provably good global routing of integrated circuits this paper investigates the global routing problem for integrated circuits we introduce a formulation on the basis of integer programming which minimizes the routing area among a limited set of steiner trees for each net indeed the involved cost function depends on the channel density of the routing which has a direct influence on the routing area our methods for solving the global routing problem employ local search heuristics sequential routing genetic routing and randomized procedures our methods for computing lower bounds are based on linear and lagrange relaxation an analysis on the tightness of the bounds indicates that the difference between the cost of the optimal integer solutions and the cost of the optimal fractional solutions is only a small number of tracks in practice moreover the analysis leads to the concept of linear preprocessing by which we exclude a large number of high cost solutions we introduce several versions of preprocessing one of which preserves the opportunity of obtaining a globally optimal solution in general all of them do so in practice linear preprocessing enables us to solve problem instances with several thousand nets provably optimal or at least provably close to optimal all methods have been implemented in the software package eridanus we present computational results the global routing problem assumes the placement of the chip components to be fixed an extension of the problem which we call global layout of integrated circuits allows the placement to be variable and searches for a placement that minimizes the routing area among a limited set of alternatives we show that the results concerning the global routing problem can be easily extended to global layout

honey pot constrained searching with local sensory information in this paper we investigate the problem of searching for a hidden target in a bounded region of the plane using an autonomous robot which is only able to use local sensory information the problem is naturally formulated in the continuous domain but the solution proposed is based on an aggregation refinement approach in which the continuous search space is partitioned into a finite collection of regions on which we define a discrete search problem a solution to the original problem is obtained through a refinement procedure that lifts the discrete path into a continuous one we show that the discrete optimization is computationally difficult np hard but there are computationally efficient approximation algorithms for solving it the resulting solution to the continuous problem is in general not optimal but one can construct bounds to gauge the cost penalty incurred due to i the discretization of the problem and ii the attempt to approximately solve the np hard problem in polynomial time numerical simulations show that the algorithms proposed behave significantly better than naive approaches such as a random walk or a greedy algorithm c 2006 elsevier ltd all rights reserved

optimal covering tours with turn costs we give the first algorithmic study of a class of covering tour problems related to the geometric traveling salesman problem find a polygonal tour for a cutter so that it sweeps out a specified region pocket in order to minimize a cost that depends mainly on the number of turns these problems arise naturally in manufacturing applications of computational geometry to automatic tool path generation and automatic inspection systems as well as arc routing postman problems with turn penalties we prove the np completeness of minimum turn milling and give efficient approximation algorithms for several natural versions of the problem including a polynomial time approximation scheme based on a novel adaptation of the m guillotine method

more on the complexity of common superstring and supersequence problems the shortest common superstring scst problem is the decision version of the problem to find for a finite set of strings l over an alphabet and an integer k n a string s of length k over such that each string in l is a substring of s analogously the shortest common supersequence scse problem is the decision version of the problem to find for a finite set of strings l over an alphabet and an integer k n a string s of length k over such that each string in l is a subsequence of s our main results are scst is np complete if the given strings have length 3 and the maximal orbit size is 8 the orbit size of a character is the number of its occurrences in the strings in l this partially solves a problem of timkovskii 1990 scst is np complete over the alphabet 0 1 even if each given string contains exactly three ones scse over the alphabet 0 1 is np complete even if the given strings all have the same length and each string contains exactly two ones moreover we introduce cyclic and permutation variants of scst and scse namely cyclic scst cyclic scse permutation scst and permutation scse the permutation scst resp cyclic scst problem is the decision version of the problem to find for a finite set of strings l over an alphabet and an integer k n a string s of length k over such that there exists a cyclic permutation of each string in l that is a substring of s permutation scse and cyclic scse are defined analogously the main results are cyclic scst and cyclic scse are np complete for strings of length 3 and polynomial time solvable for string of length 2 cyclic scst and cyclic scse are np complete for an alphabet of size 2 permutation scst is np complete if the given strings have length 3 and the maximal orbitsize is 8 permutation scst is np complete for an alphabet of size 3 and polynomial time solvable for an alphabet of size 2

