}$, the objective is to find a set of ...
-3
votes
1answer
96 views

what problem is this? [closed]

I have this instance: Let's say I have two (could be more) friends, one weighing 200 pounds and another weighing 100 pounds; I won a box with 30 chocolates in a contest and I want to divide among ...
-1
votes
1answer
1k views

Program optimization - 90/10 law

I found this "law" somewhere on Wikipedia: In software engineering, it is often a better approximation that 90% of the execution time of a computer program is spent executing 10% of the code ...
5
votes
1answer
127 views

Investigation of Symbol Minimal Context-Free Grammars for the Language $a^n$

Question Given the language $L_n = \{ a^n \}$ for a natural number $n \geq 2$. Is there a symbol minimal context-free grammar $G$ that generates $L_n$ and contains a rule of the form $A \rightarrow ...
2
votes
0answers
175 views

Quadratic Binary Optimization formulation of Steiner Tree problem

can someone point out to me a solution or give advice on how to formulate as efficiently as possible in terms of number of bits the minimum Steiner tree problem as a 0-1 quadratic optimization ...
1
vote
1answer
117 views

Looking for algorithm (or at least name) for this optimization problem

Suppose that we have $n \geq 2$ distinct triplets $t_0, t_1, ..., t_{n-1}$ of real numbers, $t_i = (x_i, l_i, r_i)$. Define $$\Delta(s) = \max_{i, j} \left[ s (x_j - x_i) + (r_j - l_i) \right]$$ The ...
1
vote
0answers
96 views

Why do people like using evolution computing techniques like GA on multi-objective optimisation?

I am new to the field of multi-objective optimisation and I try to find some books to read on this topic. Yet when I search around my library I found there are many books on using evolution computing ...
1
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0answers
229 views

Time complexity of clustering based on random walk

What is the time complexity of the following algorithm (from this paper suggested by Zhou) to partition directed graph? Can I use the complexity of eigen vector computation for this purpose? The ...
3
votes
1answer
139 views

Complexity class for Optimization problems over #P functions

Is there any complexity class which contains problems that can be expressed as an optimization over polynomially many #P functions ? i.e: $$\tilde{f}(x) = \text{Max}_{f \in F}f(x)$$ where $f\in\# ...
1
vote
0answers
82 views

Has anybody studied the problem of finding maximal weighted rooted spanning DAGs?

Let G=(V,E) be a directed weighted graph (not necessarily a tournament) and s be a special node of G so that all nodes in G are reachable from s. The problem is to find a subgraph G'=(V,E') of G so ...
0
votes
0answers
161 views

Continuous version of rod cutting

This is an attempt to extend an idea from Computer Science.. the dynamic programming based solution of the rod cutting problem (given a rod of an integral length and an array of prices for each ...
-1
votes
1answer
149 views

Is l1-norm works better that l2-norm in minimization using projection method?

Given a vector of errors $e(x)$ obtained by variable $x$ In the following problem : $min_x || e(x) ||$ Besides the robustness, consider only convergence speed, is it l1 norm works better than l2 ...
0
votes
1answer
118 views

Finding Tours through Near-Hamiltonian Paths?

Say I have a connected graph. I want to find a tour that visits each vertex at least once. It's not always possible, though, for there to be a solution if there is a bridge in the graph. Is there a ...
4
votes
1answer
156 views

Minimize in polynomial time a super-additive increasing function under linear constraints?

I am looking for references whether this problem can be doable in polynomial time (or other known approximation results): Let $f$ a super-additive function ($\forall x,y, f(x+y) \geq f(y)+f(y)$), $$ ...
2
votes
0answers
125 views

Proving greedy algorithm is optimal for a scheduling problem

First, the problem discription: For a sequence of $4n$ tasks, $a_1a_2\dots a_{4n}$, where $a_i\in\{0,1\}\forall i$, put them sequentially to the tail of one of the two initially empty queues of ...
2
votes
0answers
89 views

Optimal additive basis for decomposing/partitioning an integer as a sum of two integers

I'm going to be given a positive integer $z$, and I want to find an optimal basis $B$ that is good for $z$. A basis $B$ is a multiset of positive integers. The basis $B$ is considered good for $z$ ...
11
votes
0answers
164 views

the largest element of a matrix product

Given two matrices, I'm interested in finding the largest element of their product. I wonder if it's possible to do it significantly faster than the matrix multiplication the solution seems to ...
1
vote
1answer
156 views

Ising spin vs Pauli spin matrices [closed]

Are Ising spins scalar or operators? I am not a condensed matter physicist hence having some confusion. I have learnt about Ising models from adiabatic quantum algorithm papers. For example this ...
3
votes
3answers
666 views

