on line generalized steiner problem the generalized steiner problem gsp is defined as follows we are given a graph with non negative edge weights and a set of pairs of vertices the algorithm has to construct minimum weight subgraph such that the two nodes of each pair are connected by a path off line gsp approximation algorithms were given in agarwal et al siam j comput 24 3 1995 440 and goemans and williamson siam j comput 24 2 1995 296 we consider the on line gsp in which pairs of vertices arrive on line and are needed to be connected immediately we show that the online min cost i e greedy strategy for this problem has o log2 n competitive ratio the previous best algorithm was o nlog n competitive workshop on algorithms and data structures 1993 pp 622 633 following this work a different non greedy algorithm has been shown to achieve an o log n competitive ratio proceedings of the 29th acm symposium on theory of computing 1997 pp 344 353 we also consider the network connectivity leasing problem which is a generalization of the gsp here edges of the graph can be either bought or leased for different costs we provide simple randomized algorithm based on on line generalized steiner algorithms whose competitive ratio is within a constant factor of the best competitive algorithm for the on line gsp

using choquet integral as preference model in interactive evolutionary multiobjective optimization we propose an interactive multiobjective evolutionary algorithm that attempts to discover the most preferred part of the pareto optimal set preference information is elicited by asking the user to compare some solutions pairwise this information is then used to curb the set of compatible user s value functions and the multiobjective evolutionary algorithm is run to simultaneously search for all solutions that could potentially be the most preferred compared to previous similar approaches we implement a much more efficient way of determining potentially preferred solutions that is solutions that are best for at least one value function compatible with the preference information provided by the decision maker for the first time in the context of evolutionary computation we apply the choquet integral as a user s preference model allowing us to capture interactions between objectives as there is a trade off between the flexibility of the value function model and the complexity of learning a faithful model of user s preferences we propose to start the interactive process with a simple linear model but then to switch to the choquet integral as soon as the preference information can no longer be represented using the linear model an experimental analysis demonstrates the effectiveness of the approach

sms emoa multiobjective selection based on dominated hypervolume abstract the hypervolume measure or s metric is a frequently applied quality measure for comparing the results of evolutionary multiobjective optimisation algorithms emoa the new idea is to aim explicitly for the maximisation of the dominated hypervolume within the optimisation process a steady state emoa is proposed that features a selection operator based on the hypervolume measure combined with the concept of non dominated sorting the algorithm s population evolves to a well distributed set of solutions thereby focussing on interesting regions of the pareto front the performance of the devised s metric selection emoa sms emoa is compared to state of the art methods on two and three objective benchmark suites as well as on aeronautical real world applications

biharmonic hypersurfaces of the 4 dimensional semi euclidean space es4 abstract a submanifold m r n of a semi euclidean space e s m is said to have harmonic mean curvature vector field if h 0 where h denotes the mean curvature vector submanifolds with harmonic mean curvature vector are also known as biharmonic submanifolds in this paper we prove that every nondegenerate hypersurface of e s 4 the shape operator of which is diagonalizable with harmonic mean curvature vector field is minimal

quasi minimal surfaces of pseudo riemannian space forms with positive relative nullity abstract in this paper we consider surfaces in 4 dimensional pseudo riemannian space forms with index 2 first we obtain some of geometrical properties of such surfaces considering their relative null space then we get classifications of quasi minimal surfaces with positive relative nullity

a best possible heuristic for the k center problem in this paper we present a 2 approximation algorithm for the k center problem with triangle inequality this result is best possible since for any 2 the existence of approximation algorithm would imply that p np it should be noted that no approximation algorithm for any constant has been reported to date linear programming duality theory provides interesting insight to the problem and enables us to derive in o e log e time a solution with value no more than twice the k center optimal value a by product of the analysis is an o e algorithm that identifies a dominating set in g2 the square of a graph g the size of which is no larger than the size of the minimum dominating set in the graph g the key combinatorial object used is called a strong stable set and we prove the np completeness of the corresponding decision problem

approximation schemes for steiner forest on planar graphs and graphs of bounded treewidth we give the first polynomial time approximation scheme ptas for the steiner forest problem on planar graphs and more generally on graphs of bounded genus as a first step we show how to build a steiner forest spanner for such graphs the crux of the process is a clustering procedure called prize collecting clustering that breaks down the input instance into separate subinstances which are easier to handle moreover the terminals in different subinstances are far from each other each subinstance has a relatively inexpensive steiner tree connecting all its terminals and the subinstances can be solved almost separately another building block is a ptas for steiner forest on graphs of bounded treewidth surprisingly steiner forest is np hard even on graphs of treewidth 3 therefore our ptas for bounded treewidth graphs needs a nontrivial combination of approximation arguments and dynamic programming on the tree decomposition we further show that steiner forest can be solved in polynomial time for series parallel graphs graphs of treewidth at most two by a novel combination of dynamic programming and minimum cut computations completing our thorough complexity study of steiner forest in the range of bounded treewidth graphs planar graphs and bounded genus graphs

