an adaptive multiple restarts neural network algorithm for graph coloring abstract the graph coloring problem is amongst the most difficult ones in combinatorial optimization with a diverse set of significant applications in science and industry previous neural network attempts at coloring graphs have not worked well in particular they do not scale up to large graphs furthermore experimental evaluations on real world graphs have been lacking and so have comparisons with state of the art conventional algorithms in this paper we address all of these issues we develop an improved neural network algorithm for graph coloring that scales well with graph size the algorithm employs multiple restarts and adaptively reduces the network s size from restart as it learns bettwe ways to color a given graph hence it gets faster and leaner as it evolves we evaluate this algorithm on a structurally diverse set of graphs that arise in different applications we compare its performance with that of a state of the art conventional algorithm on identical graphs the conventional algorithm works better overall though ours is not far behind ours works better on some graphs the inherent parallel and distributed nature of our algorithm especially within a neural network architecture is a potential advantage for implementation and speed up

bounded coloring of co comparability graphs and the pickup and delivery tour combination problem the double traveling salesman problem with multiple stacks is a vehicle routing problem in which pickups and deliveries must be performed in two independent networks the items are stored in stacks and repacking is not allowed given a pickup and a delivery tour the problem of checking if there exists a valid distribution of items into s stacks of size h that is consistent with the given tours is known as pickup and delivery tour combination pdtc problem in the paper we show that the pdtc problem can be solved in polynomial time when the number of stacks s is fixed but the size of each stack is not we build upon the equivalence between the pdtc problem and the bounded coloring bc problem on permutation graphs for the latter problem s is the number of colors and h is the number of vertices that can get a same color we show that the bc problem can be solved in polynomial time when s is a fixed constant on co comparability graphs a superclass of permutation graphs to the contrary the bc problem is known to be hard on permutation graphs when h 6 is a fixed constant but s is unbounded

topological interference management through index coding this paper studies linear interference networks both wired and wireless with no channel state information at the transmitters except a coarse knowledge of the end to end one hop topology of the network that only allows a distinction between weak zero and significant nonzero channels and no further knowledge of the channel coefficients realizations the network capacity wired and degrees of freedom dof wireless are found to be bounded above by the capacity of an index coding problem for which the antidote graph is the complement of the given interference graph the problems are shown to be equivalent under linear solutions an interference alignment perspective is then used to translate the existing index coding solutions into the wired network capacity and wireless network dof solutions as well as to find new and unified solutions to different classes of all three problems

on an approximation measure founded on the links between optimization and polynomial approximation theory in order to define a polynomial approximation theory linked to combinatorial optimization closer than the existing one we first formally define the notion of a combinatorial optimization problem and then based upon this notion we introduce a notion of equivalence among optimization problems this equivalence includes for example translation or affine transformation of the objective function or yet some aspects of equivalencies between maximization and minimization problems for example the equivalence between minimum vertex cover and maximum independent set next we adress the question of the adoption of an approximation ratio respecting the defined equivalence we prove that an approximation ratio defined as a two variable function cannot respect this equivalence we then adopt a three variable function as a new approximation ratio already used by a number of researchers which is coherent to the equivalence and under the choice of the variables the new ratio is introduced by an axiomatic approach finally using the new ratio we prove approximation results for a number of combinatorial problems

on some applications of the selective graph coloring problem in this paper we present the selective graph coloring problem a generalization of the standard graph coloring problem as well as several of its possible applications given a graph with a partition of its vertex set into several clusters we want to select one vertex per cluster such that the chromatic number of the subgraph induced by the selected vertices is minimum this problem appeared in the literature under different names for specific models and its complexity has recently been studied for different classes of graphs here we describe different models some already discussed in previous papers and some new ones in very different contexts under a unified framework based on this graph problem we point out similarities between these models offering a new approach to solve them and show some generic situations where the selective graph coloring problem may be used we focus on specific graph classes motivated by each model and we briefly discuss the complexity of the selective graph coloring problem in each one of these graph classes and point out interesting future research directions

random ambiguous point of random k ω set contractive operator in this paper we introduce a new concept of random ambiguous point of random operator and investigate some problems of random ambiguous point of random k set contractive operator and obtain some new results of random k set contractive operator