positive semidefinite zero forcing numbers of two classes of graphs abstract the positive semidefinite zero forcing number is a variant of the zero forcing number which is an important parameter in the study of minimum rank maximum nullity problems in this paper we consider two classes of graphs matching chain graphs and claw free graphs we first introduce the propagation decomposition of graphs then we use this decomposition to prove a lower bound for the positive semidefinite zero forcing number of a graph we apply this lower bound to find the positive semidefinite zero forcing number of matching chain graphs we show that the positive semidefinite zero forcing number and the zero forcing number agree for matching chain graphs as a consequence we prove the conjecture about the positive semidefinite zero forcing number of the cartesian product of two paths and partially prove the conjecture about the positive semidefinite zero forcing number of the cartesian product of a cycle and a path for claw free graphs we establish a relationship between the positive semidefinite zero forcing number and the zero forcing number we also prove that it is np complete to find the positive semidefinite zero forcing number of line graphs

constructing edge disjoint steiner paths in lexicographic product networks abstract dirac showed that in a k 1 connected graph there is a path through each k vertices the path k connectivity k g of a graph g which is a generalization of dirac s notion was introduced by hager in 1986 it is natural to introduce the concept of path k edge connectivity k g of a graph g denote by g h the lexicographic product of two graphs g and h in this paper we prove that 3 g h 3 g 3 v h 4 for any two graphs g and h moreover the bound is sharp we also derive an upper bound of 3 g h that is 3 g h min 2 3 g v h 2 h g v h we demonstrate the usefulness of the proposed constructions by applying them to some instances of lexicographic product networks

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

secret key generation for a pairwise independent network model we consider secret key generation for a pairwise independent network model in which every pair of terminals observes correlated sources that are independent of sources observed by all other pairs of terminals the terminals are then allowed to communicate publicly with all such communication being observed by all the terminals the objective is to generate a secret key shared by a given subset of terminals at the largest rate possible with the cooperation of any remaining terminals secrecy is required from an eavesdropper that has access to the public interterminal communication a single letter formula for secret key capacity brings out a natural connection between the problem of secret key generation and a combinatorial problem of maximal packing of steiner trees in an associated multigraph an explicit algorithm is proposed for secret key generation based on a maximal packing of steiner trees in a multigraph the corresponding maximum rate of steiner tree packing is thus a lower bound for the secret key capacity when only two of the terminals or when all the terminals seek to share a secret key the mentioned algorithm achieves secret key capacity in which case the bound is tight

approximating the longest paths in grid graphs abstract in this paper we consider the problem of approximating the longest path in a grid graph that possesses a square free 2 factor by 1 analyzing several characteristics of four types of cross cells and 2 presenting three cycle merging operations and one extension operation we propose an algorithm that finds in an n vertex grid graph g a long path of length at least 5 6 n 2 our approximation algorithm runs in quadratic time in addition to its theoretical value our work has also an interesting application in image guided maze generation

a linear time algorithm for finding hamiltonian s t paths in even sized rectangular grid graphs with a rectangular hole a grid graph g mathrm g is a finite vertex induced subgraph of the two dimensional integer grid g infty a rectangular grid graph r m n is a grid graph with horizontal size m and vertical size n a rectangular grid graph with a rectangular hole is a rectangular grid graph r m n such that a rectangular grid subgraph r k l is removed from it the hamiltonian path problem for general grid graphs is np complete in this paper we give necessary conditions for the existence of a hamiltonian path between two given vertices in an odd sized rectangular grid graph with a rectangular hole in addition we show that how such paths can be computed in linear time

