Stephan Kottler

SAT solving with reference points

Many state-of-the-art SAT solvers use the VSIDS heuristic to make branching decisions based on the activity of variables or literals. In combination with rapid restarts and phase saving this yields a powerful decision heuristic in practice. However, there are approaches that motivate more in-depth reasoning to guide the search of the SAT solver. But more reasoning often requires more information and comes along with more complex data structures. This may sometimes even cause strong concepts to be inapplicable in practice. In this paper we present a suitable data structure for the DMRP approach to overcome the problem above. Moreover, we show how DMRP can be combined with CDCL solving to be competitive to state-of-the-art solvers and to even improve on some families of industrial instances.

Computation of renameable Horn backdoors

Satisfiability of real-world Sat instances can be often decided by focusing on a particular subset of variables - a so-called Backdoor Set. In this paper we suggest two algorithms to compute Renameable Horn deletion backdoors. Both methods are based on the idea to transform the computation into a graph problem. This approach could be used as a preprocessing to solve hard real-world Sat instances. We also give some experimental results of the computations of Renameable Horn backdoors for several real-world instances.

A new bound for an NP-hard subclass of 3-SAT using backdoors

Knowing a Backdoor Set B for a given SAT instance, satisfiability can be decided by only examining each of the 2|B| truth assignments of the variables in B. However, one problem is to efficiently find a small backdoor up to a particular size and, furthermore, if no backdoor of the desired size could be found, there is in general no chance to conclude anything about satisfiability. In this paper we introduce a complete deterministic algorithm for an NP-hard subclass of 3-SAT, that is also a subclass of Mixed Horn Formulas (MHF). For an instance of the described class the absence of two particular kinds of backdoor sets can be used to prove unsatisfiability. The upper bound of this algorithm is O(p(n) * 1.427n) which is less than the currently best upper bound for deterministic algorithms for 3-SAT and MHF.

Visualizing large and clustered networks

The need to visualize large and complex networks has strongly increased in the last decade. Although networks with more than 1000 vertices seem to be prohibitive for a comprehensive layout, real-world networks exhibit a very inhomogenous edge density that can be harnessed to derive an aesthetic and structured layout. Here, we will present a heuristic that finds a spanning tree with a very low average spanner property for the non-tree edges, the so-called backbone of a network. This backbone can then be used to apply a modified tree-layout algorithm to draw the whole graph in a way that highlights dense parts of the graph, so-called clusters, and their inter-connections.

Creating industrial-like SAT instances by clustering and reconstruction

For the optimization of SAT solvers, it is crucial that a solver can be trained on a preferably large number of instances for general or domain specific problems. Especially for domain specific problems the set of available instances can be insufficiently small. In our approach we built large sets of instances by recombining several small snippets of different instances of a particular domain. Also the fuzzer utility [3] builds industrial-like SAT instances by combining smaller pieces. However, these pieces are a combination of randomly created circuits and are not derived from an existing pool of instances. In Ansotegui [1] random pseudo-industrial instances are created in a more formal way.

Beyond unit propagation in SAT solving

The tremendous improvement in SAT solving has made SAT solvers a core engine for many real world applications. Though still being a branch-and-bound approach purposive engineering of the original algorithm has enhanced state-of-the-art solvers to tackle huge and difficult SAT instances. The bulk of solving time is spent on iteratively propagating variable assignments that are implied by decisions. In this paper we present two approaches on how to extend the broadly applied Unit Propagation technique where a variable assignment is implied iff a clause has all but one of its literals assigned to false. We propose efficient ways to utilize more reasoning in the main component of current SAT solvers so as to be less dependent on felicitous branching decisions.

Visualization of complex BPEL models

In this work, we present our approach for producing layouts of complex workflows given in the Business Process Execution Language (BPEL) [1]. BPEL is a verbose, hierarchical workflow language containing nested, alternative and concurrent execution paths. Our approach enhances the Sugiyama algorithm [2] by introducing special paths, which are constrained to be drawn in parallel, and hence, orthogonally to the layers in the Sugiyamamodel. To prove the feasibility of our approach,we have developed an extension to the collaborative BPEL development system HOBBES [3] [4]. Collaboration enhances the need for visualizations of complex workflow models, as team members have to coordinate their activities.

Proving or disproving planar straight-line embeddability onto given rectangles

Given a plane graph G = (V,E) and a rectangle we ask whether there exists a planar straight-line embedding of G onto the grid-points of the rectangle. For this NP-hard problem [5] some powerful heuristics have been developed to minimise the area of an embedding of a given graph [5,4]. Moreover, for particular families of graphs upper and lower bounds on the area have been proven [2]. However, in the general case it is not possible to ensure whether there is an embedding that preserves a particular area restriction A = h ·w. We present an implementation based on a translation into SAT to tackle this kind of problems for small graphs. We only describe the direct encoding into CNF that turned out to be most suitable.