generalized complex geometry generalized complex geometry encompasses complex and symplectic ge ometry as its extremal special cases we explore the basic properties of this geometry including its enhanced symmetry group elliptic deforma tion theory relation to poisson geometry and local structure theory we also dene and study generalized complex branes which interpolate be tween at bundles on lagrangian submanifolds and holomorphic bundles on complex submanifolds

scheduling file transfers we consider a problem of scheduling file transfers in a network so as to minimize overall finishing time although the general problem is np complete we identify polynomial time solvable special cases and derive good performance bounds for several natural approximation algorithms assuming the existence of a central controller we also show how these bounds can be maintained in a distributed regime

p k coloring problems in line graphs the p k coloring problems generalize the usual coloring problem by replacing stable sets by cliques and stable sets complexities of some variations of p k coloring problems split coloring and cocoloring are studied in line graphs polynomial algorithms or proofs of np completeness are given according to the complexity status we show that the most general p k coloring problems are more difficult than the cocoloring and the split coloring problems while there is no such relation between the last two problems we also give complexity results for the problem of finding a maximum p k colorable subgraph in line graphs finally upper bounds on the optimal values are derived in general graphs by sequential algorithms based on welsh powell and matula orderings

parameterized maximum path coloring we study the well known max path coloring problem from a parameterized point of view focusing on trees and low treewidth networks we observe the existence of a variety of reasonable parameters for the problem such as the maximum degree and treewidth of the network graph the number of available colors and the number of requests one seeks to satisfy or reject in an effort to understand the impact of each of these parameters on the problem s complexity we study various parameterized versions of the problem deriving fixed parameter tractability and hardness results both for undirected and bi directed graphs

a threshold of ln n for approximating set cover given a collection f of subsets of s 1 n setcover is the problem of selecting as few as possiblesubsets from f such that their union covers s and maxk cover is the problem of selecting k subsets from f such that their union has maximum cardinality both these problems arenp hard we prove that 1 o 1 ln n is a threshold below which setcover cannot be approximated efficiently unless np has slightlysuperpolynomial time algorithms this closes the gap up to low orderterms between the ratio of approximation achievable by the greedyalogorithm which is 1 o 1 lnn and provious results of lund and yanakakis that showed hardness ofapproximation within a ratio of log 2 n 2s0 72 ln n for max k cover we show an approximationthreshold of 1 1 e up tolow order terms under assumption that p np

singular foliations with trivial canonical class this paper describes the structure of singular codimension one foliations with numerically trivial canonical bundle on complex projective manifolds

a tutorial on the use of graph coloring for some problems in robotics we study the problem where a robot has to pick up items of different sizes which are stored along a corridor a natural requirement is that the items have to be collected in decreasing order of their sizes we deal with various systems according to the location of the entry exit station where the robot unloads the collected items after each trip along the corridor the links of these systems with generalized coloring problems and other applications such that train shunting and pallet loading problems are discussed and related results are obtained we conclude with several open questions on the topic

on fano foliations abstract in this paper we address fano foliations on complex projective varieties these are foliations whose anti canonical class k is ample we focus our attention on a special class of fano foliations namely del pezzo foliations on complex projective manifolds we show that these foliations are algebraically integrable with one exceptional case when the ambient space is p n we also provide a classification of del pezzo foliations with mild singularities

research on some problems for nonlinear operators abstract in this paper we discuss some problems for nonlinear operators in the menger pn space meanwhile we prove existence theorems for the solution of an operator equation and obtain some new results by means of the theory of topological degree for the z p s space

the graph coloring problem a neuronal network approach solution of an optimization problem with linear constraints through the continuous hopfield network chn is based on an energy or lyapunov function that decreases as the system evolves until a local minimum value is attained this approach is extended in to optimization problems with quadratic constraints as a particular case the graph coloring problem gcp is analyzed the mapping procedure and an appropriate parameter setting procedure are detailed to test the theoretical results some computational experiments solving the gcp are shown

efficient routing in optical networks this paper studies the problem of dedicating routes to connections in optical networks in optical networks the vast bandwidth available in an optical fiber is utilized by partitioning it into several channels each at a different optical wavelength a connection between two nodes is assigned a specific wavelength with the constraint that no two connections sharing a link in the network can be assigned the same wavelength this paper considers optical networks with and without switches and different types of routing in these networks it presents optimal or near optimal constructions of optical networks in these cases and algorithms for routing connections specifically permutation routing for the networks constructed here