the steiner tree packing problem in vlsi design in this paper we describe several versions of the routing problem arising in vlsi design and indicate how the steiner tree packing problem can be used to model these problems mathematically we focus on switchbox routing problems and provide integer programming formulations for routing in the knock knee and in the manhattan model we give a brief sketch of cutting plane algorithms that we developed and implemented for these two models we report on computational experiments using standard test instances our codes are able to determine optimum solutions in most cases and in particular we can show that some of the instances have no feasible solution if manhattan routing is used instead of knock knee routing

well solvable special cases of the traveling salesman problem a survey the traveling salesman problem tsp belongs to the most basic most important and most investigated problems in combinatorial optimization although it is an cal np hard problem many of its special cases can be solved efficiently in polynomial time we survey these special cases with emphasis on the results that have been obtained during the decade 1985 1995 this survey complements an earlier survey from 1985 compiled by gilmore lawler and shmoys the traveling salesman problem a guided tour of combinatorial optimization wiley chichester pp 87 143

hamiltonian paths in l shaped grid graphs grid graphs are subgraphs of the infinite 2 dimensional integer grid the hamiltonian path problem for general grid graphs is a well known np complete problem in this paper we present necessary and sufficient conditions for the existence of a hamiltonian path between two given vertices in l shaped grid graphs we also show that a hamiltonian path between two given vertices of a l shaped grid graph can be computed in linear time the hamiltonian path problem is a well known np complete problem we give necessary and sufficient conditions for the existence of a hamiltonian s t path in l shaped grid graphs we show that a hamiltonian s t path in l shaped grid graph can be computed in linear time if it does exist

maximum likelihood estimation for stationary point processes in this paper we derive the log likelihood function for point processes in terms of their stochastic intensities by using the martingale approach for practical purposes we work with an approximate log likelihood function that is shown to possess the usual asymptotic properties of a log likelihood function the resulting estimates are strongly consistent and asymptotically normal under some regularity conditions as a by product a strong law of large numbers and a central limit theorem for martingales in continuous times are derived

rectilinear group steiner trees and applications in vlsi design given a set of disjoint groups of points in the plane the rectilinear group steiner tree problem is the problem of finding a shortest interconnection under the rectilinear metric which includes at least one point from each group this is an important generalization of the well known rectilinear steiner tree problem which has direct applications in vlsi design in the detailed routing phase the logical units typically allow the nets to connect to several electrically equivalent ports we present a first tailored exact algorithm for solving the rectilinear group steiner tree problem and related variants of the problem the algorithm essentially constructs a subgraph of the corresponding hanan grid on which existing algorithms for solving the steiner tree problem in graphs are applied the reductions of the hanan grid are performed by applying point deletions and by generating full steiner trees on the remaining points experimental results for real world vlsi instances with up to 100 groups are presented

liar s domination in unit disk graphs abstract in this article we study a variant of the minimum dominating set problem known as the minimum liar s dominating set mlds problem we prove that the mlds problem is np hard in unit disk graphs we point out that the approximation guarantee of 11 2 for the approximation algorithm for unit disk graphs proposed by banerjee and bhore 2019 11 is not correct and we propose a simple o n m time 7 31 factor approximation algorithm where n and m are the number of vertices and edges respectively in the given unit disk graph finally we prove that the mlds problem admits a polynomial time approximation scheme

optimum path packing on wheels the consecutive case abstract we show that given a wheel with nonnegative edge lengths and pairs of terminals located on the wheel s outer cycle such that the terminal pairs are in consecutive order then a path packing i e a collection of edge disjoint paths connecting the given terminal pairs of minimum length can be found in strongly polynomial time moreover we exhibit for this case a system of linear inequalities that provides a complete and nonredundant description of the path packing polytope which is the convex hull of all incidence vectors of path packings and their supersets

packing steiner trees a cutting plane algorithm and computational results in this paper we describe a cutting plane algorithm for the steiner tree packing problem we use our algorithm to solve some switchbox routing problems of vlsi design and report on our computational experience this includes a brief discussion of separation algorithms a new lp based primal heuristic and implementation details the paper is based on the polyhedral theory for the steiner tree packing polyhedron developed in our companion paper this issue and meant to turn this theory into an algorithmic tool for the solution of practical problems

