difference schemes for the singularly perturbed sobolev periodic boundary problem a finite difference method is suggested and analyzed for evolution equations of sobolev type in a single space variable and with boundary layers the convergence and error estimates for an exponentially fitted difference scheme in an equidistant mesh are obtained the numerical methods discussed here are extremely robust in the sense that they have good convergence properties not only for small values of the perturbation parameter but also for moderate and large values

an efficient numerical method for singular perturbation problems in this paper we propose a method for the numerical solution of singularly perturbed two point boundary value problems bvps first we develop two schemes to integrate initial value problem ivp for system of two first order differential equations and then by using these schemes we solve the bvp precisely we convert the second order bvp into a system of first order differential equations and then apply the numerical schemes to obtain the solution in order to get an initial condition for the system we use the asymptotic approximate solution error estimates are derived and numerical examples are provided to illustrate the present method

on the complexity of submap isomorphism and maximum common submap problems generalized maps describe the subdivision of objects in cells and are widely used to model 2d and 3d images in this context several pattern recognition tasks involve solving submap isomorphism problems to decide if a map is included in another map or more generally computing maximum common submaps to measure the distance between two maps recently we have described a polynomial time algorithm for solving the submap isomorphism problem when the pattern map is connected in this paper we show that submap isomorphism is np complete when the pattern map is not connected then we characterize the inherent difficulty of submap isomorphism with respect to the number of connected components we show that it is fixed parameter tractable fpt and we give an fpt algorithm for submap isomorphism we experimentally compare this algorithm with a state of the art subgraph isomorphism algorithm for searching for patterns in an image and we show that it is both more accurate and more efficient finally we study the complexity of the maximum common submap problem and we show that it is np hard even though we restrict the problem to the search of common connected submaps highlightswe show that submap isomorphism is np complete we give a fixed parameter tractable algorithm for submap isomorphism we experimentally evaluate it to search for patterns in segmented images we show that maximum common connected submap is np hard

complexity of graph self assembly in accretive systems and self destructible systems self assembly is a process in which small objects autonomously associate with each other to form larger complexes it is ubiquitous in biological constructions at the cellular and molecular scale and has also been identified by nanoscientists as a fundamental method for building nano scale structures recent years have seen convergent interest and efforts in studying self assembly from mathematicians computer scientists physicists chemists and biologists however most complexity theoretical studies of self assembly utilize mathematical models with two limitations 1 only attraction while no repulsion is studied 2 only assembled structures of two dimensional square grids are studied in this paper we study the complexity of the assemblies resulting from the cooperative effect of repulsion and attraction in a more general setting of graphs this allows for the study of a more general class of self assembled structures than the previous tiling model we define two novel assembly models namely the accretive graph assembly model and the self destructible graph assembly model and identify a fundamental problem in them the sequential construction of a given graph we refer to it as the accretive graph assembly problem agap and the self destructible graph assembly problem dgap in the respective models our main results are i agap is np complete even if the maximum degree of the graph is restricted to 4 or the graph is restricted to be planar with maximum degree 5 ii counting the number of sequential assembly orderings that result in a target graph agap is p complete and iii dgap is pspace complete even if the maximum degree of the graph is restricted to 6 this is the first pspace complete result in self assembly we also extend the accretive graph assembly model to a stochastic model and prove that determining the probability of a given assembly in this model is p complete

finding an even simple path in a directed planar graph in this paper we show that the following problem the even simple path esp problem for directed planar graphs is solvable in polynomial time given a directed planar graph g v e and two nodes s starting node t targetnode in v find a simple path i e without repeated nodes from s to t of even length the length of the path is the number of edges it contains

