minimum fill in inapproximability and almost tight lower bounds abstract given an n n sparse symmetric matrix with m nonzero entries performing gaussian elimination may turn some zeroes into nonzero values so called fill ins the minimum fill in problem asks whether it is possible to perform the elimination with at most k fill ins we exclude the existence of polynomial time approximation schemes for this problem assuming p np and the existence of 2 o n 1 time approximation schemes for any positive assuming the exponential time hypothesis we also give a 2 o k 1 2 n o 1 parameterized lower bound all these results come as corollaries of a new reduction from vertex cover to the minimum fill in problem which might be of its own interest all previous reductions for similar problems start from some kind of graph layout problems and hence have limited use in understanding their fine grained complexity

conditional gauge and potential theory for the schrodinger operator on etend le theoreme de jauge conditionnelle a des operateurs plus generaux et a des domaines moins reguliers on obtient des resultats de theorie du potentiel pour l equation de schrodinger

approximation algorithms for minimum weight connected 3 path vertex cover abstract a k path vertex cover vcpk is a vertex set c of graph g such that every path of g on k vertices has at least one vertex in c because of its background in keeping data integrality of a network minimum vcpk problem minvcpk has attracted a lot of researches in recent years this paper studies the minimum weight connected vcpk problem minwcvcpk in which every vertex has a weight and the vcpk found by the algorithm induces a connected subgraph and has the minimum weight it is known that minwcvcpk is set cover hard we present two polynomial time approximation algorithms for minwcvcp3 the first one is a greedy algorithm achieving approximation ratio 3ln n the difficulty lies in its analysis dealing with a non submodular potential function the second algorithm is a 2 stage one finding a vcp3 in the first stage and then adding more vertices for connection we show that its approximation ratio is at most ln max 4 ln 2 where max is the maximum degree of the graph considering the inapproximability of this problem this ratio is asymptotically tight

quenching of flames by fluid advection we consider a simple scalar reaction advection diffusion equation with ignitiontype nonlinearity and discuss the following question what kinds of velocity profiles are capable of quenching any given flame provided the velocity s amplitude is adequately large even for shear flows the answer turns out to be surprisingly subtle if the velocity profile changes in space so that it is nowhere identically constant or if it is identically constant only in a region of small measure then the flow can quench any initial data but if the velocity profile is identically constant in a sizable region then the ensuing flow is incapable of quenching large enough flames no matter how much larger the amplitude of this velocity is the constancy region must be wider across than a couple of laminar propagating front widths the proof uses a linear pde associated to the nonlinear problem and quenching follows when the pde is hypoelliptic the techniques used allow the derivation of new nearly optimal bounds on the speed of traveling wave solutions c 2001 john wiley sons inc

front speed enhancement by incompressible flows in three or higher dimensions we study in dimensions n 3 the family of first integrals of an incompressible flow these are h 1 rm loc functions whose level surfaces are tangential to the streamlines of the advective incompressible field one main motivation for this study comes from earlier results proving that the existence of nontrivial first integrals of an incompressible flow q is the main key that leads to a linear speed up by a large advection of pulsating traveling fronts solving a reaction advection diffusion equation in a periodic heterogeneous framework the family of first integrals is not well understood in dimensions n 3 due to the randomness of the trajectories of q and this is in contrast with the case n 2 by looking at the domain of propagation as a union of different components produced by the advective field we provide more information about first integrals and we give a class of incompressible flows which exhibit ergodic components of positive lebesgue measure and hence are not shear flows and which under certain sharp geometric conditions speed up the kpp fronts linearly with respect to the large amplitude in the proofs we establish a link between incompressibility ergodicity first integrals and the dimension to give a sharp condition about the asymptotic behavior of the minimal kpp speed in terms of the configuration of ergodic components