degrees of freedom of interference channels with comp transmission and reception we study the degrees of freedom dof of the k user interference channel with coordinated multipoint comp transmission and reception each message is jointly transmitted by m t successive transmitters and is jointly received by m r successive receivers we refer to this channel as the comp channel with a transmit cooperation order of m t and receive cooperation order of m r since the channel has a total of k transmit antennas and k receive antennas the maximum possible dof is equal to k we show that the comp channel has k dof if and only if m t m r geq k 1 the key idea is that the zero forcing of the interference corresponding to the i rm th message at the decoder of the j rm th message where j ne i can be viewed as a shared responsibility between the m t transmitters carrying the i rm th message and the m r receivers decoding the j rm th message for the general case we derive an outer bound that states that the dof is bounded above by left lceil k m t m r 2 2 right rceil for the special case with only comp transmission i e m r 1 we propose a scheme that can achieve k m t 1 2 dof for all k and conjecture that the result holds true for all k in the proposed coding scheme the m t transmitters carrying each message are used to cancel the interference introduced by this message at the first m t 1 receivers thereby allowing each of these receivers to enjoy 1 dof and asymptotic interference alignment is used to align the interfering signals at each other receiver to occupy half the signal space the achievability proofs are based on the notion of algebraic independence from algebraic geometry

index coding an interference alignment perspective author s maleki h cadambe vr jafar sa abstract the index coding problem is studied from an interference alignment perspective providing new results as well as new insights into and generalizations of previously known results an equivalence is established between the capacity of multiple unicast index coding where each message is desired by exactly one receiver and groupcast index coding where a message can be desired by multiple receivers which settles the heretofore open question of insufficiency of linear codes for the multiple unicast index coding problem by equivalence with groupcast settings where this question has previously been answered necessary and sufficient conditions for the achievability of rate half per message in the index coding problem are shown to be a natural consequence of interference alignment constraints and generalizations to feasibility of rate 1 l 1 per message when each destination desires at least l messages are similarly obtained finally capacity optimal solutions are presented to a series of symmetric index coding problems inspired by the local connectivity and local interference characteristics of wireless networks the solutions are based on vector linear coding 1963 2012 ieee

rational morita equivalence for holomorphic poisson modules abstract we introduce a weak concept of morita equivalence in the birational context for poisson modules on complex normal poisson projective varieties we show that poisson modules on projective varieties with mild singularities are either rationally morita equivalent to a flat partial holomorphic sheaf or a sheaf with a meromorphic flat connection or a co higgs sheaf as an application we study the geometry of rank two meromorphic rank two sl 2 poisson modules which can be interpreted as a poisson analogous to transversally projective structures for codimension one holomorphic foliations moreover we describe the geometry of the symplectic foliation induced by the poisson connection on the projectivization of the poisson module

inverse chromatic number problems in interval and permutation graphs abstract given a graph g and a positive integer k the inverse chromatic number problem consists in modifying the graph as little as possible so that it admits a chromatic number not greater than k in this paper we focus on the inverse chromatic number problem for certain classes of graphs first we discuss diverse possible versions and then focus on two application frameworks which motivate this problem in interval and permutation graphs the inverse booking problem and the inverse track assignment problem the inverse booking problem is closely related to some previously known scheduling problems we propose new hardness results and polynomial cases the inverse track assignment problem motivates our study of the inverse chromatic number problem in permutation graphs we show how to solve in polynomial time a generalization of the problem with a bounded number of colors

an improved hybrid ant local search algorithm for the partition graph coloring problem in this paper we propose a hybrid ant colony optimization aco algorithm for the partition graph coloring problem pgcp given an undirected graph g v e whose nodes are partitioned into a given number of the sets the goal of the pgcp is to find a subset v v that contains exactly one node from each cluster and a coloring for v so that in the graph induced by v two adjacent nodes have different colors and the total number of used colors is minimal our hybrid algorithm is obtained by executing a local search procedure after every aco iteration the performance of our algorithm is evaluated on a set of instances commonly used as benchmark and the computational results show that compared to state of the art algorithms our improved hybrid aco algorithm achieves solid results in very short run times

