601 research outputs found
Answer Set Solving with Bounded Treewidth Revisited
Parameterized algorithms are a way to solve hard problems more efficiently,
given that a specific parameter of the input is small. In this paper, we apply
this idea to the field of answer set programming (ASP). To this end, we propose
two kinds of graph representations of programs to exploit their treewidth as a
parameter. Treewidth roughly measures to which extent the internal structure of
a program resembles a tree. Our main contribution is the design of
parameterized dynamic programming algorithms, which run in linear time if the
treewidth and weights of the given program are bounded. Compared to previous
work, our algorithms handle the full syntax of ASP. Finally, we report on an
empirical evaluation that shows good runtime behaviour for benchmark instances
of low treewidth, especially for counting answer sets.Comment: This paper extends and updates a paper that has been presented on the
workshop TAASP'16 (arXiv:1612.07601). We provide a higher detail level, full
proofs and more example
Families with infants: a general approach to solve hard partition problems
We introduce a general approach for solving partition problems where the goal
is to represent a given set as a union (either disjoint or not) of subsets
satisfying certain properties. Many NP-hard problems can be naturally stated as
such partition problems. We show that if one can find a large enough system of
so-called families with infants for a given problem, then this problem can be
solved faster than by a straightforward algorithm. We use this approach to
improve known bounds for several NP-hard problems as well as to simplify the
proofs of several known results.
For the chromatic number problem we present an algorithm with
time and exponential space for graphs of average
degree . This improves the algorithm by Bj\"{o}rklund et al. [Theory Comput.
Syst. 2010] that works for graphs of bounded maximum (as opposed to average)
degree and closes an open problem stated by Cygan and Pilipczuk [ICALP 2013].
For the traveling salesman problem we give an algorithm working in
time and polynomial space for graphs of average
degree . The previously known results of this kind is a polyspace algorithm
by Bj\"{o}rklund et al. [ICALP 2008] for graphs of bounded maximum degree and
an exponential space algorithm for bounded average degree by Cygan and
Pilipczuk [ICALP 2013].
For counting perfect matching in graphs of average degree~ we present an
algorithm with running time and polynomial
space. Recent algorithms of this kind due to Cygan, Pilipczuk [ICALP 2013] and
Izumi, Wadayama [FOCS 2012] (for bipartite graphs only) use exponential space.Comment: 18 pages, a revised version of this paper is available at
http://arxiv.org/abs/1410.220
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Prototype Freeze Trap Test
A performance evaluation was made of a prototype liquid cooled freeze trap with sodium at 350 and 1000 deg F. The sodium freeze-off function was adequate for all test conditions encountered. The freeze-off occurred satisfactorily with the larger clearance provided by a test modification to provide 0.030 eccentricity to the rotating shaft. Turning the freeze-trap handle was successful in opening the unit for gas venting when 350 deg F sodium was used. For a seal formed with 1000 deg F sodium, 16 turns of the trap handle gave no measurable gas venting at pressures up to 30 psi. Melting out the seal opened the vent satisfactorily. All the major problems encountered during the test were mechanical and associated with the rotating feature of the unit. (M.C.G.
Application of Silicon Carbide Chills in Controlling the Solidification Process of Casts Made of IN-713C Nickel Superalloy
The paper presents the method of manufacturing casts made of the IN-713C nickel superalloy using the wax lost investment castingprocess and silicon carbide chills. The authors designed experimental casts, the gating system and selected the chills material. Wax pattern,ceramic shell mould and experimental casts were prepared for the purposes of research. On the basis of the temperature distributionmeasurements, the kinetics of the solidification process was determined in the thickened part of the plate cast. This allowed to establish thequantity of phase transitions which occurred during cast cooling process and the approximate values of liquidus, eutectic, solidus andsolvus temperatures as well as the solidification time and the average value of cast cooling rate. Non-destructive testing and macroscopicanalysis were applied to determine the location and size of shrinkage defects. The authors present the mechanism of solidification andformation of shrinkage defects in casts with and without chills. It was found that the applied chills influence significantly the hot spots andthe remaining part of the cast. Their presence allows to create conditions for solidification of IN-713C nickel superalloy cast withoutshrinkage defects
Directed Subset Feedback Vertex Set Is Fixed-Parameter Tractable
Given a graph and an integer , the Feedback Vertex Set (FVS) problem
asks if there is a vertex set of size at most that hits all cycles in
the graph. The fixed-parameter tractability status of FVS in directed graphs
was a long-standing open problem until Chen et al. (STOC '08) showed that it is
FPT by giving a time algorithm. In the subset versions of
this problems, we are given an additional subset of vertices (resp., edges)
and we want to hit all cycles passing through a vertex of (resp. an edge of
). Recently, the Subset Feedback Vertex Set in undirected graphs was shown
to be FPT by Cygan et al. (ICALP '11) and independently by Kakimura et al.
