k-plexes are a formal yet exible way of de ning communities in networks. ey generalize the notion of cliques and are more appropriate in most real cases: while a node of a clique C is connected to all other nodes of C, a node of a k-plex may miss up to k connections. Unfortunately, computing all maximal k-plexes is a gruesome task and state-of-the-art algorithms can only process small-size networks. In this paper we propose a new approach for enumerating large k-plexes in networks that speeds up the search by several orders of magnitude, leveraging on (i) methods for strongly reducing the search space and (ii) e cient techniques for the computation of maximal cliques. Several experiments show that our strategy is e ective and is able to increase the size of the networks for which the computation of large k-plexes is feasible from a few hundred to several hundred thousand nodes.

Algorithms for listing the subgraphs satisfying a given property (e.g., being a clique, a cut, a cycle, etc.) fall within the general framework of set systems. A set system (U, F) uses a ground set U (e.g., the network nodes) and an indicator F ⊆ 2 U of which subsets of U have the required property. For the problem of listing all sets in F maximal under inclusion, the ambitious goal is to cover a large class of set systems, preserving at the same time the efficiency of the enumeration. Among the existing algorithms, the best-known ones list the maximal subsets in time proportional to their number but may require exponential space. In this paper we improve the state of the art in two directions by introducing an algorithmic framework that, under standard suitable conditions, simultaneously (i) extends the class of problems that can be solved efficiently to strongly accessible set systems, and (ii) reduces the additional space usage from exponential in |U| to stateless, thus accounting for just O(q) space, where q ≤ |U| is the largest size of a maximal set in F.

String data are often disseminated to support applications such as location-based service provision or DNA sequence analysis. This dissemination, however, may expose sensitive patterns that model confidential knowledge (e.g., trips to mental health clinics from a string representing a user's location history). In this paper, we consider the problem of sanitizing a string by concealing the occurrences of sensitive patterns, while maintaining data utility. First, we propose a time-optimal algorithm, TFS-ALGO, to construct the shortest string preserving the order of appearance and the frequency of all non-sensitive patterns. Such a string allows accurately performing tasks based on the sequential nature and pattern frequencies of the string. Second, we propose a time-optimal algorithm, PFS-ALGO, which preserves a partial order of appearance of non-sensitive patterns but produces a much shorter string that can be analyzed more efficiently. The strings produced by either of these algorithms may reveal the location of sensitive patterns. In response, we propose a heuristic, MCSR-ALGO, which replaces letters in these strings with carefully selected letters, so that sensitive patterns are not reinstated and occurrences of spurious patterns are prevented. We implemented our sanitization approach that applies TFS-ALGO, PFS-ALGO and then MCSR-ALGO and experimentally show that it is effective and efficient.

In this paper we propose polynomial delay algorithms for several maximal subgraph listing problems, by means of a seemingly novel technique which we call proximity search. Our result involves modeling the space of solutions as an implicit directed graph called "solution graph", a method common to other enumeration paradigms such as reverse search. Such methods, however, can become inefficient due to this graph having vertices with high (potentially exponential) degree. The novelty of our algorithm consists in providing a technique for generating better solution graphs, reducing the out-degree of its vertices with respect to existing approaches, and proving that it remains strongly connected. Applying this technique, we obtain polynomial delay listing algorithms for several problems for which output-sensitive results were, to the best of our knowledge, not known. These include Maximal Bipartite Subgraphs, Maximal k-Degenerate Subgraphs (for bounded k), Maximal Induced Chordal Subgraphs, and Maximal Induced Trees. We present these algorithms, and give insight on how this general technique can be applied to other problems.