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

on the parameterized complexity of multiple interval graph problems multiple interval graphs are a natural generalization of interval graphs where each vertex may have more than one interval associated with it many applications of interval graphs also generalize to multiple interval graphs often allowing for more robustness in the modeling of the specific application with this motivation in mind a recent systematic study of optimization problems in multiple interval graphs was initiated in this sequel we study multiple interval graph problems from the perspective of parameterized complexity the problems under consideration are k independent set k dominating set and k clique which are all known to be w 1 hard for general graphs and np complete for multiple interval graphs we prove that k clique is in fpt while k independent set and k dominating set are both w 1 hard we also prove that k independent dominating set a hybrid of the two above problems is also w 1 hard our hardness results hold even when each vertex is associated with at most two intervals and all intervals have unit length furthermore as an interesting byproduct of our hardness results we develop a useful technique for showing w 1 hardness via a reduction from the k multicolored clique problem a variant of k clique we believe this technique has interest in its own right as it should help in simplifying w 1 hardness results which are notoriously hard to construct and technically tedious

implementing the dantzig fulkerson johnson algorithm for large traveling salesman problems dantzig fulkerson and johnson 1954 introduced the cutting plane method as a means of attacking the traveling salesman problem this method has been applied to broad classes of problems in combinatorial optimization and integer programming in this paper we discuss an implementation of dantzig et al s method that is suitable for tsp instances having 1 000 000 or more cities our aim is to use the study of the tsp as a step towards understanding the applicability and limits of the general cutting plane method in large scale applications

calculations of random fixed point index in this paper we prove an important inequality and investigate some new calculating problems of random fixed point index and generalize famous theorem by means of the theory of random fixed point index

on the complexity of the selective graph coloring problem in some special classes of graphs in this paper we consider the selective graph coloring problem given an integer k 1k 1 and a graph g v e g v e with a partition v1 vpv1 vp of vv it consists in deciding whether there exists a set v v in gg such that v vi 1 v vi 1 for all i 1 p i 1 p and such that the graph induced by v v is kk colorable we investigate the complexity status of this problem in various classes of graphs

routing and wavelength assignment by partition colouring the problem of routing and wavelength assignment in all optical networks may be solved by a combined approach involving the computation of alternative routes for the lightpaths followed by the solution of a partition colouring problem in a conflict graph a new tabu search heuristic is also proposed for the partition colouring problem which may be viewed as an extension of the graph colouring problem computational experiments are reported showing that the tabu search heuristic outperforms the best heuristic for partition colouring by approximately 20 in the average and illustrating that the new approach for the problem of routing and wavelength assignment is more robust than a well established heuristic for this problem

a kobayashi hitchin correspondence for i holomorphic bundles abstract in this paper we introduce the notions of hermitian einstein metric and stability for i holomorphic vector bundles on bi hermitian manifolds moreover we establish a kobayashi hitchin correspondence for i holomorphic vector bundles on bi hermitian manifolds examples of such vector bundles include generalized holomorphic bundles on generalized kahler manifolds we also show that stability of a vector bundle in this sense can depend on the parameter

optimization by simulated annealing an experimental evaluation part ii graph coloring and number partitioning this is the second in a series of three papers that empirically examine the competitiveness of simulated annealing in certain well studied domains of combinatorial optimization simulated annealing is a randomized technique proposed by s kirkpatrick c d gelatt and m p vecchi for improving local optimization algorithms here we report on experiments at adapting simulated annealing to graph coloring and number partitioning two problems for which local optimization had not previously been thought suitable for graph coloring we report on three simulated annealing schemes all of which can dominate traditional techniques for certain types of graphs at least when large amounts of computing time are available for number partitioning simulated annealing is not competitive with the differencing algorithm of n karmarkar and r m karp except on relatively small instances moreover if running time is taken into account natural annealing schemes cannot even outperform multiple random runs of the local optimization algorithms on which they are based in sharp contrast to the observed performance of annealing on other problems

