Search

We initiate the investigation of the parameterized complexity of Diameter and Connectivity in the streaming paradigm. On the positive end, we show that knowing a vertex cover of size k allows for algorithms in the Adjacency List (AL) streaming model whose number of passes is constant and memory is O(log n) for any fixed k. Underlying these algorithms is a method to execute a breadth-first search in O(k) passes and O(klog n) bits of memory. On the negative end, we show that many other parameters lead to lower bounds in the AL model, where Ω(n/p) bits of memory is needed for any p-pass algorithm even for constant parameter values. In particular, this holds for graphs with a known modulator (deletion set) of constant size to a graph that has no induced subgraph isomorphic to a fixed graph H, for most H. For some cases, we can also show one-pass, Ω(nlog n) bits of memory lower bounds. We also prove a much stronger Ω(n2/p) lower bound for Diameter on bipartite graphs. Finally, using the insights we developed into streaming parameterized graph exploration algorithms, we show a new streaming kernelization algorithm for computing a vertex cover of size k. This yields a kernel of 2k vertices (with O(k2) edges) produced as a stream in poly(k) passes and only O(klog n) bits of memory.

There are many benefits in providing formal specifications for our software. However, teaching students to do this is not always easy as courses on formal methods are often experienced as dry by students. This paper presents a game called FormalZ that teachers can use to introduce some variation in their class. Students can have some fun in playing the game and, while doing so, also learn the basics of writing formal specifications in the form of pre- and post-conditions. Unlike existing software engineering themed education games such as Pex and Code Defenders, FormalZ takes the deep gamification approach where playing gets a more central role in order to generate more engagement. This short paper presents our work in progress: the first implementation of FormalZ along with the result of a preliminary users' evaluation. This implementation is functionally complete and tested, but the polishing of its user interface is still future work.