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

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0
votes
1answer
65 views

TSP heuristics for limited distance information

this is my first question on Theoretical CS. :) I've posted a similiar question on Mathoverflow and a friendly user advised me to post my question on this site. Problem: I'm looking for TSP ...
-1
votes
0answers
33 views

The maximum of a submodular function which has no restrictions

The problem is to verify whether the maximum is greater than 0. It is mentioned in papers and various tutorials that the problem is NP-hard. For example, in footnotes of [1] and [2]. However, ...
10
votes
0answers
197 views

How good is greedy in average?

Given a family ${\cal F}\subset 2^E$ of (feasible solutions), the maximization problem on ${\cal F}$ is, for every weighting $x:E\to \{0,1,\ldots\}$ of ground elements, to compute the maximum weight ...
0
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0answers
148 views

How to solve such a graph optimization problem?

I have a graph optimization problem which is hard to describe in the title. There is a component based system which consists of components and data transmissions between components(components and ...
5
votes
1answer
72 views

Is computing the dual optimum of a degenerate LP equivalent in complexity to solving LP?

Given a primal LP and an optimum solution thereof, it is well-known that complementary slackness conditions [1] can be used in non-degenerate cases to produce a dual optimum solution. For instance, ...
2
votes
0answers
75 views

Complexity: simulated annealing vs. quantum annealing

How do I compare the performance of simulated annealing against the performance of quantum annealing algorithms? In Convergence theorems for quantum annealing by Morita and Nishimori, it has been ...
2
votes
0answers
59 views

Dynamical systems analysis of deep learning

I am interested in finding out references that apply dynamical systems analysis to develop the "theory" of deep learning, specifically (say) feedforward deep neural nets. The only paper I seem to have ...
0
votes
0answers
46 views

Preventing cycling in the simplex method

In Matoušek and Gärtner's excellent book, Understanding and Using Linear Programming, they discuss various pivot rules and in particular ones designed specifically to avoid cycling. Unfortunately, ...
2
votes
0answers
81 views

Is minimizing sum of distances hard?

The Problem Given a set of $n$ points $S = \{v_1, v_2, \cdots, v_n\} \subset \Re^d$, find a unit vector $s \in \Re^d$ such that $s$ minimizes $$ \sum_{i=1}^{n}\sqrt{\|v_i\|^2 - \langle v_i, s ...
13
votes
1answer
201 views

Second Smallest $s$-$t$-Cut in a Network

Is anything known about the second smallest $s$-$t$-cut in a flow network? Or, more general, about this problem: Input: A network $N$ and a number $k$, all in binary. Output: A $k$th smallest ...
8
votes
0answers
240 views

Is the complexity of this covering problem known?

Let $G=(V,E)$ be a graph. A vertex set $X\subseteq V$ is called critical if $X\neq\emptyset$ and no vertex in $V\setminus X$ is adjacent to exactly one vertex in $X$. The problem is to find a vertex ...
25
votes
5answers
3k views

Is it a rule that discrete problems are NP-hard and continuous problems are not?

In my computer science education, I increasingly notice that most discrete problems are NP-complete (at least), whereas optimizing continuous problems is almost always easily achievable, usually ...
5
votes
1answer
157 views

Numerical precision in sum-of-squares method?

I have been reading a bit about the sum-of-squares method (SOS) from the survey of Barak & Steurer and the lecture notes of Barak. In both cases they sweep issues of numerical accuracy under the ...
8
votes
2answers
104 views

Reordering data to optimize for compression?

Are there any algorithms for reordering data to optimize for compression? I understand this is specific to the data and the compression algorithm, but is there a word for this topic? Where can I ...
5
votes
0answers
83 views

Optimizing over symmetric polynomials [closed]

Consider the following constraint satisfaction problem: Let $\alpha_1 , \ldots, \alpha_k \in \mathbb{R}$ be given as well as an error parameter $\epsilon$. Find $p_1, \ldots, p_n$ such that (i) $0 ...
3
votes
1answer
197 views

Good algorithms to solve ATSP

What are some good neighborhood-based local search algorithms or strategies to solve the Asymmetric TSP ? I see many 2-OPT and K-opt based algorithms (e.g. Lin-Kernighan implementations), but I think ...
2
votes
1answer
102 views

Is there a name for this Assignment definition

The standard Assignment Problem asks for an optimal one-to-one assignment between agents and tasks. Now consider the following generalization: Instead of specifying a cost of a single agent-task ...
2
votes
0answers
105 views

What is the most “unbalanced” vector between two given vectors of numbers?