the within strip discrete unit disk cover problem we present a study of the within strip discrete unit disk cover wsdudc problem which is a restricted version of the discrete unit disk cover dudc problem for the wsdudc problem there exists a set of points and a set of unit disks in the plane and the points and disk centres are conned to a strip of xed height an optimal solution to the wsdudc problem is a set of disks of minimum cardinality that covers all points in the input set we describe a range of approximation algorithms for the problem including 4 and 3 approximate algorithms which apply for strips of height 2 p 2 3 0 94 and 0 8 units respectively as well as a general scheme for any strip with less than unit height we prove that the wsdudc problem is np complete on strips of any xed height which is our most interesting result from a theoretical standpoint the result is also quite surprising since a number of similar problems are tractable on strips of xed height finally we discuss how these results may be applied to known dudc approximation algorithms

singularly perturbed differential equations with discontinuous coefficients and concentrated factors in this paper singularly perturbed one dimensional reaction diffusion equations with discontinuous coefficients and concentrated factors are examined a new formulation which allows us to reduce the solving of general interface problems to the corresponding ones with only discontinuous coefficients is proposed then a decomposition of the solution of the problem with only discontinuous coefficients into regular and singular parts shishkin decomposition is derived asymptotic expansion up to fourth order for the solution in the interfaces is also constructed

some np hard polygon decomposition problems the inherent computational complexity of polygon decomposition problems is of theoretical interest to researchers in the field of computational geometry and of practical interest to those working in syntactic pattern recognition three polygon decomposition problems are shown to be np hard and thus unlikely to admit efficient algorithms the problems are to find minimum decompositions of a polygonal region into perhaps overlapping convex star shaped or spiral subsets we permit the polygonal region to contain holes the proofs are by transformation from boolean three satisfiability a known np complete problem several open problems are discussed

new approximations for minimum weighted dominating sets and minimum weighted connected dominating sets on unit disk graphs given a node weighted graph the minimum weighted dominating set mwds problem is to find a minimum weighted vertex subset such that for any vertex it is contained in this subset or it has a neighbor contained in this set and the minimum weighted connected dominating set mwcds problem is to find a mwds such that the graph induced by this subset is connected in this paper we study these two problems on a unit disk graph a 4 e approximation algorithm for an mwds based on a dynamic programming algorithm for a min weight chromatic disk cover is presented meanwhile we also propose a 1 e approximation algorithm for the connecting part by showing a polynomial time approximation scheme for a node weighted steiner tree problem when the given terminal set is c local and thus obtain a 5 e approximation algorithm for an mwcds

planar formulae and their uses we define the set of planar boolean formulae and then show that the set of true quantified planar formulae is polynomial space complete and that the set of satisfiable planar formulae is np complete using these results we are able to provide simple and nearly uniform proofs of np completeness for planar node cover planar hamiltonian circuit and line geometric connected dominating set and of polynomial space completeness for planar generalized geography the np completeness of planar node cover and planar hamiltonian circuit and line were first proved elsewhere m r garey and d s johnson the rectilinear steiner tree is np complete siam j appl math 32 1977 pp 826 834 and m r garey d s johnson and r e tarjan the planar hamilton circuit problem is np complete siam j comp 5 1976 pp 704 714

the complexity of coloring games on perfect graphs abstract in this paper we consider the following type of game two players must color the vertices of a given graph g v e in a prescribed order in such a way that no two adjacent vertices are colored with the same color in one variant the first player which is unable to move loses the game in another variant player 1 wins the game if and only if the game ends with all vertices colored in this paper we obtain several results on the complexity of the problem to decide whether there is a winning strategy for player 1 in a given game instance when g is restricted to split graphs interval graphs or bipartite graphs

the planar k means problem is np hard in the k means problem we are given a finite set s of points in m and integer k 1 and we want to find k points centers so as to minimize the sum of the square of the euclidean distance of each point in s to its nearest center we show that this well known problem is np hard even for instances in the plane answering an open question posed by dasgupta 2007 7

corrigendum to cycle transversals in perfect graphs and cographs theoret comput sci 469 2013 15 23 abstract in this corrigendum we fix the proof of theorem 1 in brandstadt et al 2013 1