extracting embedded generalized networks from linear programming problems if a linear program lp possesses a large generalized network gn submatrix this structure can be exploited to decrease solution time the problems of finding maximum sets of gn constraints and finding maximum embedded gn submatrices are shown to be np complete indicating that reliable efficient solution of these problems is difficult therefore efficient heuristic algorithms are developed for identifying such structure and are tested on a selection of twenty three real world problems the best of four algorithms for identifying gn constraint sets finds a set which is maximum in twelve cases and averages 99 1 of maximum on average the gn constraints identified comprise more than 62 3 of the total constraints in these problems the algorithm for identifying embedded gn submatrices finds submatrices whose sizes rows plus columns average 96 8 of an lp upper bound over 91 3 of the total constraint matrix was identified as a gn submatrix in these problems on average

np hard graph problems and boundary classes of graphs any graph problem which is np hard in general graphs becomes polynomial time solvable when restricted to graphs in special classes when does a difficult problem become easy to answer this question we study the notion of boundary classes in the present paper we define this notion in its most general form describe several approaches to identify boundary classes and apply them to various graph problems

approximation algorithms for node deletion problems on bipartite graphs with finite forbidden subgraph characterization in this paper we develop approximation algorithms for a few node deletion problems when the input is restricted to be a bipartite graph we look at node deletion problems for non trivial properties which can be characterized by forbidden structure which has a bounded intersection with both the bipartitions the approximation factors obtained directly depend upon the size of the largest such intersection special instances of this general problem include problems such as the minimum chain vertex deletion minimum dissociation vertex deletion minimum bipartite claw vertex deletion minimum bi complement vertex deletion and minimum bipartite threshold vertex deletion problems the algorithms are based upon the techniques of linear programming and iterative rounding we also use the node deletion algorithms to marginally improve the trivial approximation factor for complementary problem of determining the size of the maximum sized vertex induced subgraph lying in the given graph class and prove the apx completeness of all of these problems

sharp transition between extinction and propagation of reaction with x e r this equation has been extensively studied in mathematical physical and other literature starting with the pioneering works of fisher 7 and kol mogorov petrovskii piskunov 11 in these papers 1 2 was used to describe the propagation of advantageous genes in a population the main object of study in these and many subsequent works was the existence and stability of traveling fronts for 1 2 and 1 1 in recent years most of the results have been extended to in clude an advection term u vt in 1 1 and we refer to the reviews 2 16 for an extensive bibliography the above equations are used to model more than just population genetics phe nomena when f 0 0 for 9 g 0 1 then is a combustion non linearity and 1 1 1 2 model an exothermic chemical reaction in an infinite tube with a zero heat loss boundary in particular flame propagation in a premixed combustible gas without advection see zel dovich and frank kamenetskii 17 in this setting t is the normalized temperature taking values in 0 1 we note that 1 1 is usu ally obtained from a system involving both the temperature and the concentration of the reactants after the simplifying assumption of equal thermal and material diffusivities a special case of positive used particularly in chemical and biological lit erature is the kpp type with f 6 c 0 11 in combustion models the non linearity is often considered to be of arrhenius type with slow reaction rates at low temperatures modeled by f 0 e a e l 0 this case is often approximated

partitioning a graph into small pieces with applications to path transversal given a graph g v e and an integer k in mathbb n we study k vertex separator resp k edge separator where the goal is to remove the minimum number of vertices resp edges such that each connected component in the resulting graph has less than k vertices we also study k path transversal where the goal is to remove the minimum number of vertices such that there is no simple path of length k our main results are the following improved approximation algorithms

on computing the minimum 3 path vertex cover and dissociation number of graphs the dissociation number of a graph g is the number of vertices in a maximum size induced subgraph of g with vertex degree at most 1 a k path vertex cover of a graph g is a subset s of vertices of g such that every path of order k in g contains at least one vertex from s the minimum 3 path vertex cover is a dual problem to the dissociation number for this problem we present an exact algorithm with a running time of o 1 5171 n on a graph with n vertices we also provide a polynomial time randomized approximation algorithm with an expected approximation ratio of 2311 for the minimum 3 path vertex cover

