searching and pebbling abstract we relate the search number of an undirected graph g with the minimum and maximum of the progressive pebble demands of the directed acyclic graphs obtained by orienting g towards this end we introduce node searching a slight variant of searching in which an edge is cleared by placing searchers on both of its endpoints we also show that the minimum number of searchers necessary to node search a graph equals its vertex separator plus one

tail probability approximations in the first order noncircular autoregression a saddlepoint expansion is derived for the cumulative distribution function of the least squares estimator of the autoregressive coefficient the new method is shown to be superior both analytically and numerically to many existing approximations unlike other methods the new approximation performs uniformly well over the whole range of the distribution including the extreme tail even when the sample size is as small as 10

the complexity of pursuit on a graph abstract a robber and k cops choose starting vertices in a graph and move in alternation from vertex to vertex along the edges of the graph capture occurs if a cop ever shares a vertex with the robber if k is not fixed and if either the graph is directed or initial positions are given we show that the problem is exptime complete similar techniques lead to the pspace and exptime completeness of some other combinatorial games that were previously only known to be np and pspace hard

saddlepoint expansions in finite population problems summary saddlepoint approximations are derived for the sample mean in the case where samples are obtained randomly without replacement from a finite population asymptotic properties are investigated the great accuracy is demonstrated by numerical examples extensions to more general statistics are discussed

an efficient algorithm for decomposing a polygon into star shaped polygons abstract in this paper we show how a theorem in plane geometry can be converted into a o n log n algorithm for decomposing a polygon into star shaped subsets the computational efficiency of this new decomposition contrasts with the heavy computational burden of existing methods

randomization distributions and saddlepoint approximations in generalized linear models various randomization distributions are shown to arise as conditional distributions in the setting of generalized linear models these conditional distributions admit saddlepoint approximations which can obviate the need to simulate the randomization distributions they approximate examples include multinominal and dirichlet bootstraps the jackknife and permutation distributions the double saddlepoint approximation in a regular exponential family is shown to be equivalent to conditional use of a single saddlepoint approximation when the exponential family admits to a cut

approximately exact inference for the common odds ratio in several 2 2 tables abstract the conditional maximum likelihood estimator mle of the common odds ratio in a sequence of independent 2 2 tables is known to be superior to the mantel haenszel estimator in terms of asymptotic efficiency and has the further advantage that its exact distribution is known however a long standing barrier to the widespread use of this estimator has been computational intractability in particular the calculation of significance levels confidence sets and power based on the exact distribution requires fast and efficient algorithms an important class of such algorithms form the basis of statxact a software package able to solve various aspects of the exact inference problem for a sequence of several 2 2 tables in real time we provide an alternative methodology by developing several useful saddlepoint approximations to the exact distribution of the conditional mle the approximations are derived from an interesting representation for hypergeometric random variables as a sum of independent

single step searching in weighted block graphs in this paper three types of problems for single step searching weighted graphs are investigated the summation minimization s type for short bottleneck minimization b type for short and hybrid h type for short weighted single step graph searching problems all three types are shown to be np hard but polynomial solvable for block graphs the s type problem is proved to be linearly equivalent to the optimum weight 2 independent set problem then we solve the s type problem on a block graph g in linear time by solving the optimum weight 2 independent set problem on g to solve the b type problem the first phase computes the bottleneck cost and the second phase constructs the searching plan by applying the s type algorithm using the bottleneck cost derived in the first phase finally an o e log v time algorithm for solving the h type problem on weighted block graphs is proposed

the complexity of searching a graph t parsons originally proposed and studied the following pursuit evasion problem on graphs members of a team of searchers traverse the edges of a graph g in pursuit of a fugitive who moves along the edges of the graph with complete knowledge of the locations of the pursuers what is the smallest number s g of searchers that will suffice for guaranteeing capture of the fugitive it is shown that determining whether s g k for a given integer k is np complete for general graphs but can be solved in linear time for trees we also provide a structural characterization of those graphs g with s g k for k 1 2 3