linear time algorithms for testing the realisability of line drawings of curved objects this paper shows that the semantic labelling of line drawings of curved objects with piecewise c 3 surfaces is solvable in linear time this result is robust to changes in the assumptions on object shape when all vanishing points are known a different linear time algorithm exists to solve the labelling problem furthermore in both cases all legally labelled line drawings of curved objects are shown to be physically realisable however when some but not all of the vanishing points are known when the drawing is an orthographic projection of a scene containing parallel lines or when we wish to minimise the number of phantom junctions the labelling problem becomes np hard the introduction of collinearity constraints also renders the labelling problem np complete except in the case when all vanishing points are known 1999 elsevier science b v all rights reserved

on the complexity of the planar directed edge disjoint paths problem the edge disjoint paths problem and many special cases of it are known to be np complete we present a new np completeness result for a special case of the problem namely the directed edge disjoint paths problem restricted to planar supply graphs and demand graphs consisting of two sets of parallel edges

on unique graph 3 colorability and parsimonious reductions in the plane we prove that the satisfiability resp planar satisfiability problem is parsimoniously p time reducible to the 3 colorability resp planar 3 colorability problem that means that the exact number of solutions is preserved by the reduction provided that 3 colorings are counted modulo their six trivial color permutations in particular the uniqueness of solutions is preserved which implies that unique 3 colorability is exactly as hard as unique satisfiability in the general case as well as in the planar case a consequence of our result is the dp completeness of unique 3 colorability and unique planar 3 colorability under random p time reductions it also gives a finer and unified proof of the p completeness of 3 colorability that was first obtained by linial for the general case and later by hunt et al for the planar case previous authors reductions were either weakly parsimonious with a multiplication of the numbers of solutions by an exponential factor or involved p complete intermediate counting problems derived from trivial yes decision problems

thermo elasto plastic finite element analysis of quasi state processes in eulerian reference frames an eulerian finite element formulation for quasi state one way coupled thermo elasto plastic systems is presented the formulation is suitable for modeling material processes such as welding and laser surfacing in an eulerian frame the solution field of a quasi state process becomes steady state for the heat transfer problem and static for the stress problem a mixed small deformation displacement elasto plastic formulation is proposed the formulation accounts for temperature dependent material properties and exhibits a robust convergence streamline upwind petrov galerkin supg is used to remove spurious oscillations smoothing functions are introduced to relax the non differentiable evolution equations and allow for the use of gradient stiffness solution scheme via the newton raphson method a 3 dimensional simulation of a laser surfacing process is presented to exemplify the formulation results from the eulerian formulation are in good agreement with results from the conventional lagrangian formulation however the eulerian formulation is approximately 15 times faster than the lagrangian copyright 2001 john wiley sons ltd

on a rational differential quadrature method in irregular domains for problems with boundary layers abstract a rational differential quadrature method in irregular domains rdqmid is investigated to deal with a kind of singularly perturbed problems with boundary layers through a transformation the boundary layer which may be not straight is transformed into a segment of a line parallel to one of the cartesian axes the rational differential quadrature method rdqm is applied to discretize the governing equation finally a direct expansion method of the boundary conditions dembc is raised to deal with the boundary conditions numerical experiments show that rdqmid is of high accuracy efficiency and easy to programme

the othello game on an n n board is pspace complete abstract given an arbitrary position of the othello game played on an n n board the problem of determining the winner is shown to be pspace complete it can be reduced from generalized geography played on bipartite graphs with maximum degree 3

domain imbedding methods for the stokes equations we study direct and iterative domain imbedding methods for the stokes equations on certain non rectangular domains in two space dimensions we analyze a continuous analog of numerical domain imbedding for bounded smooth domains and give an example of a simple numerical algorithm suggested by the continuous analysis this algorithms is applicable for simply connected domains which can be covered by rectangular grids with uniformly spaced grid lines in at least one coordinate direction we also discuss a related fft based fast solver for stokes problems with physical boundary conditions on rectangles and present some numerical results