strong geodetic cores and cartesian product graphs abstract the strong geodetic problem on a graph g is to determine a smallest set of vertices such that by fixing one shortest path between each pair of its vertices all vertices of g are covered to do this as efficiently as possible strong geodetic cores and related numbers are introduced sharp upper and lower bounds on the strong geodetic core number are proved using the strong geodetic core number an earlier upper bound on the strong geodetic number of cartesian products is improved it is also proved that sg g k2 sg g holds for different families of graphs a result conjectured to be true in general counterexamples are constructed demonstrating that the conjecture does not hold in general

exact algorithms for the maximum dissociation set and minimum 3 path vertex cover problems a dissociation set in a graph g v e is a vertex subset d such that the subgraph g d induced on d has vertex degree at most 1 a 3 path vertex cover in a graph is a vertex subset c such that every path of three vertices contains at least one vertex from c a vertex set d is a dissociation set if and only if v d is a 3 path vertex cover there are many applications for dissociation sets and 3 path vertex covers however it is np hard to compute a dissociation set of maximum size or a 3 path vertex cover of minimum size in graphs several exact algorithms have been proposed for these two problems and they can be solved in o 1 4658 n time in n vertex graphs in this paper we reveal some interesting structural properties of the two problems which allow us to solve them in o 1 4656 n time and polynomial space or o 1 3659 n time and exponential space

improved approximation algorithms for hitting 3 vertex paths we study the problem of deleting a minimum cost set of vertices from a given vertex weighted graph in such a way that the resulting graph has no induced path on three vertices this problem is often called cluster vertex deletion in the literature and admits a straightforward 3 approximation algorithm since it is a special case of the vertex cover problem on a 3 uniform hypergraph recently you wang and cao described an efficient 5 2 approximation algorithm for the unweighted version of the problem our main result is a 9 4 approximation algorithm for arbitrary weights using the local ratio technique we further conjecture that the problem admits a 2 approximation algorithm and give some support for the conjecture this is in sharp contrast with the fact that the similar problem of deleting vertices to eliminate all triangles in a graph is known to be ugc hard to approximate to within a ratio better than 3 as proved by guruswami and lee

stability of travelling fronts in a model for flame propagation part i linear analysis we investigate the stability of travelling wave solutions of the multidimensional thermodiffusive model for flame propagation with unit lewis number this model consists in a system of two nonlinear parabolic equations posed in an infinite cylinder with neumann boundary conditions in this paper we prove that every travelling wave solution of this model is linearly stable our tools are exponential decay estimates for solutions of elliptic equations in a cylinder and the maximum principle for parabolic equations

approximation algorithm for minimum weight connected k subgraph cover abstract for a given graph g the minimum weight connected k subgraph cover problem minwcksc is to find a minimum weight vertex subset c of g such that each connected subgraph of g on k vertices contains at least one vertex of c previously zhang et al 37 presented a k 1 approximation algorithm for minwcksc under the assumption that the girth of g which is the length of a shortest cycle of g is at least k in this paper we improve this result by showing that k 1 approximation can be achieved when the girth requirement is relaxed from k to 2 k 3

independent packings in structured graphs packing a maximum number of disjoint triangles into a given graph g is np hard even for most classes of structured graphs in contrast we show that packing a maximum number of independent that is disjoint and nonadjacent triangles is polynomial time solvable for many classes of structured graphs including weakly chordal graphs asteroidal triple free graphs polygon circle graphs and interval filament graphs these classes contain other well known classes such as chordal graphs cocomparability graphs circle graphs circular arc graphs and outerplanar graphs our results apply more generally to independent packings by members of any family of connected graphs

approximation algorithm for the minimum weight connected k subgraph cover problem a subset f of vertices is called a connected k subgraph cover vcck if every connected subgraph on k vertices contains at least one vertex from f the minimum weight connected k subgraph cover problem mwvcck has its background in the field of security and supervisory control it is a generalization of the minimum weight vertex cover problem and is related with the minimum weight k path cover problem mwvcpk which requires that every path on k vertices has at least one vertex from f a k approximation algorithm can be easily obtained by lp rounding method assuming that the girth of the graph is at least k we reduce the approximation ratio to k 1 which is tight for our algorithm