(SODA '12). We generalize the result of Chen et al. (STOC '08) by showing that
Subset Feedback Vertex Set in directed graphs can be solved in time
. By our result, we complete the picture for feedback
vertex set problems and their subset versions in undirected and directed
graphs. Besides proving the fixed-parameter tractability of Directed Subset
Feedback Vertex Set, we reformulate the random sampling of important separators
technique in an abstract way that can be used for a general family of
transversal problems. Moreover, we modify the probability distribution used in
the technique to achieve better running time; in particular, this gives an
improvement from to in the parameter dependence of
the Directed Multiway Cut algorithm of Chitnis et al. (SODA '12).Comment: To appear in ACM Transactions on Algorithms. A preliminary version
appeared in ICALP '12. We would like to thank Marcin Pilipczuk for pointing
out a missing case in the conference version which has been considered in
this version. Also, we give an single exponential FPT algorithm improving on
the double exponential algorithm from the conference versio
A tight lower bound for steiner orientation
In the STEINER ORIENTATION problem, the input is a mixed graph G (it has both directed and undirected edges) and a set of k terminal pairs T. The question is whether we can orient the undirected edges in a way such that there is a directed s⇝t path for each terminal pair (s,t)∈T. Arkin and Hassin [DAM’02] showed that the STEINER ORIENTATION problem is NP-complete. They also gave a polynomial time algorithm for the special case when k=2
.
From the viewpoint of exact algorithms, Cygan, Kortsarz and Nutov [ESA’12, SIDMA’13] designed an XP algorithm running in nO(k) time for all k≥1. Pilipczuk and Wahlström [SODA ’16] showed that the STEINER ORIENTATION problem is W[1]-hard parameterized by k. As a byproduct of their reduction, they were able to show that under the Exponential Time Hypothesis (ETH) of Impagliazzo, Paturi and Zane [JCSS’01] the STEINER ORIENTATION problem does not admit an f(k)⋅no(k/logk) algorithm for any computable function f. That is, the nO(k) algorithm of Cygan et al. is almost optimal.
In this paper, we give a short and easy proof that the nO(k) algorithm of Cygan et al. is asymptotically optimal, even if the input graph has genus 1. Formally, we show that the STEINER ORIENTATION problem is W[1]-hard parameterized by the number k of terminal pairs, and, under ETH, cannot be solved in f(k)⋅no(k) time for any function f even if the underlying undirected graph has genus 1. We give a reduction from the GRID TILING problem which has turned out to be very useful in proving W[1]-hardness of several problems on planar graphs. As a result of our work, the main remaining open question is whether STEINER ORIENTATION admits the “square-root phenomenon” on planar graphs (graphs with genus 0): can one obtain an algorithm running in time f(k)⋅nO(k√) for PLANAR STEINER ORIENTATION, or does the lower bound of f(k)⋅no(k) also translate to planar graphs
Assigning channels via the meet-in-the-middle approach
We study the complexity of the Channel Assignment problem. By applying the
meet-in-the-middle approach we get an algorithm for the -bounded Channel
Assignment (when the edge weights are bounded by ) running in time
. This is the first algorithm which breaks the
barrier. We extend this algorithm to the counting variant, at the
cost of slightly higher polynomial factor.
A major open problem asks whether Channel Assignment admits a -time
algorithm, for a constant independent of . We consider a similar
question for Generalized T-Coloring, a CSP problem that generalizes \CA. We
show that Generalized T-Coloring does not admit a
-time algorithm, where is the
size of the instance.Comment: SWAT 2014: 282-29
Atomistic models of carbonate minerals: bulk and surface structures, defects, and diffusion
We review the use of interatomic potentials to describe the bulk and surface behavior of carbonate materials. Interatomic pair potentials, describing the Ca2+-O interactions and the C-O bonding of the CO22 anion group, are used to evaluate the lattice, elastic, dielectric, and vibrational data for calcite and aragonite. The resulting potential parameters for the carbonate group were then successfully transferred to models of the structures of rhombohedral carbonates of Mn, Fe, Mg, Ni, Zn, Co, and Cd. Simulations of the (1014) cleavage surface of calcite, magnesite, and dolomite show that these surfaces undergo relaxation leading to the rotation and distortion of the carbonate group with associated movement of cations. The influence of water on the surface structure has been investigated for monolayer coverage. The extent of carbonate group distortion is greater for the dry surfaces compared to the hydrated surfaces, and for the dry calcite relative to that for dry dolomite or magnesite. Point defect calculations for the doping of calcite indicate an increase in defect formation energy with increasing size of the substituting divalent ion. Migration energies for Ca, Mg, and Mn in calcite suggest a strong preference for diffusion along pathways roughly parallel to the c-axis rather than along the ab-plane
Approximation Algorithms for Connected Maximum Cut and Related Problems
An instance of the Connected Maximum Cut problem consists of an undirected
graph G = (V, E) and the goal is to find a subset of vertices S V
that maximizes the number of edges in the cut \delta(S) such that the induced
graph G[S] is connected. We present the first non-trivial \Omega(1/log n)
approximation algorithm for the connected maximum cut problem in general graphs
using novel techniques. We then extend our algorithm to an edge weighted case
and obtain a poly-logarithmic approximation algorithm. Interestingly, in stark
contrast to the classical max-cut problem, we show that the connected maximum
cut problem remains NP-hard even on unweighted, planar graphs. On the positive
side, we obtain a polynomial time approximation scheme for the connected
maximum cut problem on planar graphs and more generally on graphs with bounded
genus.Comment: 17 pages, Conference version to appear in ESA 201
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