vertex disjoint packing of two steiner trees polyhedra and branch and cut consider the problem of routing the electrical connections among two large terminal sets in circuit layout a realistic model for this problem is given by the vertex disjoint packing of two steiner trees 2vpst which is known to be np complete this work presents an investigation on the 2vpst polyhedra the main idea is to start from facet defining inequalities for a vertex weighted steiner tree polyhedra some of these inequalities are proven to also define facets for the packing polyhedra while others are lifted to derive new important families of inequalities including proven facets separation algorithms are provided branch and cut implementation issues are also discussed including some new practical techniques to improve the performance of the algorithm the resulting code is capable of solving problems on grid graphs with up to 10000 vertices and 5000 terminals in a few minutes

perfect omniscience perfect secrecy and steiner tree packing we consider perfect secret key generation for a pairwise independent network model in which every pair of terminals share a random binary string with the strings shared by distinct terminal pairs being mutually independent the terminals are then allowed to communicate interactively over a public noiseless channel of unlimited capacity all the terminals as well as an eavesdropper observe this communication the objective is to generate a perfect secret key shared by a given set of terminals at the largest rate possible and concealed from the eavesdropper first we show how the notion of perfect omniscience plays a central role in characterizing perfect secret key capacity second a multigraph representation of the underlying secrecy model leads us to an efficient algorithm for perfect secret key generation based on maximal steiner tree packing this algorithm attains capacity when all the terminals seek to share a key and in general attains at least half the capacity third when a single helper terminal assists the remaining user terminals in generating a perfect secret key we give necessary and sufficient conditions for the optimality of the algorithm also a weak helper is shown to be sufficient for optimality

an asymptotically optimal push pull method for multicasting over a random network we consider all cast and multicast flow problems where either all of the nodes or only a subset of the nodes may be in session traffic from each node in the session has to be sent to every other node in the session if the session does not consist of all the nodes the remaining nodes act as relays the nodes are connected by undirected links whose capacities are independent and identically distributed random variables we study the asymptotics of the capacity region with network coding in the limit of a large number of nodes and show that the normalized sum rate converges to a constant almost surely we then provide a decentralized push pull algorithm that asymptotically achieves this normalized sum rate without network coding

a branch and cut algorithm for the resolution of large scale symmetric traveling salesman problems an algorithm is described for solving large scale instances of the symmetric traveling salesman problem stsp to optimality the core of the algorithm is a polyhedral cutting plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph the cuts are generated by several identification procedures that have been described in a companion paper whenever the cutting plane procedure does not terminate with an optimal solution the algorithm uses a tree search strategy that as opposed to branch and bound keeps on producing cuts after branching the algorithm has been implemented in fortran two different linear programming lp packages have been used as the lp solver the implementation of the algorithm and the interface with one of the lp solvers is described in sufficient detail to permit the replication of our experiments computational results are reported with up to 42 stsps with sizes rangin

the hamiltonian properties of supergrid graphs in this paper we first introduce a novel class of graphs namely supergrid supergrid graphs include grid graphs and triangular grid graphs as their subgraphs the hamiltonian cycle and path problems for grid graphs and triangular grid graphs were known to be np complete however they are unknown for supergrid graphs the hamiltonian cycle path problem on supergrid graphs can be applied to control the stitching traces of computerized sewing machines in this paper we will prove that the hamiltonian cycle problem for supergrid graphs is np complete it is easily derived from the hamiltonian cycle result that the hamiltonian path problem on supergrid graphs is also np complete we then show that two subclasses of supergrid graphs including rectangular parallelism and alphabet always contain hamiltonian cycles

a framework for exponential time hypothesis tight algorithms and lower bounds in geometric intersection graphs we give an algorithmic and lower bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds it can be applied to intersection graphs