a spectral embedding method applied to the advection diffusion equation in order to solve partial differential equations in complex geometries with a spectral type method one describes an embedding approach which essentially makes use of fourier expansions and boundary integral equations for the advection diffusion equation the method is based on an efficient helmholtz solver the accuracy of which is tested by considering 1d and 2d helmholtz like problems finally the capabilities of the method are pointed out by considering a 2d advection diffusion problem in a hexagonal geometry

on the construction of graphs with a planar bipartite double cover from boolean formulas and its application to counting satisfying solutions abstract we address the problem to construct a graph g with binary edge weights from the incidence graph of a boolean formula in a way that g has a planar bipartite double cover g this allows one to use the identity between the permanent of g s adjacency matrix a g and the number of perfect matchings of g i e perm a g pm g due to the algorithm of fisher kasteleyn and temperlay fkt the right hand side of the equation can be counted in polynomial time if g is planar we prove a theorem that describes necessary conditions for the gadgets i e small subgraphs with certain properties of g to allow a planar bipartite double cover g for arbitrary 3cnf formulas and the known approaches to build g our theorem shows that gadgets which enable a planar bipartite double cover do not exist however we show that for certain classes of boolean formulas e g 5 pl rtw 2cnf 7 pl rtw 2cnf and 3 forest 3cnf such gadgets exist hence these counting problems are in p the results probably extended to other moduli p and perhaps further counting classes

a displacement based reference frame formulation for steady state thermo elasto plastic material processes a reference frame formulation for steady state thermo elasto plastic processes is presented the displacement and history dependent response fields appear as the primary variables in this mixed formulation unlike displacement based lagrangian formulations our formulation does not require a transient analysis to simulate a steady state process and yields results that are free of numerical oscillations and which require considerably less computational effort and unlike velocity based eulerian methods our formulation does not require free surface corrections or streamline integration algorithms a laser surface treatment process is simulated and our results are in agreement with those obtained from a computationally intensive transient lagrangian analysis

the computational complexity of probabilistic inference using bayesian belief networks research note abstract bayesian belief networks provide a natural efficient method for representing probabilistic dependencies among a set of variables for these reasons numerous researchers are exploring the use of belief networks as a knowledge representation in artificial intelligence algorithms have been developed previously for efficient probabilistic inference using special classes of belief networks more general classes of belief networks however have eluded efforts to develop efficient inference algorithms we show that probabilistic inference using belief networks is np hard therefore it seems unlikely that an exact algorithm can be developed to perform probabilistic inference efficiently over all classes of belief networks this result suggests that research should be directed away from the search for a general efficient probabilistic inference algorithm and toward the design of efficient special case average case and approximation algorithms

the tractability of segmentation and scene analysis one of the fundamental problems in computer vision is the segmentation of an image into semantically meaningful regions based only on image characteristics a single segmentation can be determined using a linear number of evaluations of a uniformity predicate however minimising the number of regions is shown to be an np complete problem we also show that the variational approach to segmentation based on minimising a criterion combining the overall variance of regions and the number of regions also gives rise to an np complete problem when a library of object models is available segmenting the image becomes a problem of scene analysis a sufficient condition for the reconstruction of a 3d scene from a 2d image to be solvable in polynomial time is that the scene contains no cycles of mutually occluding objects and that no range information can be deduced from the image it is known that relaxing the no cycles condition renders the problem np complete we show that relaxing the no range information condition also produces an np complete problem

the complexity of the residual node connectedness reliability problem this paper considers a probabilistic network in which the edges are perfectly reliable but the nodes fail with some known probabilities the network is in an operational state if the surviving nodes induce a connected graph the residual node connectedness reliability r g of a network g is the probability that the graph induced by the surviving nodes is connected this reliability measure is very different from the widely studied k terminal network reliability measure it is proven that the problem of computing the residual connectedness reliability is np hard by showing that the problem of counting the number of node induced connected subgraphs of a given graph is bf p complete the problem remains bf p complete for split graphs as well as planar and bipartite graphs