classification of spatial surfaces with parallel mean curvature vector in pseudo euclidean spaces of arbitrary dimension spatial surfaces with parallel mean curvature vector play some important roles in general relativity theory of harmonic maps as well as in differential geometry recently spatial surfaces in four dimensional minkowski space time with parallel mean curvature vector were classified by chen and van der veken complete classification of parallel surfaces in 4 dimensional lorentzian space forms tohoku math j 61 1 2009 in this article we completely classify spatial surfaces with parallel mean curvature vector in pseudo euclidean spaces of arbitrary dimension the main result states that there exist 16 families of such surfaces as by product we achieve the complete classification of spatial surfaces with parallel mean curvature vector in minkowski space times of arbitrary dimension

hypervolume based multiobjective optimization theoretical foundations and practical implications in recent years indicator based evolutionary algorithms allowing to implicitly incorporate user preferences into the search have become widely used in practice to solve multiobjective optimization problems when using this type of methods the optimization goal changes from optimizing a set of objective functions simultaneously to the single objective optimization goal of finding a set of m points that maximizes the underlying indicator understanding the difference between these two optimization goals is fundamental when applying indicator based algorithms in practice on the one hand a characterization of the inherent optimization goal of different indicators allows the user to choose the indicator that meets her preferences on the other hand knowledge about the sets of m points with optimal indicator values the so called optimal m distributions can be used in performance assessment whenever the indicator is used as a performance criterion however theoretical studies on indicator based optimization are sparse one of the most popular indicators is the weighted hypervolume indicator it allows to guide the search towards user defined objective space regions and at the same time has the property of being a refinement of the pareto dominance relation with the result that maximizing the indicator results in pareto optimal solutions only in previous work we theoretically investigated the unweighted hypervolume indicator in terms of a characterization of optimal m distributions and the influence of the hypervolume s reference point for general bi objective optimization problems in this paper we generalize those results to the case of the weighted hypervolume indicator in particular we present general investigations for finite m derive a limit result for m going to infinity in terms of a density of points and derive lower bounds possibly infinite for placing the reference point to guarantee the pareto front s extreme points in an optimal m distribution furthermore we state conditions about the slope of the front at the extremes such that there is no finite reference point that allows to include the extremes in an optimal m distribution contradicting previous belief that a reference point chosen just above the nadir point or the objective space boundary is sufficient for obtaining the extremes however for fronts where there exists a finite reference point allowing to obtain the extremes we show that for m to infinity a reference point that is slightly worse in all objectives than the nadir point is a sufficient choice last we apply the theoretical results to problems of the zdt dtlz and wfg test problem suites

a partition based relaxation for steiner trees the steiner tree problem is a classical np hard optimization problem with a wide range of practical applications in an instance of this problem we are given an undirected graph g v e a set of terminals r subseteq v and non negative costs c e for all edges e in e any tree that contains all terminals is called a steiner tree the goal is to find a minimum cost steiner tree the vertices v backslash r are called steiner vertices the best approximation algorithm known for the steiner tree problem is a greedy algorithm due to robins and zelikovsky siam j discrete math 19 1 122 134 2005 it achieves a performance guarantee of 1 frac ln 3 2 approx 1 55 the best known linear programming lp based algorithm on the other hand is due to goemans and bertsimas math program 60 145 166 1993 and achieves an approximation ratio of 2 2 r in this paper we establish a link between greedy and lp based approaches by showing that robins and zelikovsky s algorithm can be viewed as an iterated primal dual algorithm with respect to a novel lp relaxation the lp used in the first iteration is stronger than the well known bidirected cut relaxation an instance is b quasi bipartite if each connected component of g backslash r has at most b vertices we show that robins and zelikovsky s algorithm has an approximation ratio better than 1 frac ln 3 2 for such instances and we prove that the integrality gap of our lp is between frac 8 7 and frac 2b 1 b 1

screw invariant marginally trapped surfaces in minkowski 4 space a spacelike surface in a lorentzian manifold whose mean curvature vector is lightlike everywhere is called marginally trapped the classification of marginally trapped surfaces in minkowski 4 space which are invariant under a subgroup of the lorentz group that leaves invariant a lightlike direction i e the so called screw invariant surfaces is obtained as corollaries the screw invariant marginally trapped surfaces with harmonic mean curvature vector and with prescribed gaussian curvature are explicitly described

addendum to classification of marginally trapped lorentzian flat surfaces in e24 and its application to biharmonic surfaces abstract due to omission an additional family shall be added to the list of marginally trapped lorentzian flat surfaces in e 2 4 given in theorem 4 1 of b y chen classification of marginally trapped lorentzian flat surfaces in e 2 4 and its application to biharmonic surfaces j math anal appl 340 2008 861 875