Maximize quadratic function subject to linear constraints

Can one maximize $\sum_i c_i x_i^2$ where the $c_i$ are constants (possibly negative), subject to linear constraints over the $x_i$? This paper seems to come close to answering "no." They show it is ...
0
votes
1answer
2k views

Quantum annealing vs adiabatic quantum computation

I had this impression that quantum annealing is an optimization technique which may or may not produce exact solutions. On the other hand adiabatic quantum computation always gives exact solutions ...
3
votes
0answers
72 views

Closest Vector Problem with sparse basis and target vector

The Closest Vector Problem (and related problems) is random self-reducible and in general is NP-Hard, making it a useful tool in cryptography research and post-quantum public key crypto. For a variety ...
10
votes
0answers
171 views

Expected length of a self-avoiding random walk

We're given an arbitrary graph $G=(V,E)$. A self-avoiding random walk is a random walk such that in each step, a random neighbour which was not previously visited is chosen, if such one exists. ...
1
vote
0answers
270 views

Confusion related to L1 and L2 svm [closed]

I have this confusion related to L1 and L2 svm. It is given in this paper that The dual problem is given by $$ min(\alpha) = 1/2*\alpha^T\hat Q\alpha - e^T\alpha $$ subject to $$ 0 <= \alpha_i ...
1
vote
1answer
170 views

Poly-time Algorithm for Non-Linear Optimization

As we know, linear programming is one of the most basic area of optimization theory, and computing an optimal solution can be excuted within poly-time. My question is about an extention of this ...
2
votes
2answers
265 views

Undecidability of program optimization

A program is an encoded Turing Machine. And a size optimizer of a program is a TM $M_1$ such that: On any input $M$, $M_1$ outputs $M_{min}$ such that $M_{min}$ is the shortest TM which is ...
3
votes
1answer
188 views

A weighted sorting problem

Given a data matrix $D=[d_1 ... d_N]$, one would like to sort it in terms of rows such that the weighted distance of sorted $d$s to a target vector $y$ is being minimized. It can be formulated as ...
1
vote
0answers
140 views

What does “no integrality gap” implies?

I'm currently working on a linear time heuristic for the rectangle decomposition of binary matrix. This problem has a polynomial time solution, which in our case it too slow for large scale ...
-2
votes
2answers
276 views

how do you turn an algorithm for a decision problem into an algorithm for an optimization problem?

It is well-known, I believe, that theoretically, in quite a few cases, an algorithm that solves a decision problem can be turned into an algorithm that solves the corresponding optimization problem. ...
2
votes
0answers
69 views

Small area containing large amount of patterns

The problem: I come across a theoretical problem when designing characters for electron-Beam lithography. Abstractly, given an integer $m$, let $\mathcal{M}$ be the set of $(0,1)$-matrix $A_{p\times ...
3
votes
0answers
204 views

Slightly Faster Exponential Algorithm for Integer Programming with Multi-linear Variables

Integer programing is one of the most narutal optimization tools. As an analogy of DNF or CNF in the Boolean function theory, we can consider the following equation. $x_{1}x_{2}x_{3}+$ ...
1
vote
0answers
151 views

What is the shape of cost function of weighted graph matching problem?

According to Umeyama, the weighted graph matching problem can be formulated as $min_P || PA_GP^T - A_H ||$ s.t. $P$ is a permutation matrix. where $A_G$ and $A_H$ are n-by-n matrices If we relax ...
3
votes
0answers
128 views

Existence of complete “asymptotic” optimization problems

Define a function $u:\lbrace 0,1 \rbrace^* \rightarrow \mathbb{R}$ to be an asymptotic optimization problem when the following conditions hold: There is an algorithm $U$ which computes the first $n$ ...
8
votes
2answers
531 views

Generating interesting combinatorial optimization problems

I'm teaching a course on meta-heuristics and need to generate interesting instances of classic combinatorial problems for the term project. Let's focus on TSP. We are tackling graphs of dimension ...
0
votes
0answers
92 views

Nonmetric TSP and Functional Compleixty Classes

Non-metric TSP that is TSP and some instance is not hold the triangle inequality is NP-hard by gap-reduction method. Is this general TSP a complete problem in some functional complexity classes ? ...
-1
votes
1answer
312 views

Integer compression

I'm looking to devise a scheme for compressing integers which have a known sampled distribution (they might be clustered around a value, say, or have several areas of differing density). So far, I've ...
2
votes
0answers
100 views

Benchmarks for approximation algorithms

I'm working on a Haskell library for approximation algorithms. In particular, I'm working on Partition, Knapsack, Vertex Cover, and possibly a few others. Of course, I'd like to benchmark my library ...