optimization of thermo elasto plastic processes using eulerian sensitivity analysis a computational scheme for the analysis and optimization of quasi static thermo mechanical processes is presented in this paper in order to obtain desirable mechanical transformations in a workpiece using a thermal treatment process the optimal control parameters need to be determined the problem is addressed by posing the process as a decoupled thermo mechanical finite element problem and performing an optimization using gradient methods the forward problem is solved using the eulerian formulation since it is computationally more efficient compared to an equivalent lagrangian formulation the design sensitivities required for the optimization are developed analytically using direct differentiation this systematic design approach is applied to optimize a laser forming process the objective is to maximize the angular distortion of a specimen subject to the constraint that the phase transition temperature is not exceeded at any point in the model copyright 2003 john wiley sons ltd

a polyhedral description of kernels let g be a digraph and let g be the linear system consisting of nonnegativity stability and domination inequalities we call g kernel ideal if h defines an integral polytope for each induced subgraph h of g and we call g kernel mengerian if h is totally dual integral tdi for each induced subgraph h of g in this paper we show that a digraph is kernel ideal iff it is kernel mengerian iff it contains none of three forbidden structures our characterization yields a polynomial time algorithm for the minimum weighted kernel problem on kernel ideal digraphs we also prove that it is np hard to find a kernel of minimum size even in a planar bipartite digraph with maximum degree at most three

finding k disjoint paths in a directed planar graph it is shown that for each fixed k the problem of finding k pairwise vertex disjoint directed paths between given pairs of terminals in a directed planar graph is solvable in polynomial time

on the continuous fermat weber problem we give the firstexact algorithmic study of facility location problems that deal with finding a median for acontinuum of demand points in particular we consider versions of the continuousk median fermat weber problem where the goal is to select one or more center points that minimize the average distance to a set of points in a demandregion in such problems the average is computed as an integral over the relevant region versus the usual discrete sum of distances the resulting facility location problems are inherently geometric requiring analysis techniques of computational geometry we provide polynomial time algorithms for various versions of thel1 1 median fermat weber problem we also consider the multiple center version of thel1k median problem which we prove is np hard for largek

the minimum broadcast time problem for several processor networks abstract broadcasting is the information dissemination process in a communication network a subset of processors v 0 v called originators knows an unique message which has to be transferred by calls between adjacent processors each call requires one time unit and each processor can participate in at most one call per time unit the problem is to find a schedule such that the time needed to inform all processors is less than or equal to a deadline k n we present np completeness results for this problem restricted to several communication networks bipartite planar graphs grid graphs complete grid graphs split graphs and chordal graphs with constant deadline k 2 or one originator v 0

finite element superconvergence on shishkin mesh for 2 d convection diffusion problems in this work the bilinear finite element method on a shishkin mesh for convection diffusion problems is analyzed in the two dimensional setting a superconvergence rate o n 2 ln2 n en 1 5lnn in a discrete e weighted energy norm is established under certain regularity assumptions this convergence rate is uniformly valid with respect to the singular perturbation parameter e numerical tests indicate that the rate o n 2ln2 n is sharp for the boundary layer terms as a by product an e uniform convergence of the same order is obtained for the l2 norm furthermore under the same regularity assumption an e uniform convergence of order n 3 2ln5 2n en 1ln1 2n in the l norm is proved for some mesh points in the boundary layer region

bottleneck steiner trees in the plane a steiner tree with maximum weight edge minimized is called a bottleneck steiner tree bst the authors propose a theta mod rho mod log mod rho mod time algorithm for constructing a bst on a point set rho with points labeled as steiner or demand a lower bound in the linear decision tree model is also established it is shown that if it is desired to minimize further the number of used steiner points then the problem becomes np complete it is shown that when locations of steiner points are not fixed the problem remains np complete however if the topology of the final tree is given then the problem can be solved in theta mod rho mod log mod rho mod time the bst problem can be used for example in vlsi layout communication network design and facility location problems