an analysis of the hypervolume sharpe ratio indicator abstract set quality indicators have been used in evolutionary multiobjective optimization algorithms emoas to guide the search process recently a new class of set quality indicators combining the selection of solutions with fitness assignment has been proposed this class is based on a formulation of fitness assignment as a portfolio selection problem where solutions are seen as assets whose returns are random variables and fitness represents the investment in such assets solutions the hypervolume sharpe ratio hsr indicator is an instance of this class of indicators which has led to promising results as part of an emoa denominated the portfolio optimization selection evolutionary algorithm posea in this paper the class of sharpe ratio indicators is formalized and the hsr indicator is studied in regard to monotonicity sensitivity to objective scaling and dependence on its parameters in addition optimal distributions on two objective linear fronts and the corresponding fitness assignments are characterized such optimal distributions turn out to be identical to those of the hypervolume indicator on the same fronts experimental results complement the analysis

parallel surfaces in lorentzian three manifolds admitting a parallel null vector field we classify parallel surfaces in lorentzian three manifolds admitting a parallel null vector field some families of semi parallel surfaces are also described

when trees collide an approximation algorithm for thegeneralized steiner problem on networks we give the first approximation algorithm for the generalized network steiner problem a problem in network design an instance consists of a network with link costs and for each pair i j of nodes an edge connectivity requirement r ij the goal is to find a minimum cost network using the available links and satisfying the requirements our algorithm outputs a solution whose cost is within 2 lceil log 2 r 1 rceil of optimal where r is the highest requirement value in the course of proving the performance guarantee we prove a combinatorial min max approximate equality relating minimum cost networks to maximum packings of certain kinds of cuts as a consequence of the proof of this theorem we obtain an approximation algorithm for optimally packing these cuts we show that this algorithm has application to estimating the reliability of a probabilistic network

weakly trapped submanifolds immersed in generalized robertson walker spacetimes abstract we deal with codimension two weakly trapped submanifolds that is the mean curvature vector field is causal immersed in a generalized robertson walker grw spacetime under suitable hypothesis we are able to prove that such a spacelike submanifold is immersed into a slice of the ambient space for this we use three main core concepts the well known generalized maximum principle of omori and yau stochastic completeness and another appropriate maximum principle at infinity due to yau we also construct a nontrivial example of weakly trapped submanifold in the static grw spacetime r h 2 r illustrating the importance of our results

a 2 approximation algorithm and beyond for the minimum diameter k steiner forest problem abstract given an edge weighted undirected graph g v e w and a subset t v of p terminals a k steiner forest spanning all the terminals in t includes k branches where every branch is a steiner tree the diameter of a k steiner forest is referred to as the maximum distance between two terminals of a branch this paper studies the minimum diameter k steiner forest problem mdksfp and establishes the relationship between mdksfp and the absolute k steiner center problem akscp we first obtain a 2 factor dual approximation algorithm for akscp and then achieve a 2 approximation algorithm for mdksfp based on the 2 approximation to akscp furthermore we develop an improved 2 approximation algorithm for mdksfp where 1 in general by perturbing the sites of facilities and re clustering the terminals

classification of lorentzian surfaces with parallel mean curvature vector in pseudo euclidean spaces spatial surfaces with parallel mean curvature vector in pseudo euclidean spaces of arbitrary dimension and index were classified by b y chen in this work we give a complete classification of lorentzian surfaces with parallel mean curvature vector in pseudo euclidean spaces of arbitrary dimension and index consequently the problem to classify all the surfaces with parallel mean curvature vector in pseudo euclidean spaces has been solved

spatial and lorentzian surfaces in robertson walker space times let l14 f c i fs gfc be a robertson walker space time which does not contain any open subset of constant curvature in this paper we provide a general study of nondegenerate surfaces in l14 f c first we prove the nonexistence of marginally trapped surfaces with positive relative nullity then we classify totally geodesic submanifolds finally we classify the family of surfaces with parallel second fundamental form and the family of totally umbilical surfaces with parallel mean curvature vector

homothetic and conformal symmetries of solutions to einstein s equations we present several results about the nonexistence of solutions of einstein s equations with homothetic or conformal symmetry we show that the only spatially compact globally hyperbolic spacetimes admitting a hypersurface of constant mean extrinsic curvature and also admitting an infinitesimal proper homothetic symmetry are everywhere locally flat this assumes that the matter fields either obey certain energy conditions or are the yang mills or massless klein gordon fields we find that the only vacuum solutions admitting an infinitesimal proper conformal symmetry are everywhere locally flat spacetimes and certain plane wave solutions we show that if the dominant energy condition is assumed then minkowski spacetime is the only asymptotically flat solution which has an infinitesimal conformal symmetry that is asymptotic to a dilation in other words with the exceptions cited homothetic or conformal killing fields are in fact killing in spatially compact or asymptotically flat spactimes in the conformal procedure for solving the initial value problem we show that data with infinitesimal conformal symmetry evolves to a spacetime with full isometry