a primal dual approximation algorithm for the vertex cover p3 problem we introduce the vertex coverp n vcp n problem that is the problem of finding a minimum weight set email protected v such that the graph g v f has no p n where p n is a path with n vertices the problem also has its application background in this paper we first show that the vcp n problem is np hard for any integer n 2 then we restrict our attention to the vcp 3 problem and give a 2 approximation algorithm using the primal dual method

improved upper bounds for vertex cover this paper presents an o 1 2738 k kn time polynomial space algorithm for vertex cover improving the previous o 1 286 k kn time polynomial space upper bound by chen kanj and jia most of the previous algorithms rely on exhaustive case by case branching rules and an underlying conservative worst case scenario assumption the contribution of the paper lies in the simplicity uniformity and obliviousness of the algorithm presented several new techniques as well as generalizations of previous techniques are introduced including general folding struction tuples and local amortized analysis the algorithm also improves the o 1 2745 kk 4 kn time exponential space upper bound for the problem by chandran and grandoni

diffusion and mixing in fluid flow we study enhancement of diffusive mixing on a compact riemannian manifold by a fast incompressible flow our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small in an arbitrarily short time provided that the flow amplitude is large enough the necessary and suficient condition on such flows is expressed naturally in terms of the spectral properties of the dynamical system associated with the flow in particular we find that weakly mixing flows always enhance dissipation in this sense the proofs are based on a general criterion for the decay of the semigroup generated by an operator of the form g ial with a negative unbounded self adjoint operator g a self adjoint operator l and parameter a 1 in particular they employ the rage theorem describing evolution of a quantum state belonging to the continuous spectral subspace of the hamiltonian related to a classical theorem of wiener on fourier transforms of measures applications to quenching in reaction diffusion equations are also considered

a general approximation technique for constrained forest problems we present a general approximation technique for a large class of graph problems our technique mostly applies to problems of covering at minimum cost the vertices of a graph with trees cycles or paths satisfying certain requirements in particular many basic combinatorial optimization problems fit in this framework including the shortest path minimum cost spanning tree minimum weight perfect matching traveling salesman and steiner tree problems our technique produces approximation algorithms that run in o n 2 log n time and come within a factor of 2 of optimal for most of these problems for instance we obtain a 2 approximation algorithm for the minimum weight perfect matching problem under the triangle inequality our running time of o n 2 log n time compares favorably with the best strongly polynomial exact algorithms running in o n 3 time for dense graphs a similar result is obtained for the 2 matching problem and its variants we also derive the first approximation algorithms for many np complete problems including the non fixed point to point connection problem the exact path partitioning problem and complex location design problems moreover for the prize collecting traveling salesman or steiner tree problems we obtain 2 approximation algorithms therefore improving the previously best known performance guarantees of 2 5 and 3 respectively math programming 59 1993 pp 413 420

existence and nonexistence of traveling waves and reaction diffusion front propagation in periodic media we review the existence results of traveling wave solutions to the reaction diffusion equations with periodic diffusion convection coefficients and combustion bistable nonlinearities we prove that whenever traveling waves exist the solutions of the initial value problem with either frontlike or pulselike data propagate with the constant effective speeds of traveling waves in all suitable directions in the case of bistable nonlinearity and one space dimension we give an example of nonexistence of traveling waves which causes quenching localization of wavefront propagation quenching localization only occurs when the variations of the media from their constant mean values are large enough our related numerical results also provide evidence for this phenomenon in the parameter regimes not covered by the analytical example finally we comment on the role of the effective wave speeds in determining the effective wavefront equation hamilton jacobi equation of the reactiondiffusion equations under the small diffusion fast reaction limit with a formal geometric optics expansion