approximation algorithms for pspace hard hierarchically and periodically specified problems we study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in t lengauer j assoc comput mach 36 1989 pp 474 509 or are specified by one dimensional finite narrow periodic specifications as in e wanke paths and cycles in finite periodic graphs in lecture notes in comp sci 711 springer verlag new york 1993 pp 751 760 we show that for most of the problems pi considered when specified using k level restricted hierarchical specifications or k narrow periodic specifications the following hold let rho be any performance guarantee of a polynomial time approximation algorithm for pi when instances are specified using standard specifications then forall epsilon 0 pi has a polynomial time approximation algorithm with performance guarantee 1 epsilon rho pi has a polynomial time approximation scheme when restricted to planar instances these are the first polynomial time approximation schemes for pspace hard hierarchically or periodically specified problems since several of the problems considered are pspace hard our results provide the first examples of natural pspace hard optimization problems that have polynomial time approximation schemes this answers an open question in condon et al chicago j theoret comput sci 1995 article 4

radiocoloring in planar graphs complexity and approximations the frequency assignment problem fap in radio networks is the problem of assigning frequencies to transmitters by exploiting frequency reuse while keeping signal interference to acceptable levels the fap is usually modelled by variations of the graph coloring problem a radiocoloring rc of a graph g v e is an assignment function v n such that u v 2 when u v are neighbors in g and u v 1 when the distance of u v in g is two the number of discrete frequencies and the range of frequencies used are called order and span respectively the optimization versions of the radiocoloring problem rcp are to minimize the span or the order in this paper we prove that the radiocoloring problem for general graphs is hard to approximate unless np zpp within a factor of n1 2 e for any e 0 where n is the number of vertices of the graph however when restricted to some special cases of graphs the problem becomes easier we prove that the min span rcp is np complete for planar graphs next we provide an o n time algorithm v n which obtains a radiocoloring of a planar graph g that approximates the minimum order within a ratio which tends to 2 where the maximum degree of g finally we provide a fully polynomial randomized approximation scheme fpras for the number of valid radiocolorings of a planar graph g with colors in the case where 4 50

on the proper orientation number of bipartite graphs an orientation of a graph g is a digraph d obtained from g by replacing each edge by exactly one of the two possible arcs with the same endvertices for each v v g the indegree of v in d denoted by d d v is the number of arcs with head v in d an orientation d of g is proper if d d u d d v for all u v e g the proper orientation number of a graph g denoted by g is the minimum of the maximum indegree over all its proper orientations in this paper we prove that g g g 2 1 if g is a bipartite graph and g 4 if g is a tree it is well known that g g for every graph g however we prove that deciding whether g g 1 is already an np complete problem on graphs with g k for every k 3 we also show that it is np complete to decide whether g 2 for planar subcubic graphs g moreover we prove that it is np complete to decide whether g 3 for planar bipartite graphs g with maximum degree 5

optimization of thermal processes using an eulerian formulation and application in laser surface hardening a systematic design approach has been developed for thermal processes combining the nite element method design sensitivity analysis and optimization conductive heat transfer is solved in an eulerian formulation where the heat ux is xed in space and the material ows through a control volume for constant velocity and heat ux distribution the eulerian formulation reduces to a steady state problem whereas the lagrangian formulation remains transient the reduction to a steady state problem drastically improves the computational e ciency streamline upwinding petrov galerkin stabilization is employed to suppress the spurious oscillations design sensitivities of the temperature eld are computed using both the direct di erentiation and the adjoint methods the systematic approach is applied in optimizing the laser surfacing process where a moving laser beam heats the surface of a plate and hardening is achieved by rapid cooling due to the heat transfer below the surface the optimization objective is to maximize the rate of surface hardening constraints are introduced on the computed temperature and temperature rate elds to ensure that phase transformations are activated and that melting does not occur copyright 2000 john wiley sons ltd

spectral methods for partial differential equations in irregular domains the spectral smoothed boundary method in this paper we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no flux boundary conditions the idea is to embed the domain into a box and use a smoothing term to encode the boundary conditions into a modified equation that can be approached by standard spectral methods the main features of this method are its capability to deal with domains of arbitrary shape and its easy implementation via fast fourier transform routines we discuss several examples of practical interest and test the results against standard numerical methods