orienting cayley graphs generated by transposition trees day and tripathi k day a tripathi unidirectional star graphs inform process lett 45 1993 123 129 proposed an assignment of directions on the star graphs and derived attractive properties for the resulting directed graphs cheng and lipman e cheng m j lipman on the day tripathi orientation of the star graphs connectivity inform process lett 73 2000 5 10 e cheng m j lipman connectivity properties of unidirectional star graphs congr numer 150 2001 33 42 studied the connectivity properties of these unidirectional star graphs the class of star graphs is a special case of cayley graphs generated by transposition trees in this paper we give directions on these graphs and study the connectivity properties of the resulting unidirectional graphs

the generalized 3 connectivity of star graphs and bubble sort graphs for s g let s denote the maximum number r of edge disjoint trees t 1 t 2 t r in g such that v t i v t j s for any i j 1 2 r and i j for every 2 k n the generalized k connectivity of g k g is defined as the minimum s over all k subsets s of vertices i e k g min s s v g a n d s k clearly 2 g corresponds to the traditional connectivity of g the generalized k connectivity can serve for measuring the capability of a network g to connect any k vertices in g cayley graphs have been used extensively to design interconnection networks in this paper we restrict our attention to two classes of cayley graphs the star graphs sn and the bubble sort graphs bn and investigate the generalized 3 connectivity of sn and bn we show that 3 s n n 2 and 3 b n n 2

linear time algorithms for the hamiltonian problems on distance hereditary graphs a hamiltonian path of a graph g is a simple path that contains each vertex of g exactly once a hamiltonian cycle of a graph is a simple cycle with the same property the hamiltonian path resp cycle problem involves testing whether a hamiltonian path resp cycle exists in a graph the 1hp resp 2hp problem is to determine whether a graph has a hamiltonian path starting from a specified vertex resp starting from a specified vertex and ending at the other specified vertex the hamiltonian problems include the hamiltonian path hamiltonian cycle 1hp and 2hp problems a graph is a distance hereditary graph if each pair of vertices is equidistant in every connected induced subgraph containing them in this paper we present a unified approach to solving the hamiltonian problems on distance hereditary graphs in linear time

solution of large scale symmetric travelling salesman problems in this paper we report on a cutting plane procedure with which we solved symmetric travelling salesman problems of up to 1000 cities to optimality our implementation is based on a fast lp solver ibm s mpsx and makes effective use of polyhedral results on the symmetric travelling salesman polytope we describe the important ingredients of our code and give an extensive documentation of its computational performance

reconstructing polygons from scanner data a range finding scanner can collect information about the shape of an unknown polygonal room in which it is placed suppose that a set of scanners returns not only a set of points but also additional information such as the normal to the plane when a scan beam detects a wall we consider the problem of reconstructing the floor plan of a room from different types of scan data in particular we present algorithmic and hardness results for reconstructing two dimensional polygons from point wall pairs point normal pairs and visibility polygons the polygons may have restrictions on topology e g to be simply connected or geometry e g to be orthogonal we show that this reconstruction problem is np hard under most models but that some restrictive assumptions do allow polynomial time reconstruction algorithms

rainbow connections for outerplanar graphs with diameter 2 and 3 abstract an edge colored graph g is rainbow connected if every two vertices are connected by a path whose edges have distinct colors the rainbow connection number of a connected graph g denoted by rc g is the smallest number of colors that are needed in order to make g rainbow connected it was proved that computing rc g is an np hard problem as well as that even deciding whether a graph has rc g 2 is np complete li et al proved that rc g 5 if g is a bridgeless graph with diameter 2 while rc g 9 if g is a bridgeless graph with diameter 3 furthermore uchizawa et al showed that determining the rainbow connection number of graphs is strongly np complete even for outerplanar graphs in this paper we give upper bounds of the rainbow connection number of outerplanar graphs with small diameters

