AlgoLab is a research group focused on designing, studying, analyzing and implementing efficient algorithms, mainly combinatorial algorithms, for computational problems. The group is associated with the CS Dept. of Univ. Milano-Bicocca, but includes members of neighboring universities and research groups.
While the focus is on Computer Science, we are an interdisciplinary group, without defined boundaries on the fields of application of the algorithms studied. We are especially interested into algorithms and data structure to manage massive datasets (Big Data), as trivial or brute-force algorithms can suffice on modest dataset. On the other hand Big Data require linear or sublinear time algorithms with very small space requirements — such as streaming algorithms and succint data structures — or parallel algorithm.
Some more specialized topics of interests are:
- Text algorithms and data structures. We study algorithms and data structures for indexing and querying huge text collections.
- Combinatorics on words. We study different notions of distance between words, with a focus on classical definitions such as the longest common subsequence and the shortest common supersequence.
- Algorithms on trees. We study combinatorial algorithms for tree comparison and phylogeny reconstruction from matrices that encode the set of characters that the leaves have (e.g. the perfect phylogeny problem).
- Graph algorithms. We study some notions of graph decompositions — such as modular decomposition — and graph-based clustering (consensus and correlation clustering).
- Connections between texts and graphs. Modeling text problems, such as the shortest superstring problem, as graph problem is a powerful tool to develop new algorithms. All known genome assembler (a genome is essentially a very long string which must be reconstructed from a set of substrings) are built upon the notion of string graph or de Bruijn graph.
- Computational, approximation and fixed-parameter complexity. We study how different parameters determine whether a certain problem admits and efficient solution, while classical computational complexity focuses on a single parameter: the size of the instance.
We strive for a delicate balance between theoretical and experimental aspects, as we believe it is the only way that a research activity that can produce results useful outside academia. In fact, there are several algorithms that are efficient from a theoretical viewpoint (that is, polynomial time algorithm) but they do not have an efficient implementation, either because the algorithm engineering that is necessary to this purpose has not been done, or is impossible to do. On the other hand, there are some cases where exponential or super-polynomial time complexity result in implementations that are efficient in practice (such as the simplex algorithm).
Often efficient implementations stems form combinatorial properties of the instances that we want to solve, and it is hard to find a priori which properties can lead to fast implementations. An example is the Burrows-Wheeler Transform that is based on sorting all rotations of the text, has been introduced to compress texts but, a decade later, has shifted its main application in text indexing.