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

saddlepoint approximations in resampling methods summary saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications examples include mean estimation ratio estimation two sample comparisons and autoregressive estimation

on a convex hull algorithm for polygons and its application to triangulation problems abstract a frequently used algorithm for finding the convex hull of a simple polygon in linear running time has been recently shown to fail in some cases due to its simplicity the algorithm is nevertheless attractive in this paper it is shown that the algorithm does in fact work for a family of simple polygons known as weakly externally visible polygons some application areas where such polygons occur are briefly discussed in addition it is shown that with a trivial modification the algorithm can be used to internally and externally triangulate certain classes of polygons in 0 n time

approximation properties for group algebras and group von neumann algebras let g be a locally compact group let c g resp vn g be the c algebra resp the von neumann algebra associated with the left regular representation i of g let a g be the fourier algebra of g and let moa g be the set of completely bounded multipliers of a g with the completely bounded norm moa g is a dual space and we say that g has the approximation property ap if there is a net ua of functions in a g with compact support such that ua a 1 in the associated weak topology in particular g has the ap if g is weakly amenable a g has an approximate identity that is bounded in the completely bounded norm for a discrete group f we show that f has the ap x c f has the slice map property for subspaces of any c algebra x vn jt has the slice map property for a weakly closed subspaces of any von neumann algebra property se the semidirect product of weakly amenable groups need not be weakly amenable we show that the larger class of groups with the ap is stable with respect to semidirect products and more generally this class is stable with respect to group extensions we also obtain some results concerning crossed products for example we show that the crossed product m a g of a von neumann algebra m with property s by a group g with the ap also has property s

saddlepoint expansions for sums of markov dependent variables on a continuous state space based on the conjugate kernel studied in iscoe et al 1985 we derive saddlepoint expansions for either the density or distribution function of a sumf x1 f x n where thex i s constitute a markov chain the chain is assumed to satisfy a strong recurrence condition which makes the results here very similar to the classical results for i i d variables in particular we establish also conditions under which the expansions hold uniformly over the range of the saddlepoint expansions are also derived for sums of the formf x1 x0 f x2 x1 f x n xn 1 although the uniformity result just mentioned does not generalize

saddlepoint approximations of marginal densities and confidence intervals in the logistic regression measurement error model the aim of this note is to use the saddlepoint approximation by gatto and ronchetti 1996 in the logistic regression measurement error model with medical data sets we approximate the marginal densities of the estimator and use them for obtaining second order accurate confidence intervals with the bias correction proposed by efron 1987 the logistic regression measurement error model relates a binary response variable to predictor variables or covariates which are measured with errors for example it is not possible to measure the exact blood glucose level because some random variations due to the accuracy of the measure instrument the contents of the last meal or the blood sample preservation affect the accuracy of the measure when an imperfect measurement proxy is used instead of the true predictor an asymptotically unbiased estimator for the regression coefficients was proposed by stefanski and carroll 1985 saddlepoint approximations lead to accurate approximations of densities and tail probabilities the introduction of the saddlepoint approximation into statistics goes back to daniels 1954 for a general reference see field and ronchetti 1990 for recent applications see wang 1993 ronchetti and welsh 1994 li et al 1995 and davison hinkley and wharton 1995 section 2 summarizes the derivation of the unbiased estimator and the steps leading to the saddlepoint approximation numerical examples are presented in section 3 comparisons with standard normal approximations and with monte carlo bootstrap approximations are also shown some final remarks are given in section 4 the monte carlo bootstrap approximations are based on 10 000 resamplings these approximations do not change if we increase the number of resamplings in our comparisons we do not consider the edgeworth approximation which is often inaccurate in the tails of the distribution see field and ronchetti 1990

ordered structural shape matching with primitive extraction by mathematical morphology abstract structural shape matching procedures begin by decomposing the shapes to be matched into primitive parts and extracting the properties of and relationships among these primitives the resultant structural descriptions are matched to structural models usually via a tree search whose time is exponential in the number of primitives in this paper we introduce a new fast method of structural shape matching called ordered structural matching which has polynomial time complexity instead of exponential the approach presented also uses mathematical morphology to rapidly decompose the shapes into primitives to be used in the matching the primitives so produced are pieces of the original shape but not necessarily those pieces that a human would select the method has been tested on the toy task of determining which plastic shapes match the shapes of the holes in a child s six sided toy box it is also directly applicable to the inspection and manipulation of certain airplane parts