fixed parameter algorithms for rectilinear steiner tree and rectilinear traveling salesman problem in the plane abstract given a set p of n points with their pairwise distances the traveling salesman problem tsp asks for a shortest tour that visits each point exactly once a tsp instance is rectilinear when the points lie in the plane and the distance considered between two points is the l1 distance in this paper a fixed parameter algorithm for the rectilinear tsp is presented and relies on techniques for solving tsp on bounded treewidth graphs it proves that the problem can be solved in o nh7h where h n denotes the number of horizontal lines containing the points of p the same technique can be directly applied to the problem of finding a shortest rectilinear steiner tree that interconnects the points of p providing a o nh5h time complexity both bounds improve over the best time bounds known for these problems

routing through virtual paths in layered telecommunication networks we study a network configuration problem in telecommunications where one wants to set up paths in a capacitated network to accommodate given point to point traffic demand the problem is formulated as an integer linear programming model where 0 1 variables represent different paths an associated integral polytope is studied and different classes of facets are described these results are used in a cutting plane algorithm computational results for some realistic problems are reported

hamilton paths in grid graphs a grid graph is a node induced finite subgraph of the infinite grid it is rectangular if its set of nodes is the product of two intervals given a rectangular grid graph and two of its nodes we give necessary and sufficient conditions for the graph to have a hamilton path between these two nodes in contrast the hamilton path and circuit problem for general grid graphs is shown to be np complete this provides a new relatively simple proof of the result that the euclidean traveling salesman problem is np complete

fault tolerant hamiltonicity in a class of faulty meshes abstract this paper addresses the hamiltonian properties of rectangular meshes with faulty nodes we present a necessary and sufficient condition for an m n mesh m 4 and n 4 are even with two faulty nodes to have a fault free hamiltonian cycle which generalizes a result owing to kim and yoon j s kim s h yoon embedding of rings in 2 d meshes and tori with faulty nodes journal of systems architecture 43 9 1997 643 654 we also describe an efficient scheme for constructing such a fault free hamiltonian cycle if there is

boundary properties of graphs for algorithmic graph problems the notion of a boundary graph property was recently introduced as a relaxation of that of a minimal property and was applied to several problems of both algorithmic and combinatorial nature in the present paper we first survey recent results related to this notion and then apply it to two algorithmic graph problems hamiltonian cycle and vertexk colorability in particular we discover the first two boundary classes for the hamiltonian cycle problem and prove that for any k 3 there is a continuum of boundary classes for vertexk colorability

bounded degree minimum radius spanning trees in wireless sensor networks in this paper we study the problem of computing a spanning tree of a given undirected disk graph such that the radius of the tree is minimized subject to a given degree constraint d we first introduce an 8 4 bicriteria approximation algorithm for unit disk graphs which is a special case of disk graphs that computes a spanning tree such that the degree of any nodes in the tree is at most d 8 and its radius is at most email protected opt where opt is the minimum possible radius of any spanning tree with degree bound d we also introduce an a 2 bicriteria approximation algorithm for disk graphs that computes a spanning tree whose maximum node degree is at most d email protected and whose radius is bounded by email protected opt where a is a non constant value that depends on m and k with m being the number of distinct disk radii and k being the ratio of the largest and the smallest disk radius

an efficient certifying algorithm for the hamiltonian cycle problem on circular arc graphs abstract a certifying algorithm for a problem is an algorithm that provides a certificate with each answer that it produces the certificate is an evidence that can be used to authenticate the correctness of the answer a hamiltonian cycle in a graph is a simple cycle in which each vertex of the graph appears exactly once the hamiltonian cycle problem is to determine whether or not a graph contains a hamiltonian cycle the best result for the hamiltonian cycle problem on circular arc graphs is an o n 2 log n time algorithm where n is the number of vertices of the input graph in fact the o n 2 log n time algorithm can be modified as a certifying algorithm although it was published before the term certifying algorithms appeared in the literature however whether there exists an algorithm whose time complexity is better than o n 2 log n for solving the hamiltonian cycle problem on circular arc graphs has been opened for two decades in this paper we present an o n time certifying algorithm to solve this problem where represents the maximum degree of the input graph the certificates provided by our algorithm can be authenticated in o n time

