In the family of clustering problems we are given a set of objects (vertices of the graph), together with some observed pairwise similarities (edges). The goal is to identify clusters of similar objects by slightly modifying the graph to obtain a cluster graph (disjoint union of cliques). Hüffner et al. (Theory Comput. Syst. 47(1), 2010) initiated the parameterized study of CLUSTER VERTEX DELE-TION, where the allowed modification is vertex deletion, and presented an elegant O min(2 k k 6 log k + n 3 , 2 k km √ n log n) -time fixed-parameter algorithm, parameterized by the solution size. In the last 5 years, this algorithm remained the fastest known algorithm for CLUSTER VERTEX DELETION and, thanks to its simplicity, became one of the textbook examples of an application of the iterative compression principle. In our work we break the 2 k -barrier for CLUSTER VERTEX DELETION and present an O(1.9102 k (n + m))-time branching algorithm. We achieve this improvement by a number of structural observations which we incorporate into the algorithm's branching steps.A preliminary version of this work has been presented at CSR 2014.

In the family of clustering problems, we are given a set of objects (vertices of the graph), together with some observed pairwise similarities (edges). The goal is to identify clusters of similar objects by slightly modifying the graph to obtain a cluster graph (disjoint union of cliques).Hüffner et al. [Theory Comput. Syst. 2010] initiated the parameterized study of Cluster Vertex Deletion, where the allowed modification is vertex deletion, and presented an elegant O(2 k k 9 + nm)-time fixed-parameter algorithm, parameterized by the solution size. In our work, we pick up this line of research and present an O(1.9102 k (n + m))-time branching algorithm.

Recent advancements in hardware accelerators such as Tensor Processing Units (TPUs) speed up computation time relative to Central Processing Units (CPUs) not only for machine learning but, as demonstrated here, also for scientific modeling and computer simulations. To study TPU hardware for distributed scientific computing, we solve partial differential equations (PDEs) for the physics simulation of fluids to model riverine floods. We demonstrate that TPUs achieve a two orders of magnitude speedup over CPUs. Running physics simulations on TPUs is publicly accessible via the Google Cloud Platform, and we release a Python interactive notebook version of the simulation.

Abstract-In the standard set reconciliation problem, there are two parties A1 and A2, each respectively holding a set of elements S1 and S2. The goal is for both parties to obtain the union S1 ∪ S2. In many distributed computing settings the sets may be large but the set difference |S1 −S2|+|S2 −S1| is small. In these cases one aims to achieve reconciliation efficiently in terms of communication; ideally, the communication should depend on the size of the set difference, and not on the size of the sets.Recent work has considered generalizations of the reconciliation problem to multi-party settings, using a framework based on a specific type of linear sketch called an Invertible Bloom Lookup Table. Here, we consider multi-party set reconciliation using the alternative framework of characteristic polynomials, which have previously been used for efficient pairwise set reconciliation protocols, and compare their performance with Invertible Bloom Lookup Tables for these problems.

Parse trees are fundamental syntactic structures in both computational linguistics and compilers construction. We argue in this paper that, in both fields, there are good incentives for model-checking sets of parse trees for some word according to a context-free grammar. We put forward the adequacy of propositional dynamic logic (PDL) on trees in these applications, and study as a sanity check the complexity of the corresponding model-checking problem: although complete for exponential time in the general case, we find natural restrictions on grammars for our applications and establish complexities ranging from nondeterministic polynomial time to polynomial space in the relevant cases.