searching for a mobile intruder in a polygonal region the problem of searching for a mobile intruder in a simple polygon by a single mobile searcher is considered this paper investigates the capabilities of searchers having different degrees of visibility by introducing the searcher having k flashlights whose visibility is limited to k rays emanating from his position and the searcher having a point light source who can see in all directions simultaneously this paper presents necessary and sufficient conditions for a polygon to be searchable by various searchers the paper also introduces a class of polygons for which the searcher having two flashlights is as capable as the searcher having a point light source and it gives a simple necessary and sufficient condition for such polygons to be searchable by the searcher having two flashlights the complexity of generating a search schedule under some of these conditions is also discussed many of the results are proved using chord systems that represent the visibility relations among the vertices and edges o

guarding a set of line segments in the plane we consider the following problem given a finite set of straight line segments in the plane find a set of points of minimum size so that every segment contains at least one point in the set this problem can be interpreted as looking for a minimum number of locations of policemen guards cameras or other sensors that can observe a network of streets corridors tunnels tubes etc we show that the problem is strongly np complete even for a set of segments with a cubic graph structure but in p for tree structures

general saddlepoint approximations of marginal densities and tail probabilities saddlepoint approximations of marginal densities and tail probabilities of general nonlinear statistics are derived these are based on the expansion of the statistic up to the second order their accuracy is shown in a variety of examples including logit and probit models and rank estimators for regression

the searchlight scheduling problem the problem of searching for a mobile robber in a simple polygon by a number of searchlights is considered a searchlight is a stationary point which emits a single ray that cannot penetrate the boundary of the polygon the direction of the ray can be changed continuously and a point is detected by a searchlight at a given time if and only if it is on the ray a robber is a point that can move continuously with unbounded speed first it is shown that the problem of obtaining a search schedule for an instance having at least one searchlight on the polygon boundary can be reduced to that for instances having no searchlight on the polygon boundary the reduction is achieved by a recursive search strategy called the one way sweep strategy then various sufficient conditions for the existence of a search schedule are presented by using the concept of a searchlight visibility graph finally a simple necessary and sufficient condition for the existence of a search schedule for instances having exactly two sea

computing conforming partitions of orthogonal polygons with minimum stabbing number abstract let p be an orthogonal polygon with n vertices a partition of p into rectangles is called conforming if it results from cutting p along a set of interior disjoint line segments each having both endpoints on the boundary of p the stabbing number of a partition of p into rectangles is the maximum number of rectangles stabbed by any orthogonal line segment inside p in this paper we consider the problem of finding a conforming partition of p with minimum stabbing number we first give an o n log n time algorithm to solve the problem when p is a histogram for an arbitrary orthogonal polygon even with holes we give an integer programming formulation of the problem and show that a simple rounding results in a 2 approximation algorithm for the problem finally we show that the problem is np hard if p is allowed to have holes

an optimal algorithm for solving the searchlight guarding problem on weighted trees abstract in this paper we propose a new graph problem on a connected weighted undirected graph called the searchlight guarding problem consider that there is a fugitive who moves along the edges of a graph at any speed we want to place a set of searchlights at vertices to search the edges of the graph and capture the fugitive suppose that it costs some building cost to place a searchlight at some vertex the searchlight guarding problem is to allocate a set s of searchlights such that the summation of the building costs is minimized if there is more than one set of searchlights with the minimum building cost then find the one with the minimum searching time that is where the time slot needed to capture the fugitive is minimum we first prove that the problem is np hard on weighted bipartite graphs then an o n time optimal algorithm is designed to solve the problem on weighted trees where n is the number of the vertices of the given weighted tree the algorithm is divided into two phases in the first phase we find the set of searchlights with the minimum guarding cost and assign the searching directions of all edges by the dynamic programming strategy in the second phase the searched time slots of each edge are determined both phases take linear time

biometrika centenary sample surveys summary despite karl pearson s stated aim that the evolutionist has to become in the widest sense of the words a registrar general for all forms of life the papers published in biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s there has been little work on sampling in the life sciences with the exception of capture recapture methods the major areas have been in variable probability designs the foundations of inference for finite populations analytic surveys and the role of selection mechanisms in inference in recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory with interesting consequences for both areas