Let $\mathbb{R}_+$ be the set of non-negative real numbers. Let $m$ be a positive integer and $\leq_m$ the product ordering on $\mathbb{R}_+^m$. That is, $\leq_m$ is the partial ordering on ...
0
votes
0answers
104 views

Steiner Tree and minimum spanning tree

If I must connect: $$2^k$$ terminals in a Steiner Tree choosen randomly and connect them with the cheapest component; "loss - contracting algorithm" is a good way? Or is an "Iterative Randomized ...
2
votes
1answer
117 views

minimal finite automata given in-words and out-words

this seems an interesting FSM optimization problem; have not seen it studied, wondering if it has been and/ or looking for other insight. given: two finite sets of words $S_{in}$ and $S_{out}$. ...
0
votes
0answers
58 views

Approximation Algorithm for TSP-like problem

Suppose we are given a graph with distances for each of the edges and merit for each of the nodes. What are the best (approximation) algorithms for computing the the most meritorious simple path with ...
1
vote
0answers
66 views

Follow the Perturbed Leader for nonlinear cost functions

The famous FTPL algorithm [1] is analyzing linear cost function. Is there any generalized proof for nonlinear functions known? Note that in the last paragraph of [1] it says "It would be great to ...
1
vote
1answer
46 views

direct connection between gradient descent and follow the (perturbed) leader algorithm or weighted majority?

Is there a direct conversion between gradient descent ([1], Alg 1 ) and any of the following algorithms? 1) Weighted Majority: http://onlineprediction.net/?n=Main.WeightedMajorityAlgorithm 2) ...
1
vote
2answers
116 views

Finding the paths through a graph that reuse as many of the nodes as possible

I'm implementing an encryption algorithm which does a bunch xor operations to mix up the columns. Because I want to find the lower bound of the number of ...
17
votes
2answers
176 views

Minimal cumulative set sum

Consider this problem: Given a list of finite sets, find an ordering $s_1, s_2, s_3, \ldots$ that minimizes $|s_1| + |s_1 \cup s_2| + |s_1 \cup s_2 \cup s_3| + \ldots$. Are there known algorithms ...
13
votes
0answers
114 views

What is the state of the art in cache algorithm theory?

I recently became interested in the general problem of optimizing memory usage in a situation where there is more than one kind of memory available, and there is a trade-off between the capacity of a ...
3
votes
1answer
109 views

Approximation algorithms for min vector subset-sum over GF(2)

In this question vzn asked about the following problem, which I'll call Vector-Subset-Sum. Given a set of vectors $v_i$ over GF(2) and a target vector $y$, is there a subset of the $v_i$ summing ...
0
votes
1answer
92 views

Finding optimal subset for quadratic function

Given a set of $n$ elements $e_1,...e_n$ where each element $i$ is associated with two positive integers $\alpha_i$ and $\beta_i$. Given another integer $\lambda$, the goal is to find a set $S$ of ...
12
votes
2answers
383 views

What is this variant of set cover problem known as?

Input is a universe $U$ and a family of subsets of $U$, say, ${\cal F} \subseteq 2^U$. We assume that the subsets in ${\cal F}$ can cover $U$, i.e., $\bigcup_{E\in {\cal F}}E=U$. An incremental ...
5
votes
0answers
140 views

lower bound for difference between max cut and min cut

Let $G=(V,E)$ be a graph on $n$ vertices with edge weights $w=(w_e)_{e\in E}$. Let $M^+$ and $M^-$ be the maximum and the minimum cut values, i.e. ...
1
vote
0answers
164 views

Dynamic Programming with two optimization goals

I am working on the problem of distributed database query planning. Existing work [1] uses dynamic programming to search the potential query plan space and find the one with minimal cost. However, I ...
1
vote
0answers
281 views

exact cover set problem

i am searching an heuristic algorithm for a weighted exact cover problem shown here: http://en.wikipedia.org/wiki/Exact_cover On my research i only found algorithm which calculates all solutions ...
8
votes
1answer
366 views

Fast algorithm for weighted bipartite matching problem

I have a set of $n$ agents and a set of $n$ tasks, and I need to assign each agent to exactly one task such that a cost is minimised. Some agents are incompatible with some tasks. I have an ...
7
votes
0answers
93 views

Computing the most likely winner in elections : intermediate case between Kemeny and Borda?