packing steiner trees polyhedral investigations letg v e be a graph andt v be a node set we call an edge sets a steiner tree fort ifs connects all pairs of nodes int in this paper we address the following problem which we call the weighted steiner tree packing problem given a graphg v e with edge weightswe edge capacitiesce e e and node sett1 tn find edge setss1 sn such that eachsk is a steiner tree fortk at mostce of these edge sets use edgee for eache e and the sum of the weights of the edge sets is minimal our motivation for studying this problem arises from a routing problem in vlsi design where given sets of points have to be connected by wires we consider the steiner tree packing problem from a polyhedral point of view and define an associated polyhedron called the steiner tree packing polyhedron the goal of this paper is to partially describe this polyhedron by means of inequalities it turns out that under mild assumptions each inequality that defines a facet for the single steiner tree polyhedron can be lifted to a facet defining inequality for the steiner tree packing polyhedron the main emphasis of this paper lies on the presentation of so called joint inequalities that are valid and facet defining for this polyhedron inequalities of this kind involve at least two steiner trees the classes of inequalities we have found form the basis of a branch cut algorithm this algorithm is described in our companion paper in this issue

send and split method for minimum concave cost network flows many problems from inventory production and capacity planning and from network design exhibit scale economies and can be formulated in terms of finding minimum additive concave cost nonnegative network flows we reduce the problem to an equivalent one in which the arc flow costs are nonnegative and give a dynamic programming method called the send and split method to solve it the main work of the method entails repeatedly solving set splitting and minimum cost chain problems in uncapacitated networks with n nodes a arcs and d 1 demand nodes i e nodes with nonzero exogenous demand the algorithm requires up to n2 13d s2d operations additions and comparisons where s n log2n 3a is the number of operations required to solve a minimum cost chain problem with nonnegative arc costs on the augmented graph formed by appending a node and an arc thereto from each node in the graph if also the network is k planar i e the graph is planar with all demand nodes lying on the boundary of k faces the method requires at most n2 kd3k sd2k operations the algorithm can be applied to capacitated networks because they can be reduced to equivalent uncapacitated ones these results unify significantly generalize e g to cyclic problems and sometimes improve upon e g for tandem facilities known polynomial time dynamic programming algorithms for wagner and whitin s wagner h m whitin t m 1958 dynamic version of the economic lot size model management sci 5 89 96 dynamic economic order quantity problem zangwill s zangwill w i 1969 a backlogging model and a multi echelon model of a dynamic economic lot size production system a network approach management sci 15 506 527 generalization to tandem facilities and veinott s veinott jr a f 1969 minimum concave cost solution of leontief substitution models of multi facility inventory systems oper res 17 262 291 increasing capacity warehousing problem the networks for the finite period versions of these problems are each 1 planar the method improves upon zangwill s zangwill w i 1968 minimum concave cost flows in certain networks management sci 14 429 450 related oand running time dynamic programming method for finding minimum additive concave cost non negative flows in circuitless single source networks we also implement the method to solve in polynomial time the d 1 demand node and k planar versions of the minimum cost forest and steiner problems in graphs the running time for the d 1 demand node steiner problem in graphs is comparable to that of dreyfus and wagner s dreyfus s e wagner r a 1971 the steiner problem in graphs networks1 195 207 method