kernels for packing and covering problems abstract we show how the notion of combinatorial duality related to the well known notion of duality from linear programming may be used for translating kernel results obtained for packing problems into kernel results for covering problems we exemplify this approach by having a closer look at the problems of packing a graph with vertex disjoint trees or vertex disjoint stars with r edges the case r 2 has been studied in several other papers by establishing a general notion of a crown we show how linear size vertex kernels can be efficiently achieved for the mentioned problems

efficient algorithm for the vertex cover pk problem on cacti abstract given a graph g v e the vertex cover p k vcp k problem is to find a minimum set f v such that every path of order k in g contains at least one vertex from f for any integer k 2 the vcp k problem for general graphs is np hard the paper presents an efficient algorithm for the vcp k problem on cacti

hitting subgraphs in p4 tidy graphs abstract vertex cover number which is one of the most basic graph invariants can be viewed as the smallest number of vertices that hit or that belong to every subgraph k2 in a graph g in this paper we consider the next two smallest cases of connected graphs which are the path p3 and the cycle c3 the problem is to minimize the set of vertices that hit every subgraph h in g where h is one of the two graphs we focus on computational aspects of these two variations of the vertex cover number we show that both problems are np complete even in the class of graphs that have no induced cycles of length t where t 4 8 in fact in the p3 hitting case the problem is np complete in even smaller family of graphs where also triangles are forbidden on the positive side we prove a complementary result that in graphs with no induced p4 the so called cographs both problems become linear moreover we consider a generalization of cographs p4 tidy graphs for which we establish an efficient algorithm for both problems

front propagation in reactive systems with anomalous diffusion abstract we study front propagation of reactive fields in systems whose diffusive behavior is anomalous both superdiffusive and subdiffusive the features of the front propagation depend not only on the scaling exponent x t 2 t 2 but also on the detailed shape of the probability distribution of the diffusive process from the analysis of different systems we have three possible behavior of front propagation the usual fisher kolmogorov like scenario i e the field has a spatial exponential tail moving with constant speed v f and thickness the field has a spatial exponential tail but v f and change in time as a power law and finally the field has a spatial power law tail and v f increases exponentially in time a linear analysis of the front tail is in quantitative agreement with the numerical simulations it is remarkable the fact that anomalous diffusion is neither necessary nor sufficient condition for the linear front propagation moreover if the probability distribution of the transport process follows the scaling relation given by the flory argument the front propagation is standard fisher kolmogorov like even in presence of super or sub diffusion

simultaneous consecutive ones submatrix and editing problems classical complexity and fixed parameter tractable results abstract a binary matrix m has the consecutive ones property c1p for rows resp columns if there exists a permutation of its columns resp rows that arranges the ones consecutively in all the rows resp columns if m has the c1p for rows and the c1p for columns then m is said to have the simultaneous consecutive ones property sc1p in this article we consider the classical complexity and fixed parameter tractability of a few variants of decision problems related to the sc1p given a binary matrix m and a positive integer d we focus on problems that decide whether there exists a set of rows columns and rows as well as columns respectively of size at most d in m whose deletion results in a matrix with the sc1p we also consider problems that decide whether there exists a set of 0 entries 1 entries and 0 entries as well as 1 entries respectively of size at most d in m whose flipping results in a matrix with the sc1p in this paper we show that all the above mentioned problems are np complete we could also prove that all these problems are fixed parameter tractable with respect to solution size as the parameter except for two variants flipping 1 entries and flipping 0 1 entries we also give improved fpt algorithms for certain problems on restricted binary matrices

the k path vertex cover in cartesian product graphs and complete bipartite graphs abstract for a graph g and a positive integer k a subset s of vertices of g is called a k path vertex cover if s intersects all paths of order k in g the cardinality of a minimum k path vertex cover is denoted by k g and called the k path vertex cover number of g in this paper we study some cartesian product graphs and give several estimations and the exact values of k g