Given $n$ possible alternatives satisfying some unknown linear ordering, a multiset of pairwise votes, i.e., a matrix $M\in\mathbb{N}^{n\times n}$: $M_{i,j}$ counts the number of votes for which ...
0
votes
0answers
53 views

LP solver for sparse, PSD and strictly diagonally dominant matrix

I have a linear problem with a sparse, psd and strictly diagonally dominant matrix. Can you please point me to some known best solvers (in terms of runtime, or easy to be practically optimized for ...
6
votes
0answers
212 views

NP-hardness of tasks graph assignment to two heterogenous servers

I have a problem with determinig if the following assignment problem is NP-hard. Any comments and suggestions would be appreciated. Problem definition Given is a directed acyclic graph $G=(V,E)$ ...
1
vote
0answers
112 views

Automatically Adapting Forgetting Factor for Online EM

I've been reading some interesting papers recently on methods for automatically and adaptively setting the learning rate in stochastic gradient descent (SGD). In particular, "No more pesky learning ...
2
votes
0answers
55 views

Linear ordering of bipartite tournament graphs

I have an ordered bipartite graph such that every node of the first node set is connected to every node in the second node set by an edge of a given direction (i.e., a so-called bipartite tournament ...
1
vote
0answers
68 views

Proof of convergence of alternative minimization/maximization [duplicate]

Given a problem \begin{equation} \max_{x\in X} \min_{y \in Y} f(x,y) \end{equation} where $f$ is strongly convex in $Y$ and strongly concave in $X$ How to show that the following iterative ...
3
votes
2answers
160 views

Iteratively minimizing the function

Consider the problem \begin{equation} \min_{x\in X, y \in Y} f(x,y) \end{equation} Can I solve the problem by iteratively solving the following two sub problems? \begin{equation} x_{k+1} = ...
0
votes
0answers
34 views

arithmetic formula simplication

Consider a function $f : \mathbb R^m \rightarrow \mathbb R^n$. Function $f$ can be written down as a simple arithmetic program. It uses addition, subtraction, multiplication and division - however, ...
4
votes
3answers
496 views

Is it possible to optimize the calculation of $ax+b$ once I know $a$ and $b$?

An "algorithm" for calculating $ax+b$ would take the steps Calculate $a$ times $x$ Calculate $b$ plus the result of previous line. But if the values of $a$ and $b$ are known, can we create a more ...
7
votes
3answers
189 views

Job scheduling: minimizing number of reads

Consider the following scheduling problem: input: set of computations $C = \{c_1, ..., c_n\}$ set of computing nodes $P = \{p_1, ..., p_n\}$ Dependency graph $D$ between jobs (DAG) $(c_i,c_j)$ ...
0
votes
0answers
78 views

Are there any approaches to the following scheduling problem?

Consider the following problem: we are given $K$ tasks $\langle n_1, n_2, ..., n_K \rangle$. Every task $n_i$ is qualified with two parameters: The time it takes to be completed ($t_i$) and, The ...
1
vote
0answers
73 views

Gilmore-Lawler bound for the QAP

I'm stuck with trying to implement the Gilmore-Lawler bound procedure for the quadratic assignment problem (QAP). That is, a bound one can use with a branch and bound algorithm to solve the QAP. I'm ...
2
votes
1answer
308 views

Existing benchmarks for scheduling problems?

Which benchmarks exist to evaluate the performance of algorithms for Job-Shop or Flow-shop scheduling problems?
2
votes
1answer
123 views

NP-hardness of a bilinear program?

Given $a_i, b_i, c_i, d_{ij}\in [0,1]$ for $i,j\in [n]$ and $i\neq j$ such that $\sum_{i\in [n]} a_i=1$ and $d_{ij}=d_{ji}$. I have the following bilinear program: max $\sum_{i=1}^n (x_i-a_i)y_i$ ...
6
votes
0answers
165 views

Is there a programming language where any arbitrary recursive function can be fused?

Compilers like GHC for Haskell use inlining as one of its most important optimising tools. Doing that is not possible for recursive functions, in general. A few techniques have been developed to amend ...
4
votes
0answers
121 views

Generating quadratic optimization problems amenable to quantum annealing

Some context: there is a current debate in adiabatic quantum computing over whether a particular machine, the D-Wave quantum annealer, can outperform a classical algorithm [*]. Earlier this year, a ...
1
vote
0answers
96 views

Optimization as LP on the convex hull of its solution space

I have heard claims that for a certain class of optimization problems, one can re-write the problem as a linear-programming problem on the convex hull of the solution space of the original problem ...