the complexity of understanding line drawings of origami scenes this paper deals with the interpretation of line drawings of origami scenes kanade 1980 that is scenes obtained by assembling planar panels of negligible thickness and it addresses the computational complexity of the problem of consistently assigning suitable labels to the segments describing 3d properties as convexity concavity and occlusion labeling problem the main results of the paper are the following a the labeling problem for line drawings of origami scenes is np as for the case of trihedral scenes b the problem remains np even if the location of the vanishing points in the image plane is given whereas for trihedral scenes the problem was polynomially solvable c in case the vanishing points are known the labeling problem can be subdivided into two subproblems the paneling problem and the labeling a paneled line drawing problem which are both polynomially solvable there may be however exponentially many legal panelings to check against labelability

cycle transversals in perfect graphs and cographs a cycle transversal or feedback vertex set of a graph g is a subset t v g such that t v c 0 for every cycle c of g this work considers the problem of finding special cycle transversals in perfect graphs and cographs we prove that finding a minimum cycle transversal t in a perfect graph g is np hard even for bipartite graphs with maximum degree four since g t is acyclic this result implies that finding a maximum acyclic induced subgraph of a perfect graph is also np hard other special properties of t are considered a clique stable respectively cycle transversal or simply cct sct respectively is a cycle transversal which is a clique stable set respectively recognizing graphs which admit a cct can be done in polynomial time however no structural characterization of such graphs is known even for perfect graphs we characterize cographs with cct in terms of forbidden induced subgraphs and describe their structure this leads to linear time recognition of cographs with cct we also prove that deciding whether a perfect graph admits an sct is np complete we characterize cographs with sct in terms of forbidden induced subgraphs this characterization also leads to linear time recognition

holographic algorithms the power of dimensionality resolved valiant s theory of holographic algorithms is a novel methodology to achieve exponential speed ups in computation a fundamental parameter in holographic algorithms is the dimension of the linear basis vectors we completely resolve the problem of the power of higher dimensional bases we prove that 2 dimensional bases are universal for holographic algorithms

tangent operators and design sensitivity formulations for transient non linear coupled problems with applications to elastoplasticity tangent operators and design sensitivities are derived for transient non linear coupled problems the solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods the derived formulations are suitable for finite element implementations analyses of systems with materials that exhibit history dependent response may be obtained directly by applying the analyses of transient non linear coupled systems rate independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes

the complexity of planar counting problems we prove the p hardness of the counting problems associated with various satisfiability graph and combinatorial problems when restricted to planar instances these problems include 3sat 1 3sat 1 ex3sat minimum vertex cover minimum dominating set minimum feedback vertex set x3c partition into triangles and clique cover we also prove the np completeness of the ambiguous satisfiability problems j b saxe two papers on graph embedding problems tech report cmu cs 80 102 dept of computer science carnegie mellon univ pittsburgh pa 1980 and the dp completeness with respect to random polynomial reducibility of the unique satisfiability problems l g valiant and v v vazirani np is as easy as detecting unique solutions in proc 17th acm symp on theory of computing 1985 pp 458 463 associated with several of the above problems when restricted to planar instances previously very few p hardness results no sf np hardness results and no dp completeness results were known for counting problems ambiguous satisfiability problems and unique satisfiability problems respectively when restricted to planar instances assuming sf p neq np one corollary of the above results is that there are no epsilon approximation algorithms for the problems of maximizing or minimizing a linear objective function subject to a planar system of linear inequality constraints over the integers

following a curve with the discrete frechet distance finding the similarity between curves is an important problem that comes up in many areas such as 3d modeling gis applications ordering and reachability a related problem is to find one of the curves given a measure of similarity and another curve given a set of points s a polygonal curve p and an e 0 the discrete set chain matching problem is to find another polygonal curve q such that the nodes of q are points in s and d f p q e here d f is the discrete frechet distance between the two polygonal curves for the first time we study the set chain matching problem based on the discrete frechet distance rather than the continuous frechet distance we further extend the problem based on unique or non unique nodes and on limiting the number of points used we prove that three of the variations of the set chain matching problem are np complete for the version of the problem that is polynomial we give an o p s time greedy solution