a ptas for the minimum weight connected vertex cover p 3 problem on unit disk graphs let g v e be a weighted graph i e with a vertex weight function w v r we study the problem of determining a minimum weight connected subgraph of g that has at least one vertex in common with all paths of length two in g it is known that this problem is np hard for general graphs we first show that it remains np hard when restricted to unit disk graphs our main contribution is a polynomial time approximation scheme for this problem if we assume that the problem is c local and the unit disk graphs have minimum degree of at least two

node deletion problems on bipartite graphs a set of problems which has attracted considerable interest recently is the set of node deletion problems the general node deletion problem can be stated as follows given a graph find the minimum number of nodes whose deletion results in a subgraph satisfying property r in ly this problem was shown to be np complete for a large class of properties the class of properties that are hereditary on induced subgraphs using a small number of reduction schemes from the node cover problem since the node cover problem becomes polynomial on bipartite graphs it might be hoped that this is the case with other node deletion problems too in this paper we characterize those properties for which the bipartite restriction of the node deletion problem is polynomial and those for which it remains np complete similar results follow for analogous problems on other structures such as families of sets hypergraphs and 0 1 matrices for example in the case of matrices our result states that ifm is a class of 0 1 matrices which is closed under permutation and deletion of rows and columns then finding the largest submatrix inm of a matrix is polynomial if the matrices ofm have bounded rank and np complete otherwise 1 introduction a common approach when faced with an np complete problem c k gj is to restrict its input domain with the hope that the problem may become solvable in polynomial time under the restriction in fact it turns out that sometimes this is the case for example the node cover problem np complete on general graphs k can be solved efficiently when restricted to bipartite graphs this follows from k6nig s theorem that the node covering number of a bipartite graph equals the number of edges in a maximum matching and moreover a minimum node cover can be found efficiently from a maximum matching when the graph is bipartite see for example la in other cases however the node cover problem continues to be np complete under restriction for example the node cover problem on planar graphs gjs much work has been done recently kd ly ldl on a class of problems called the node deletion or maximum subgraph problems the general node deletion problem can be stated as follows given a graph or digraph g find a set of nodes of minimum cardinality whose deletion results in a graph or digraph satisfying a property r several of the known np complete problems such as the node cover the max clique the feedback node set k as well as some polynomial problems such as the connectivity of a graph e it can be formulated in an obvious way as node deletion problems by specifying appropriately the property r

elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena this paper is concerned with the asymptotic behaviour of the principal eigenvalue of some linear elliptic equations in the limit of high first order coefficients roughly speaking one of the main results says that the principal eigenvalue with dirichlet boundary conditions is bounded as the amplitude of the coefficients of the first order derivatives goes to infinity if and only if the associated dynamical system has a first integral and the limiting eigenvalue is then determined through the minimization of the dirichlet functional over all first integrals a parabolic version of these results as well as other results for more general equations are given some of the main consequences concern the influence of high advection or drift on the speed of propagation of pulsating travelling fronts

quenching of combustion by shear flows we consider a model describing premixed combustion in the presence of fluid flow reaction diffusion equation with passive advection and ignition type nonlinearity what kinds of velocity profiles are capable of quenching suppressing any given flame provided the velocity s amplitude is adequately large even for shear flows the solution turns out to be surprisingly subtle in this paper we provide a sharp characterization of quenching for shear flows the flow can quench any initial data if and only if the velocity profile does not have an interval larger than a certain critical size where it is identically constant the efficiency of quenching depends strongly on the geometry and scaling of the flow we discuss the cases of slowly and quickly varying flows proving rigorously scaling laws that have been observed earlier in numerical experiments the results require new estimates on the behavior of the solutions to advectionenhanced diffusion equation also known as passive scalar in physical literature a classical model describing a wealth of phenomena in nature the technique involves probabilistic and pde estimates in particular applications of malliavin calculus and central limit theorem for martingales

on the hardness of approximating minimum vertex cover we prove the minimum vertex cover problem to be np hard to approximate to within a factor of 1 3606 extending on previous pcp and hardness of approximation technique to that end one needs to develop a new proof framework and to borrow and extend ideas from several fields