the complexity of path coloring and call scheduling abstract modern high performance communication networks pose a number of challenging problems concerning the efficient allocation of resources to connection requests in all optical networks with wavelength division multiplexing connection requests must be assigned paths and colors wavelengths such that intersecting paths receive different colors and the goal is to minimize the number of colors used this path coloring problem is proved np hard for undirected and bidirected ring networks path coloring in undirected tree networks is shown to be equivalent to edge coloring of multigraphs which implies a polynomial time optimal algorithm for trees of constant degree as well as np hardness and an approximation algorithm with absolute approximation ratio 4 3 and asymptotic approximation ratio 1 1 for trees of arbitrary degree for bidirected trees path coloring is shown to be np hard even in the binary case a polynomial time optimal algorithm is given for path coloring in undirected or bidirected trees with n nodes under the assumption that the number of paths touching every single node of the tree is o log n 1 e call scheduling is the problem of assigning paths and starting times to calls in a network with bandwidth reservation such that the maximum completion time is minimized in the case of unit bandwidth requirements unit edge capacities and unit call durations call scheduling is equivalent to path coloring if either the bandwidth requirements or the call durations can be arbitrary call scheduling is shown np hard for virtually every network topology

the double travelling salesman problem with multiple stacks formulation and heuristic solution approaches this paper introduces the double travelling salesman problem with multiple stacks and presents four different metaheuristic approaches to its solution the double tsp with multiple stacks is concerned with determining the shortest route performing pickups and deliveries in two separated networks one for pickups and one for deliveries using only one container repacking is not allowed instead each item can be positioned in one of several rows in the container such that each row can be considered a lifo last in first out stack but no mutual constraints exist between the rows two different neighbourhood structures are developed for the problem and used with each of three local search metaheuristics additionally some simpler removal and reinsertion operators are used in a large neighbourhood search framework finally some computational results are given along with lower bounds on the objective value

a heuristic approach for combined equipment planning and routing in multi layer sdh wdm networks abstract the paper deals with a multi layer network design problem for a high speed telecommunication network based on synchronous digital hierarchy sdh and wavelength division multiplex wdm technology the network has to carry a certain set of demands with the objective of minimizing the investment in the equipment the different layers are the fiber layer 2 5 gbit s 10 gbit s and wdm systems several variations of the problem including path protected demands and specific types of cross connect equipment are considered the problem is described as a mixed integer linear programming model and some results for small networks are presented two greedy heuristics a random start heuristic and a grasp like approach are implemented to solve large real world problems

the degrees of freedom of isotropic mimo interference channels without state information at the transmitters this paper fully determines the degree of freedom dof region of two user interference channels with arbitrary number of transmit and receive antennas in the case of isotropic and independent or block wise independent fading where the channel state information is available to the receivers but not to the transmitters thus the dof gap between previous upper and lower bounds due to the authors vaze and varanasi and huang jafar shamai and vishwanath is closed the dof result characterizes the capacity region to the first order of the logarithm of the signal to noise ratio snr in the high snr regime the dof region is achievable by using random gaussian codebooks independent of the channel states which implies that it is impossible to increase the dof using beamforming and interference alignment in the absence of channel state information at the transmitters

the np completeness of edge coloring we show that it is np complete to determine the chromatic index of an arbitrary graph the problem remains np complete even for cubic graphs

routing and wavelength assignment in optical networks using bin packing based algorithms this paper addresses the problem of routing and wavelength assignment rwa of static lightpath requests in wavelength routed optical networks the objective is to minimize the number of wavelengths used this problem has been shown to be np complete and several heuristic algorithms have been developed to solve it we suggest very efficient yet simple heuristic algorithms for the rwa problem developed by applying classical bin packing algorithms the heuristics were tested on a series of large random networks and compared with an efficient existing algorithm for the same problem results indicate that the proposed algorithms yield solutions significantly superior in quality not only with respect to the number of wavelength used but also with respect to the physical length of the established lightpaths comparison with lower bounds shows that the proposed heuristics obtain optimal or near optimal solutions in many cases

