Related papers: Combinatorial Structure of the Deterministic Seria…
Seriation is a problem consisting of seeking the best enumeration order of a set of units whose interrelationship is described by a bipartite graph, that is, a graph whose nodes are partitioned in two sets and arcs only connect nodes in…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a…
Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of…
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
The Algorithm Selection Problem is concerned with selecting the best algorithm to solve a given problem on a case-by-case basis. It has become especially relevant in the last decade, as researchers are increasingly investigating how to…
A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively splits the set of classes into two subsets, and trains a binary classifier to distinguish…
In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems. We…
We study the problem of circular seriation, where we are given a matrix of pairwise dissimilarities between $n$ objects, and the goal is to find a {\em circular order} of the objects in a manner that is consistent with their dissimilarity.…
A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively applies binary splits to divide the set of classes into two subsets, and trains a binary…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span…
We devise a unified framework for the design of canonization algorithms. Using hereditarily finite sets, we define a general notion of combinatorial objects that includes graphs, hypergraphs, relational structures, codes, permutation…
We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the…
The problem of linear and circular permutations of n identical objects in m boxes, where a limit l is imposed on the number of objects in a box, is considered. In the linear case, where the boxes are arranged as a row, two methods of…
The problem of ranking can be described as follows. We have a set of combinatorial objects $S$, such as, say, the k-subsets of n things, and we can imagine that they have been arranged in some list, say lexicographically, and we want to…
Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and leads to many links with permutation patterns. We present…
Complex structures are typical in machine learning. Tailoring learning algorithms for every structure requires an effort that may be saved by defining a generic learning procedure adaptive to any complex structure. In this paper, we propose…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…