monotonicity of non deterministic graph searching in graph searching a team of searchers are aiming at capturing a fugitive moving in a graph in the initial variant called invisible graph searching the searchers do not know the position of the fugitive until they catch it in another variant the searchers permanently know the position of the fugitive i e the fugitive is visible this latter variant is called visible graph searching a search strategy that catches any fugitive in such a way that the part of the graph reachable by the fugitive never grows is called monotone a priori monotone strategies may require more searchers than general strategies to catch any fugitive this is however not the case for visible and invisible graph searching two important consequences of the monotonicity of visible and invisible graph searching are 1 the decision problem corresponding to the computation of the smallest number of searchers required to clear a graph is in np and 2 computing optimal search strategies is simplified by taking into account that there exist some that never backtrack fomin et al f v fomin p fraigniaud n nisse nondeterministic graph searching from pathwidth to treewidth in proceedings of the 30th international symposium on mathematical foundations of computer science mfcs 05 2005 pp 364 375 introduced an important graph searching variant called non deterministic graph searching that unifies visible and invisible graph searching in this variant the fugitive is invisible and the searchers can query an oracle that permanently knows the current position of the fugitive the question of the monotonicity of non deterministic graph searching was however left open in this paper we prove that non deterministic graph searching is monotone in particular this result is a unified proof of monotonicity for visible and invisible graph searching as a consequence the decision problem corresponding to non deterministic graph searching belongs to np moreover the exact algorithms designed by fomin et al do compute optimal non deterministic search strategies

general saddlepoint approximations with applications to l statistics abstract saddlepoint approximations are extended to general statistics the technique is applied to derive approximations to the density of linear combinations of order statistics including trimmed means a comparison with exact results shows the accuracy of these approximations even in very small sample sizes

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

recontamination does not help to search a graph this paper is concerned with a game on graphs called graph searching the object of this game is to clear all edges of a contaminated graph clearing is achieved by moving searchers a kind of token along the edges of the graph according to clearing rules certain search strategies cause edges that have been cleared to become contaminated again megiddo et al 9 conjectured that every graph can be searched using a minimum number of searchers without this recontamination occurring that is without clearing any edge twice in this paper this conjecture is proved this places the graph searching problem in np completing the proof by megiddo et al that the graph searching problem is np complete furthermore by eliminating the need to consider recontamination this result simplifies the analysis of searcher requirements with respect to other properties of graphs

an optimal algorithm for solving the searchlight guarding problem on weighted interval graphs abstract in this paper a graph problem on connected weighted undirected graphs called the searchlight guarding problem is considered assume that there is a fugitive who moves along the edges of the graph at a random speed the task involves placing a set of searchlights at vertices to search the edges of the graph and to spot the fugitive suppose that placing a searchlight at some vertex incurs some building cost the searchlight guarding problem is to allocate a set s of searchlights at the vertices such that the total cost of the vertices in s is minimized if there is more than one set of searchlights each with a minimum building cost then identify the set with the minimum search time that is where the time slots needed to spot the fugitive is the minimum as is well established the problem is np hard on weighted bipartite graphs but is linear time solvable on weighted trees in this paper the design of a linear time optimal algorithm for the searchlight guarding problem on weighted interval graphs is presented it entails two phases in the first phase a set of searchlights with minimum guarding cost is identified and the search directions of all edges are assigned to achieve this task a new problem called the edge direction assignment problem is first defined and the problem on weighted complete split graphs is solved by the greedy strategy based on this computational result the problem of finding the set of searchlights with minimum guarding cost and assigning the search directions of all edges is solved by the dynamic programming strategy then in the second phase the search time slots of each edge are determined on the basis of the results of the first phase and on some properties of interval graphs

multipliers of the fourier algebras of some simple lie groups and their discrete subgroups for any amenable locally compact group g the space of multipliers ma g of the fourier algebra a g coincides with the space b g of functions on g that are linear combinations of continuous positive definite functions we prove that ma g b g 0 for many non amenable connected groups more specifically we prove that moa g b g 0 for the classical complex lie groups and the general lorentz groups soo n 1 n 2 moa g is a certain subspace of ma g which we call the space of completely bounded multipliers of a g unlike ma g the space moa g has nice stability properties with respect to direct products of groups it is known that the fourier algebra of the free group on n generators n 2 2 admits an unbounded approximate unit pn which is bounded in the multiplier norm we extend this result to any closed subgroup of the general lorentz group soo n 1 moreover we show that for these groups pn can be chosen to be bounded with respect to the moa g norm by a duality argument we obtain that the reduced c algebra of every discrete subgroup of soo n 1 has the completely bounded approximation property in particular this property holds for c f2 the reduced c algebra of the free group on two generators we also prove

