Ernst Althaus

Power efficient range assignment for symmetric connectivity in static ad hoc wireless networks

In this paper we study the problem of assigning transmission ranges to the nodes of a static ad hoc wireless network so as to minimize the total power consumed under the constraint that enough power is provided to the nodes to ensure that the network is connected. We focus on the Min-Power Symmetric Connectivity problem, in which the bidirectional links established by the transmission ranges are required to form a connected graph.Implicit in previous work on transmission range assignment under asymmetric connectivity requirements is the proof that Min-Power Symmetric Connectivity is NP-hard and that the MST algorithm has a performance ratio of 2. In this paper we make the following contributions: (1) we show that the related Min-Power Symmetric Unicast problem can be solved efficiently by a shortest-path computation in an appropriately constructed auxiliary graph; (2) we give an exact branch and cut algorithm based on a new integer linear program formulation solving instances with up to 35–40 nodes in 1 hour; (3) we establish the similarity between Min-Power Symmetric Connectivity and the classic Steiner Tree problem in graphs, and use this similarity to give a polynomial-time approximation scheme with performance ratio approaching 5/3 as well as a more practical approximation algorithm with approximation factor 11/6; and (4) we give the results of a comprehensive experimental study comparing new and previously proposed heuristics with the above exact and approximation algorithms.

A combinatorial approach to protein docking with flexible side-chains

Rigid body docking approaches are not sufficient to predict the structure of a protein complex from the unbound (native) structures of the two proteins. Accounting for side—chain flexibility is an important step towards fully flexible protein docking. This work describes an approach that allows conformational flexibility for the side—chains while keeping the protein backbone rigid. Starting from candidates created by a rigid docking algorithm, we demangle the side—chains of the docking site, thus creating reasonable approximations of the true complex structure. These structures are ranked with respect to the binding free energy. We present two new techniques for side—chain demangling. Both approaches are based on a discrete representation of the side—chain conformational space by the use of a rotamer library. This leads to a combinatorial optimization problem. For the solution of this problem we propose a fast heuristic approach and an exact, albeit slower method using branch—&—cut techniques. As a test set we use the unbound structures of three proteases and the corresponding protein inhibitors. For each of the examples the highest—ranking conformation produced was a good approximation of the true complex structure.

Computing Locally Coherent Discourses

We present the first algorithm that computes optimal orderings of sentences into a locally coherent discourse. The algorithm runs very efficiently on a variety of coherence measures from the literature. We also show that the discourse ordering problem is NP-complete and cannot be approximated.

Approximating k-hop minimum-spanning trees

Given a complete graph on~n nodes with metric edge costs, the minimum-costk-hop spanning tree (kHMST) problem asks for a spanning tree of minimum total cost such that the longest root-leaf-path in the tree has at most k edges. We present an algorithm that computes such a tree of total expected cost O(logn) times that of a minimum-cost k-hop spanning-tree.

A combinatorial approach to protein docking with flexible side chains.

Rigid-body docking approaches are not sufficient to predict the structure of a protein complex from the unbound (native) structures of the two proteins. Accounting for side chain flexibility is an important step towards fully flexible protein docking. This work describes an approach that allows conformational flexibility for the side chains while keeping the protein backbone rigid. Starting from candidates created by a rigid-docking algorithm, we demangle the side chains of the docking site, thus creating reasonable approximations of the true complex structure. These structures are ranked with respect to the binding free energy. We present two new techniques for side chain demangling. Both approaches are based on a discrete representation of the side chain conformational space by the use of a rotamer library. This leads to a combinatorial optimization problem. For the solution of this problem, we propose a fast heuristic approach and an exact, albeit slower, method that uses branch-and-cut techniques. As a test set, we use the unbound structures of three proteases and the corresponding protein inhibitors. For each of the examples, the highest-ranking conformation produced was a good approximation of the true complex structure.

Superposition modulo linear arithmetic SUP(LA)

The hierarchical superposition based theorem proving calculus of Bachmair, Ganzinger, and Waldmann enables the hierarchic combination of a theory with full first-order logic. If a clause set of the combination enjoys a sufficient completeness criterion, the calculus is even complete. We instantiate the calculus for the theory of linear arithmetic. In particular, we develop new effective versions for the standard superposition redundancy criteria taking the linear arithmetic theory into account. The resulting calculus is implemented in SPASS(LA) and extends the state of the art in proving properties of first-order formulas over linear arithmetic.

An efficient graph algorithm for dominance constraints

Dominance constraints are logical descriptions of trees that are widely used in computational linguistics. Their general satisfiability problem is known to be NP-complete. Here we identify normal dominance constraints and present an efficient graph algorithm for testing their satisfiability in deterministic polynomial time. Previously, no polynomial time algorithm was known.

Computing H/D-Exchange rates of single residues from data of proteolytic fragments

BackgroundProtein conformation and protein/protein interaction can be elucidated by solution-phase Hydrogen/Deuterium exchange (sHDX) coupled to high-resolution mass analysis of the digested protein or protein complex. In sHDX experiments mutant proteins are compared to wild-type proteins or a ligand is added to the protein and compared to the wild-type protein (or mutant). The number of deuteriums incorporated into the polypeptides generated from the protease digest of the protein is related to the solvent accessibility of amide protons within the original protein construct.ResultsIn this work, sHDX data was collected on a 14.5 T FT-ICR MS. An algorithm was developed based on combinatorial optimization that predicts deuterium exchange with high spatial resolution based on the sHDX data of overlapping proteolytic fragments. Often the algorithm assigns deuterium exchange with single residue resolution.ConclusionsWith our new method it is possible to automatically determine deuterium exchange with higher spatial resolution than the level of digested fragments.

Computing H/D-exchange speeds of single residues from data of peptic fragments

Determining the hydrogen-deuterium exchange speeds of single residues from data for peptic fragments obtained by FT-ICS MS is currently mainly done by manual interpretation. We provide an automated method based on combinatorial optimization. More precisely, we present an algorithm that enumerates all possible exchange speeds for single residues that explain the observed data of the peptic fragments.

Improving linear programming approaches for the steiner tree problem

We present two theoretically interesting and empirically successful techniques for improving the linear programming approaches, namely graph transformation and local cuts, in the context of the Steiner problem. We show the impact of these techniques on the solution of the largest benchmark instances ever solved.