Questions tagged [heuristics]

A heuristic is a procedure that can apply generically to many problems (for example gradient descent, alternating optimization, simulated annealing) but will typically not have formal guarantees associated with its use.

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39 views

Matching of two weighted graphs allowing one-to-many mapping

I am looking for a heuristic for a graph matching problem as follows. Given two graphs: $A$ (consisting of nodes $a_i$) and $B$ (consisting of nodes $b_i$). Typically the size of $B$ is larger than ...
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132 views

Is it possible to prove that a general purpose integer factorization algorithm must contain a loop?

1) Let $A$ be a (general purpose) algorithm that factors $n$. Suppose $A$ contains a loop (which is hard to imagine if not impossible that it does not.) If $A$ contains nested loops then these loops ...
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32 views

Pass ordering for greedy local search algorithms

Apologies in advance for the slightly general question - I'm really looking for pointers to research / good keywords to look for. I have a problem with the following setup: I have a (finite) totally ...
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85 views

On the goal of learned clause database reduction in CDCL SAT solvers

Modern SAT solvers frequently reduce the size of their learned clause database in order to keep its size as manageable as possible. This has as effect not to slow down the speed of unit propagations. ...
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241 views

Understanding performance of QFBV SMT solvers

SMT solvers such as Z3 or Boolector use a complex set of heuristics to solve problems. However, this also makes predicting the performance of such a solver for a given problem very hard. My question ...
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664 views

List of NP-hard problems, where there is active research in practical heuristics

I am looking for list of NP-hard optimization problems, where there is active research in practical heuristic for solving them and there are common benchmarks, which people try to beat. Examples ...
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86 views

Practical/heuristic algorithm for multi set-cover

Consider a universe $N$ containing $n$ elements, and a collection of sets $\mathcal{C}$, over $N$. The $k$-multiset multicover (MSMC) problem is to cover all elements of the universe $N$ at least $k$ ...
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Theoretical explanations for practical success of SAT solvers?

What theoretical explanations are there for the practical success of SAT solvers, and can someone give a "wikipedia-style" overview and explanation tying them all together? By analogy, the smoothed ...
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Are there any heuristic-free NP complete problems?

Are there any NP complete problems with no infinite subset of instances $\Phi$ such that membership in $\Phi$ can be decided in polynomial time, and for all $x \in \Phi$, $x$ can be solved in ...
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210 views

Finding smallest context free grammar that generates a set of sets

Are there any results known about the size of smallest context free grammar that generates a set of sets? That is, I am given an alphabet $\Sigma$ as well as a set $S \subseteq \mathbb{P}(\Sigma)$ ...
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165 views

Are there any heuristics that works solely on graphs?

I'm exploring heuristics in A* and apparently all heuristics require coordinates of all the locations to calculate a h-cost. This is fine if you are working on grids, but what if you need to work ...
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311 views

Packing $n$ objects into $m$ bins whose size is variable

Assume we have $n$ fixed size objects with sizes $O_1$ to $O_n$. Also, assume we have $m$ bins with size $a \times B_1$ to $a \times B_m$ in which $a$ is a real number and $a\ge1$. We want to put ...
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Complexity of minimizing monotone arithmetical formulas

Let's say that I have a multi-variate arithmetical expression $A(x_1, \ldots, x_n)$ that uses addition and multiplication operations and is also in a very simple form of sums of products, e.g., $A_1(...
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68 views

Looking for reference proving polynomial-time bounds for A* search under specific conditions

In the textbook "Artificial Intelligence - A Modern Approach" (Russel, Norvig), it mentions that a sufficient criteria for the A* search algorithm to complete in polynomial time is for the heuristic ...
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139 views

Pathfinding search over a space with known changing costs

I'm working on a research project which involves iterative pathfinding over a space whose cells have danger values that change over time. More specifically, the danger values represent bad weather, ...
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82 views

Approximations for the Stable Fixtures Problem

I have a set of N items, each with a subset of those items they can be paired with; each pair has a weight. I'd like to choose pairs to maximize the total weight, subject to each item being in at ...
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224 views

Heuristic with worst-case exponential complexity

I have been working with some colleagues on a metaheuristic for an NP-Hard optimization problem. It is a genetic algorithm using a steady-state population replacement strategy (at each iteration a ...
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137 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 ...
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Hardness of Covering Arrays with $v=t=6$

A covering array is an $N \times k$ array with each entry as one of $v$ symbols, where for every $t$ columns all possible $v^t$ tuples appears at least once. The covering array number (CAN) is the ...
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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 ...
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Is this NP-Hard or does a known optimal polynomial time solution exist? [closed]

Suppose we have 10 items, each of a different cost Items: {1,2,3,4,5,6,7,8,9,10} Cost: {2,5,1,1,5,1,1,3,4,10} and 3 customers {A,B,C}. Each customer has a requirement for a set ...
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209 views

Literature for Generalized Load Balancing

i am looking for literature on this kind of problem. $$ \begin{align} \min_x \max_k &\quad \sum_{i,j} x_{ij}c_{ijk}\\ \text{subject to}&\\ &\sum_j x_{ij}=1,&& \forall i\in\mathcal ...
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762 views

Heuristics for tsp without triangle inequality

Every heuristic for the traveling salesman problem that I know of (Nearest-Neighbour, Christofides, Held-Karp, ...) assumes that the triangle inequality holds. Are there heuristics to solve the tsp ...
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192 views

Exploring a DFA, with no feedback

Let $M=(\Sigma,S,s_0,\delta)$ be an (unknown) deterministic finite-state automaton (DFA), with alphabet $\Sigma$, statespace $S$, start state $s_0 \in S$, and transition relation $\delta$. I want to ...
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Fast treewidth algorithms

I would like to compute the treewidth of a graph. There are really good heuristics for other NP-hard graph problems such as VF2 for subgraph isomorphism, with code available in igraph for example. I ...
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2k views

Approximation for metric TSP: Worst case using nearest neighbor heuristic?