front quenching in the g equation model induced by straining of cellular flow we study homogenization of the g equation with a flow straining term or the strain g equation in two dimensional periodic cellular flow the strain g equation is a highly non coercive and non convex level set hamilton jacobi equation the main objective is to investigate how the flow induced straining the nonconvex term influences front propagation as the flow intensity a increases three distinct regimes are identified when a is below the critical level homogenization holds and the turbulent flame speed st effective hamiltonian is well defined for any periodic flow with small divergence and is enhanced by the cellular flow as st o a log a in the second regime where a is slightly above the critical value homogenization breaks down and st is not well defined along any direction solutions become a mixture of a fast moving part and a stagnant part when a is sufficiently large the whole flame front ceases to propagate forward due to the flow induced straining in particular along directions p 1 0 and 0 1 st is well defined again with a value of zero trapping a partial homogenization result is also proved if we consider a similar but relatively simpler hamiltonian the trapping occurs along all directions the analysis is based on the two player differential game representation of solutions selection of game strategies and trapping regions and construction of connecting trajectories

a multi start iterated greedy algorithm for the minimum weight vertex cover p3 problem abstract given a vertex weighted graph g v e and a positive integer k 2 the minimum weight vertex cover pk mwvcpk problem is to find a vertex subset f v with minimum total weight such that every path of order k in g contains at least one vertex in f for any integer k 2 the mwvcpk problem for general graphs is np hard in this paper we restrict our attention to the mwvcp3 problem and present a multi start iterated greedy algorithm to solve the mwvcp3 problem the experiments are carried out on randomly generated instances with up to 1000 vertices and 250000 edges our work is the first one to adopt heuristic algorithms to solve the mwvcp3 problem and the experimental results show that our algorithm performs reasonably well in practice

approximation algorithm for connected bounded degree deletion problem on unit disk graphs abstract in this paper we study the minimum connected k bounded degree node deletion problem min c kbdnd for a connected graph g a constant k and a weight function w v r a vertex set c v g is a kbdnd set if the maximum degree of graph g c is at most k if furthermore the subgraph of g induced by c is connected then c is a ckbdnd set the goal of minwkbdnd resp minwckbdnd is to find a kbdnd set resp ckbdnd set with the minimum weight in this paper we focus on their cardinality versions with w v 1 v v which are denoted as minkbdnd and minckbdnd this paper presents a 1 e and a 3 76 approximation algorithm for minkbdnd and minckbdnd on unit disk graphs respectively where 0 e 1 is an arbitrary constant

eigenvalues in potential theory on etudie les valeurs propres dans le cadre general des espaces harmoniques on applique les resultats a l equation de schrodinger independante du temps

parameterized algorithm for 3 path vertex cover abstract in the 3 path vertex cover problem the input is an undirected graph g and an integer k the goal is to decide whether there is a set of vertices s of size at most k such that every path with 3 vertices in g contains at least one vertex of s in this paper we give a parameterized algorithm for 3 path vertex cover whose time complexity is o 1 713 k our algorithm is faster than previous algorithms for this problem

stability of travelling fronts in a model for flame propagation part ii nonlinear stability this paper is concerned with the nonlinear stability of the travelling wave solutions of the multidimensional thermodiffusive model for flame propagation with unit lewis number the model consists in a semilinear parabolic equation in an infinite cylinder with neumann boundary conditions we prove that any solution which is initially close to a travelling wave will converge to a translate of that wave

fronts in reactive convection bounds stability and instability this paper examines a simplified active combustion model in which the reaction influences the flow we consider front propagation in a reactive boussinesq system in an infinite vertical strip nonlinear stability of planar fronts is established for narrow domains when the rayleigh number is not too large planar fronts are shown to be linearly unstable with respect to long wavelength perturbations if the rayleigh number is sufficiently large we also prove uniform bounds on the bulk burning rate and the nusselt number in the kpp reaction case 2003 wiley periodicals inc