A Backtracking Algorithmic Toolbox for Solving the Subgraph Isomorphism Problem

The subgraph isomorphism problem asks whether a given graph is a subgraph of another graph. It is one of the most general NP-complete problems since many other problems (e.g., Hamiltonian cycle, clique, independent set, etc.) have a natural reduction to subgraph isomorphism. Furthermore, there is a variety of practical applications where graph pattern matching is the core problem. Developing efficient algorithms and solvers for this problem thus enables good solutions to a variety of different practical problems. In this chapter, the authors present and experimentally explore various algorithmic refinements and code optimizations for improving the performance of subgraph isomorphism solvers. In particular, they focus on algorithms that are based on the backtracking approach and constraint satisfaction programming. They gather experiences from many state-of-the-art algorithms as well as from their engagement in this field. Lessons learned from engineering such a solver can be utilized in many other fields where backtracking is a prominent approach for solving a particular problem.

Studying the history of tumor evolution from single-cell sequencing data by exploring the space of binary matrices

Single-cell sequencing data has great potential in reconstructing the evolutionary history of tumors. Rapid advances in single-cell sequencing technology in the past decade were followed by the design of various computational methods for inferring trees of tumor evolution. Some of the earliest of these methods were based on the direct search in the space of trees. However, it can be shown that instead of this tree search strategy we can perform a search in the space of binary matrices and obtain the most likely tree directly from the most likely among the candidate binary matrices. The search in the space of binary matrices can be expressed as an instance of integer linear or constraint satisfaction programming and solved by some of the available solvers, which typically provide a guarantee of optimality of the reported solution. In this review, we first describe one convenient tree representation of tumor evolutionary history and present tree scoring model that is most commonly used in the available methods. We then provide proof showing that the most likely tree of tumor evolution can be obtained directly from the most likely matrix from the space of candidate binary matrices. Next, we provide integer linear programming formulation to search for such matrix and summarize the existing methods based on this formulation or its extensions. Lastly, we present one use-case which illustrates how binary matrices can be used as a basis for developing a fast deep learning method for inferring some topological properties of the most likely tree of tumor evolution.

AUTOMATIC GENERATION OF CROSSWORD PUZZLES

Crossword puzzles are used everyday by millions of people for entertainment, but have applications also in educational and rehabilitation contexts. Unfortunately, the generation of ad-hoc puzzles, especially on specific subjects, typically requires a great deal of human expert work. This paper presents the architecture of WebCrow-generation, a system that is able to generate crosswords with no human intervention, including clue generation and crossword compilation. In particular, the proposed system crawls information sources on the Web, extracts definitions from the downloaded pages using state-of-the-art natural language processing techniques and, finally, compiles the crossword schema with the extracted definitions by constraint satisfaction programming. The system has been tested on the creation of Italian crosswords, but the extensive use of machine learning makes the system easily portable to other languages.