I'm looking at different heuristics that approximate solutions for a metric Traveling Salesman Problem. I was wondering if there is a worst case ratio of tours calculated by the nearest neighbor ...
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417 views

Simplification of weighted NFA

What options does one have for the simplification (meaning reduction in the number of states) of weighted NFA over the probability semiring? From my understanding one can determinize, and then ...
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152 views

Find index set partition that has large projections

I have a multiset $S$ of $n$-bit strings. Let $1_S(s)$ denote the number of times that string $s$ appears in $S$, i.e., the multiplicity of $s$ in $S$. I want to find a partition of $\{1,2,\dots,n\}$...
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120 views

Balanced partitioning of a set of axis-parallel 2D rectangles

Fix a constant $0<\alpha<1/2$. The problem is the following. Suppose there are $N$ axis-parallel rectangles on the 2D plane with weights $w_1, w_2,\ldots, w_N$ and with coordinates all in the ...
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776 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 $200$...
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310 views

Find the nearest $d+1$ corners of a cube in $\mathbb{R}^d$

How can one find the $d+1$ corners of the unit cube in $\mathbb{R}^d$ nearest a point $x$ in the cube ? Use the L1 metric, so that in 4d |$x$ - 0000| = $\sum {x_i}$, |$x$ - 0001| = $x_3 + x_2 + x_1 + ...
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Tractability of mutual information-augmented ensemble classification algorithms

I am seeking to augment random forest classification using Shannon-Weaver mutual information as a metaheuristic to partition candidate datasets. Specifically, I am trying to determine if such an ...
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438 views

Cheapest dissection of a grid polygon into rectangles with cost

My problem: Dissect a grid polygon into rectangles. (A grid polygon is a rectilinear polygon all of whose vertices have integer coordinates.) The rectangles must be taken from a predefined set (which ...
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what is the best heuristic to solve 3AP with Euclidean costs?

As is well known, assignment problems for $n$-partite graphs, with $n$>2 are NP-hard, where as assignment problems on bipartite graphs can be solved in polynomial time using the Kuhn's Hungarian ...
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408 views

Does this bin packing problem have a name?

My problem is related to the standard bin packing problem (where you have bins of capacity $1$, items of capacity $(0,1]$, and want to pack the items into as few bins as possible), but there are a ...
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274 views

Self-organizing Sequential Search Heuristics

I've read the paper by Jon L. Bentley "Amortized analyses of self-organizing sequential search heuristics". It deals with different schemes for improving linear search. (such as after every access to ...
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Resources to get started on fractional graph coloring algorithms

I'm interested in using fractional graph coloring algorithms/solvers to solve a problem, where is a good place to start? I'm looking to find basic/introductory to state-of-the-art algorithms more ...
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555 views

Decentralized algorithm for determining influential nodes in social networks

In this paper by Kempe-Kleinberg-Tardos, the Authors propose a greedy algorithms based on submodular functions to determine the $k$ most influential nodes in a graph, with applications to social ...
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1answer
158 views

Local Smoothness vs optimisation in combinatorial problems

Local smoothness is often mentioned in literature analysing different heuristics and meta-heuristics for combinatorial optimisation. What is meant precisely by local smoothness is often left out, but ...
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1k views

Successful application of branch-and-bound methods for NP-hard problems

Branch and bound is an effective heuristic for search problems, and Wikipedia lists a number of hard problems where branch-and-bound has been used. However, I haven't been able to find references to ...
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Theoretical study of coordinate descent methods

I'm preparing some course material on heuristics for optimization, and have been looking at coordinate descent methods. The setting is here a multivariate function $f$ that you wish to optimize. $f$ ...
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619 views

A search problem and no algorithm for it

I would like to learn about the following search problem, in particular, which kind of algorithms exist for it. Suppose we have a huge search space $S$. For each element $s \in S$, we have the weight ...
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351 views

Heuristics for graph bisection

i'm trying to find an algorithm that will divide my graph in 2 parts by telling me what connections should be broken but the 2 parts should contain about the same number of nodes its for a practical ...
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318 views

Heuristics for Optimization

Since it's Friday, it's time for a CW question. I'm looking for heuristics that have wide use in optimization problems. To limit the scope to more 'theory-friendly' heuristics, here are the rules (...
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145 views

Does the cohomological approach to Boolean complexity nicely model any BDD heuristics?

In this question, I learned that complexity theorists had considered using Grothendieck topologies to model Boolean circuits. This has not, apparently, led to any new lower bounds yet, but I'm not so ...
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What is the maximum number of stable marriages for an instance of the Stable Marriage Problem?

Stable Marriage Problem: http://en.wikipedia.org/wiki/Stable_marriage_problem I am aware that for an instance of a SMP, many other stable marriages are possible apart from the one returned by the ...
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270 views

Good MCMC methods for exploring the space of independent sets

Let $G$ be an edge-weighted graph, and let (S, V-S) be a feasible pair if S is a maximal independent set. The weight of a feasible pair is computed by finding for each element of V-S the lightest edge ...
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813 views

Ant colony optimization for traveling salesman problem with changing graph-nodes/vertices

Are there any publications focusing on solving TSP with ant colony optimization that consider small changes in the graph's nodes or vertices? So what I have is: a traveling salesman problem (TSP) ...
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1answer
671 views

Heuristics for the minimum-weight $k$-clique problem

Hello Does someone have an idea for heuristics for the problem: Given undirected weighted(weights on edges) complete graph $G(V,E)[|V|=n,|E| = m]$, find a clique of size $k < n$(k is number of ...