noncharacteristic embeddings of the n dimensional torus in the n 2 dimensional torus we construct certain exotic embeddings of the n torus tn in tn 2 in the standard homotopy class we turn an embedding f tn tn 2 characteristic if there exists some map a tn 2 tn 2 in the standard homotopy class with the property that a o f tn tn 2 is the standard coordinate inclusion and a tn 2 f tn c tn 2 tn we find examples of noncharacteristic embeddings f in dimensions n 4k 1 n 5 and show that these examples are not even cobordant to characteristic embeddings we let g denote the fundamental group of the complement of the standard coordinate inclusion tn 2 tn then we can associate to f a real valued signature function on the set of j dimensional unitary representations of g where g denotes the fundamental group of the localization of tn 2 tn with respect to homology with local coefficients in z zn 2 this function is a cobordism invariant which has certain periodicity properties for characteristic embeddings we verify that this periodicity does not hold for our examples f implying that they are not characteristic additional results include a proof that the examples f become cobordant to characteristic embeddings upon taking the cartesian product with the identity map on a circle

filtered likelihood for point processes abstract point processes are widely used in finance and economics to model the timing of defaults market transactions unemployment spells births and a range of other events we develop and analyze likelihood estimators for the parameters of a marked point process and incompletely observed explanatory factors that influence the arrival intensity and mark distribution we establish an approximation to the likelihood and analyze the convergence and large sample properties of the associated estimators numerical results illustrate the behavior of our estimators

on the complexity of unique solutions on montre que le probleme de savoir si un cas du probleme du commis voyageur a une solution uniquement optimale est complet pour 2 p

estimation of a low intensity filtered poisson process in additive white gaussian noise a poisson gauss process is defined as the sum of a filtered poisson process a poisson process passed through a linear filter and a white gaussian noise this model describes the electrical signal at the output of an optical measuring unit consisted of a photodetector and its following amplifying circuits the intensity of the poisson process in this model is proportional to the received optical power with the observations of a poisson gauss process three estimation problems are considered minimum mean squared error estimation of the poisson process at every fixed but arbitrary time minimum mean squared error estimation of the poisson intensity and the maximum likelihood estimation of the intensity the solutions to these problems are presented in terms of a complicated functional of the observed poisson gauss process which is hard to compute for an arbitrary value of the poisson intensity however under a low intensity regime nonlinear filtering schemes are developed to efficiently compute this functional this special case provides a signal processing framework for single photon detection a technology dedicated to measurement of low optical powers

the geometric maximum traveling salesman problem we consider the traveling salesman problem when the cities are points in n x211d d for some fixed d and distances are computed according to geometric distances determined by some norm we show that for any polyhedral norm the problem of finding a tour of maximum length can be solved in polynomial time if arithmetic operations are assumed to take unit time our algorithms run in time o nf 2 log n where f is the number of facets of the polyhedron determining the polyhedral norm thus for example we have o n2 log n algorithms for the cases of points in the plane under the rectilinear and sup norms this is in contrast to the fact that finding a minimum length tour in each case is np hard our approach can be extended to the more general case of quasi norms with a not necessarily symmetric unit ball where we get a complexity of o n2f 2 log n for the special case of two dimensional metrics with f 4 which includes the rectilinear and sup norms we present a simple algorithm with o n running time the algorithm does not use any indirect addressing so its running time remains valid even in comparison based models in which sorting requires n log n time the basic mechanism of the algorithm provides some intuition on why polyhedral norms allow fast algorithms complementing the results on simplicity for polyhedral norms we prove that for the case of euclidean distances in n x211d d for d 3 the maximum tsp is np hard this sheds new light on the well studied difficulties of euclidean distances

decomposing matrices into blocks in this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so called bordered block diagonal form more precisely given some matrix a we try to assign as many rows as possible to some number beta of blocks of size kappa such that no two rows assigned to different blocks intersect in a common column bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems we show that various matrices from the linear programming and mixed integer programming libraries netlib and miplib can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality these computations are done with a branch and cut algorithm based on polyhedral investigations of the matrix decomposition problem in practice however one would use heuristics to find a good decomposition we present several heuristic ideas and test their performance finally we investigate the usefulness of optimal matrix decompositions into bordered block diagonal form for integer programming by using such decompositions to guide the branching process in a branch and cut code for general mixed integer programs