resampling inference with complex survey data abstract methods for standard errors and confidence intervals for nonlinear statistics such as ratios regression and correlation coefficients have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement in particular the important special case of two sampled clusters per stratum these methods include the customary linearization or taylor method and resampling methods based on the jackknife and balanced repeated replication brr unlike the jackknife or the brr the linearization method is applicable to general sampling designs but it involves a separate variance formula for each nonlinear statistic thereby requiring additional programming efforts both the jackknife and the brr use a single variance formula for all nonlinear statistics but they are more computing intensive the resampling methods developed here retain these features of the jackknife and the brr yet permit extension to more complex designs involving sampling without replace

computing the vertex separation of unicyclic graphs we describe an o n log n algorithm for the computation of the vertex separation of unicyclic graphs the algorithm also computes a linear layout with optimal vertex separation in the same time bound pathwidth node search number and vertex separation are different ways of defining the same notion path decompositions and search strategies can be derived from linear layouts the algorithm applies existing linear time techniques for the computation of the vertex separation of trees together with corresponding optimal layouts we reformulate the earlier work on the linear time computation of optimal layouts a polynomial time algorithm for the problem on unicyclic graphs can be inferred from existing more general methods for graphs of fixed treewidth since unicyclic graphs have treewidth two but the time complexity of the resulting method would seem to be an inordinately high order polynomial our algorithm we claim is practical the addition of one edge to a tree does seem to require a considerably more elaborate algorithm

mapping ideals of quantum group multipliers abstract we study the dual relationship between quantum group convolution maps l 1 g l g and completely bounded multipliers of g for a large class of locally compact quantum groups g we completely isomorphically identify the mapping ideal of row hilbert space factorizable convolution maps with m c b l 1 g yielding a quantum gilbert representation for completely bounded multipliers we also identify the mapping ideals of completely integral and completely nuclear convolution maps the latter coinciding with l 1 b g where b g is the quantum bohr compactification of g for quantum groups whose dual has bounded degree we show that the completely compact convolution maps coincide with c b g our techniques comprise a mixture of operator space theory and abstract harmonic analysis including fubini tensor products the non commutative grothendieck inequality quantum eberlein compactifications and a suitable notion of inner co amenable quantum group that we introduce and for which we exhibit examples from the bicrossed product construction our main results are new even in the setting of group von neumann algebras v n g for quasi sin locally compact groups g

the summation and bottleneck minimization for single step searching on weighted graphs abstract in this paper three types of problems for single step searching weighted graphs are defined they are the summation cost minimization the bottleneck cost minimization and a hybrid to minimize the maximum of the summation cost and the bottleneck cost all three are shown to be np hard but polynomially solvable for trees the bottleneck minimization is shown to be reducible to the summation minimization problem

weakly almost periodic functions and fourier stieltjes algebras of locally compact groups a noncompact locally compact group g is called an eberlein group if w g b g where w g is the algebra of continuous weakly almost periodic functions on g and b g is the uniform closure of the fourier stieltjes algebra of g we show that if g is a noncompact in group or a noncompact nilpotent group then w g b g contains a linear isometric copy of l in particular g is not an eberlein group on the other hand finite direct products of eucidean motion groups and by a result of w veech noncompact semisimple analytic groups with finite centers are eberlein groups 1 introduction let g be a locally compact group c g the space of bounded continuous complex valued functions on g with the sup norm w g the space of continuous weakly almost periodic w a p functions on g b g the fourier stieltjes algebra of g and b g its uniform closure in c g it is known that b g c w g and if g is compact then c g w g b g therefore in this paper g is assumed to be noncompact in his efforts to characterize w a p functions w f eberlein first raised the question whether for abelian g b g w g w rudin 24 made the initial contribution to this question by showing that b g c w g if g is abelian and contains a discrete subgroup which is not of bounded order and d ramirez 23 by studying discrete abelian groups with bounded orders together with the structure theorem for locally compact abelian groups was able to show that rudin s conclusion holds for all abelian groups see the monographs 4 and 11 for complete accounts of this result in this paper we will extend rudin ramirez result to include many nonabelian groups our main result is the following