a rational spectral collocation method with adaptively transformed chebyshev grid points a spectral collocation method based on rational interpolants and adaptive grid points is presented the rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed chebyshev points the locations of the grid points are adapted to singularities of the underlying solution and the locations of these singularities are approximated by the locations of poles of chebyshev pade approximants numerical experiments on two time dependent problems one with finite time blow up and one with a moving front indicate that the method far outperforms the standard chebyshev spectral collocation method for problems whose solutions have singularities in the complex plane close to 1 1

computing coverage kernels under restricted settings abstract given a set b of d dimensional boxes i e axis aligned hyperrectangles a minimum coverage kernel is a subset of b of minimum size covering the same region as b computing it is np hard but as for many similar np hard problems e g box cover and orthogonal polygon covering the problem becomes solvable in polynomial time under restrictions on b we show that computing minimum coverage kernels remains np hard even when restricting the graph induced by the input to a highly constrained class of graphs alternatively we present two polynomial time approximation algorithms for this problem one deterministic with an approximation ratio within o log n and one randomized with an improved approximation ratio within o lg opt with high probability

on the complexity of labeling perspective projections of polyhedral scenes abstract this paper investigates the computational time complexity of the labeling problem for line drawings of trihedral scenes it is shown that the class of problems having polynomial complexity is larger than the simple case of line drawings of legoland scenes kirousis and papadimitriou 1988 once the location of the vanishing points in the image plane is known the labeling problem can be solved in time o nn where n is the number of segments and n is the number of vanishing points the vanishing points can be given a priori otherwise can in many cases be detected by standard techniques from the line drawing itself the np completeness of the labeling problem for line drawings of trihedral scenes kirousis and papadimitriou 1988 is then due to the lack of knowledge about the vanishing points which is equivalent to the knowledge of the possible directions for the edges these results help draw a more accurate boundary between the problems in the interpretation of line drawings that are polynomially solvable and those that are np complete

on finding short resolution refutations and small unsatisfiable subsets we consider the parameterized problems of whether a given set of clauses can be refuted within k resolution steps and whether a given set of clauses contains an unsatisfiable subset of size at most k we show that both problems are complete for the class w 1 the first level of the w hierarchy of fixed parameter intractable problems our results remain true if restricted to 3 sat instances and or to various restricted versions of resolution including tree like resolution input resolution and read once resolution applying a metatheorem of frick and grohe we show that restricted to classes of sets of clauses of locally bounded treewidth the considered problems are fixed parameter tractable for example the problems are fixed parameter tractable for planar cnf formulas

the directed hausdorff distance between imprecise point sets we consider the directed hausdorff distance between point sets in the plane where one or both point sets consist of imprecise points an imprecise point is modelled by a disc given by its centre and a radius the actual position of an imprecise point may be anywhere within its disc due to the direction of the hausdorff distance and whether its tight upper or lower bound is computed there are several cases to consider for every case we either show that the computation is np hard or we present an algorithm with a polynomial running time further we give several approximation algorithms for the hard cases and show that one of them cannot be approximated better than with factor 3 unless p np

on the complexity of clustering with relaxed size constraints in fixed dimension abstract we study the computational complexity of the problem of computing an optimal clustering a 1 a 2 a k of a set of points assuming that every cluster size a i belongs to a given set m of positive integers we present a polynomial time algorithm for solving the problem in dimension 1 i e when the points are simply rational values for an arbitrary set m of size constraints which extends to the l 1 norm an analogous procedure known for the euclidean norm moreover we prove that in dimension 2 assuming euclidean norm the problem is strongly np hard with size constraints m 2 4 this result is extended also to the size constraints m 2 3 both in the case of euclidean and l 1 norm