Fixed cardinality stable sets

Given an undirected graph G=(V,E) and a positive integer k in {1, ..., |V|}, we initiate the combinatorial study of stable sets of cardinality exactly k in G. Our aim is to instigate the polyhedral investigation of the convex hull of fixed cardinality stable sets, inspired by the rich theory on the classical structure of stable sets. We introduce a large class of valid inequalities to the natural integer programming formulation of the problem. We also present simple combinatorial relaxations based on computing maximum weighted matchings, which yield dual bounds towards finding minimum-weight fixed cardinality stable sets, and particular cases which are solvable in polynomial time.publishedVersio

JGraphT -- A Java library for graph data structures and algorithms

Mathematical software and graph-theoretical algorithmic packages to efficiently model, analyze and query graphs are crucial in an era where large-scale spatial, societal and economic network data are abundantly available. One such package is JGraphT, a programming library which contains very efficient and generic graph data-structures along with a large collection of state-of-the-art algorithms. The library is written in Java with stability, interoperability and performance in mind. A distinctive feature of this library is the ability to model vertices and edges as arbitrary objects, thereby permitting natural representations of many common networks including transportation, social and biological networks. Besides classic graph algorithms such as shortest-paths and spanning-tree algorithms, the library contains numerous advanced algorithms: graph and subgraph isomorphism; matching and flow problems; approximation algorithms for NP-hard problems such as independent set and TSP; and several more exotic algorithms such as Berge graph detection. Due to its versatility and generic design, JGraphT is currently used in large-scale commercial, non-commercial and academic research projects. In this work we describe in detail the design and underlying structure of the library, and discuss its most important features and algorithms. A computational study is conducted to evaluate the performance of JGraphT versus a number of similar libraries. Experiments on a large number of graphs over a variety of popular algorithms show that JGraphT is highly competitive with other established libraries such as NetworkX or the BGL.Comment: Major Revisio

A Framework for Symmetric Part Detection in Cluttered Scenes

The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favor as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial parts. However, today's recognition systems are faced with cluttered scenes, and the assumption that a closed contour exists, i.e. that figure-ground segmentation has been solved, renders much of the medial axis community's work inapplicable. In this article, we review a computational framework, previously reported in Lee et al. (2013), Levinshtein et al. (2009, 2013), that bridges the representation power of the medial axis and the need to recover and group an object's parts in a cluttered scene. Our framework is rooted in the idea that a maximally inscribed disc, the building block of a medial axis, can be modeled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes.Comment: 10 pages, 8 figure

QuASeR -- Quantum Accelerated De Novo DNA Sequence Reconstruction

In this article, we present QuASeR, a reference-free DNA sequence reconstruction implementation via de novo assembly on both gate-based and quantum annealing platforms. Each one of the four steps of the implementation (TSP, QUBO, Hamiltonians and QAOA) is explained with simple proof-of-concept examples to target both the genomics research community and quantum application developers in a self-contained manner. The details of the implementation are discussed for the various layers of the quantum full-stack accelerator design. We also highlight the limitations of current classical simulation and available quantum hardware systems. The implementation is open-source and can be found on https://github.com/prince-ph0en1x/QuASeR.Comment: 24 page