mixed searching and proper path width abstract this paper considers a mixed search game which is a natural generalization of edge search and node search games extensively studied so far we establish a relationship between the mixed search number of a graph g and the proper path width of g introduced by the authors in a previous paper we also prove complexity results

weakly almost periodic functions and thin sets in discrete groups a subset e of an infinite discrete group g is called i an rw set if any bounded function on g supported by e is weakly almost periodic ii a weak p sidon set 1 p 2 if on 11 e the lp norm is bounded by a constant times the maximal c norm of i i g iii a t set if xe n e and ex n e are finite whenever x e and iv an ft set if it is a finite union of t sets in this paper we study relationships among these four classes of thin sets we show among other results that a every infinite group g contains an rw set which is not an ft set b countable weak p sidon sets 1 p 4 3 are f t sets

some geometric properties on the fourier and fourier stieltjes algebras of locally compact groups arens regularity and related problems let g be a locally compact topological group and a g b g be respectively the fourier and fourier stieltjes algebras of g it is one of the purposes of this paper to investigate the rnp radon nikodym property and some other geometric properties such as weak rnp the dunford pettis property and the schur property on the algebras a g and b g and to relate these properties to the properties of the multiplication operator on the group c algebra c g we also investigate the problem of arens regularity of the projective tensor products c g a when b g c g has the rnp and a is any c algebra some related problems on the measure algebra the group algebra and the algebras a p g pf p g pm p g 1 p are also discussed

the searchlight problem for road networks we consider the problem of searching for a mobile intruder hiding in a road network given as the union of two or more lines or two or more line segments in the plane some of the intersections of the road network are occupied by stationary guards equipped with a number of searchlights each of which can emit a single ray of light in any direction along the lines or line segments it is on the goal is to detect the intruder that is to illuminate its location guards may alter the direction in which they aim a searchlight but need to switch it off for some finite time interval to effect the change in contrast the intruder may move with arbitrary speed along the network but cannot pass guards and exploit this time interval to recontaminate previously illuminated sections of the network for various classes of road networks characterized by the number n of lines or line segments comprising it and the number g n 1 of possible locations of guards fixed in advance and guaranteed to give complete coverage we present several upper and lower bounds on the worst case number of searchlights each placed at one of the guard positions required to successfully search a given road network in particular we prove the following results 1 min 2 g 1 n 2 searchlights are sometimes necessary and min 7 3 g n 1 are always sufficient for searching a road network given as the union of n lines 2 g log n g searchlights are sometimes necessary and o g 2 log n searchlights are always sufficient for searching a road network given as the union of n line segments and3 at most one searchlight per guard position and hence a total of at most g searchlights is always sufficient for searching a road network given as the union of axis aligned lines or line segments the proofs of the upper bounds induce algorithms for generating a search schedule for detecting the intruder using the claimed number of searchlights the problem of searching for an intruder hiding in a road network is introduced upper and lower bounds on the worst case number of searchlights are presented the proofs of the upper bounds induce algorithms for generating a search schedule

an annotated bibliography on guaranteed graph searching graph searching encompasses a wide variety of combinatorial problems related to the problem of capturing a fugitive residing in a graph using the minimum number of searchers in this annotated bibliography we give an elementary classification of problems and results related to graph searching and provide a source of bibliographical references on this field

completely bounded multipliers of the fourier algebra of a simple lie group of real rank one the fourier algebra a g of a locally compact group g is the space of matrix coefficients of the regular representation and is the predual of the yon neumann algebra vn g generated by the regular representation of g on l 2 g a multiplier m of a g is a bounded operator on a g given by pointwise multiplication by a function on g also denoted m we say m is a completely bounded multiplier ofa g if the transposed operator on vn g is completely bounded definition below it may be possible to find a net ofa g functions m i ie i say such that mi tends to

computational complexity of art gallery problems we study the computational complexity of the art gallery problem originally posed by klee and its variations specifically the problem of determining the minimum number of vertex guards that can see an n wall simply connected art gallery is shown to be np hard the proof can be modified to show that the problems of determining the minimum number of edge guards and the minimum number of point guards in a simply connected polygonal region are also np hard as a byproduct the problem of decomposing a simple polygon into a minimum number of star shaped polygons such that their union is the original polygon is also shown to be np hard