on the synergistic benefits of alternating csit for the miso broadcast channel the degrees of freedom dofs of the two user multiple input single output miso broadcast channel bc are studied under the assumption that the form ii i 1 2 of the channel state information at the transmitter csit for each user s channel can be either perfect p delayed d or not available n i e i1 i2 p n d and therefore the overall csit can alternate between the nine resulting states i1i2 the fraction of time associated with csit state i1i2 is denoted by the parameter i1i2 and it is assumed throughout that i1i2 i2i1 i e pn np pd dp dn nd under this assumption of symmetry the main contribution of this paper is a complete characterization of the dof region of the two user miso bc with alternating csit surprisingly the dof region is found to depend only on the marginal probabilities p d n i2 pi2 i2 di2 i2 ni2 i2 p d n which represent the fraction of time that any given user e g user 1 is associated with perfect delayed or no csit respectively as a consequence the dof region with all nine csit states d i1i2 i1 i2 p d n is the same as the dof region with only three csit states d pp dd nn under the same marginal distribution of csit states i e pp dd nn p d n the sum dof value can be expressed as dof min 4 2 p 3 1 p d from which one can uniquely identify the minimum required marginal csit fractions to achieve any target dof value as p d min 3 2 dof 2 1 1 2 dof when dof 4 3 2 and p d min 0 dof 1 when dof 0 4 3 the results highlight the synergistic benefits of alternating csit and the tradeoffs between various forms of csit for any given dof value partial results are also presented for the multiuser miso bc with m transmit antennas and k single antenna users for this problem the minimum amount of perfect csit required per user to achieve the maximum dofs of min m k is characterized by the minimum amount of csit per user we refer to the minimum fraction of time that the transmitter has access to perfect and instantaneous csit from a user through a novel converse proof and an achievable scheme it is shown that the minimum fraction of time perfect csit is required per user in order to achieve the dof of min m k is given by min m k k

using intermediate infeasible solutions to approach vehicle routing problems with precedence and loading constraints logistics and transportation issues have been receiving increasing attention during the last decades and their requirements have gradually changed making it necessary to take into account new situations and conditions the double traveling salesman problem with multiple stacks dtspms is a pickup and delivery problem in which some additional precedence and loading constraints are imposed on the vehicle to be used in this paper we approach the problem using intermediate infeasible solutions to diversify the search process and we develop some fixing procedures and infeasibility measures to deal with this kind of solutions and take advantage of their potential

poisson modules and degeneracy loci in this paper we study the interplay between modules and sub objects in holomorphic poisson geometry in particular we dene a new notion of residue for a poisson module analogous to the poincar e residue of a meromorphic volume form of particular interest is the interaction between the residues of the canonical line bundle of a poisson manifold and its degeneracy loci where the rank of the poisson structure drops as an application we provide new evidence in favour of bondal s conjecture that the rank 2k locus of a fano poisson manifold always has dimension 2k 1 in particular we show that the conjecture holds for fano fourfolds we also apply our techniques to a family of poisson structures dened by fe gin and odesski where the degeneracy loci are given by the secant varieties of elliptic normal curves

generalized network design problems abstract network design problems ndp consist of identifying an optimal subgraph of a graph subject to side constraints in generalized ndp the vertex set is partitioned into clusters and the feasibility conditions are expressed in terms of the clusters several applications of generalized ndp arise in the fields of telecommunications transportation and biology the aim of this review article is to formally define generalized ndp to study their properties and to provide some applications

the complexity of multiterminal cuts in the multiterminal cut problem one is given an edge weighted graph and a subset of the vertices called terminals and is asked for a minimum weight set of edges that separates each terminal from all the others when the number k of terminals is two this is simply the mincut max flow problem and can be solved in polynomial time it is shown that the problem becomes np hard as soon as k 3 but can be solved in polynomial time for planar graphs for any fixed k the planar problem is np hard however if k is not fixed a simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2 2 k of the optimal cut weight is also described

irreducible components of the space of holomorphic foliations of degree two in cp n n 3 in this paper we will prove that the space of holomorphic fo liations of codimension 1 and degree 2 in cp n n 3 has six irreducible components

topological interference management with transmitter cooperation interference networks with no channel state information at the transmitter except for the knowledge of the connectivity graph have been recently studied under the topological interference management framework in this paper we consider a similar problem with topological knowledge but in a distributed broadcast channel setting i e a network where transmitter cooperation is enabled we show that the topological information can also be exploited in this case to strictly improve the degrees of freedom dof as long as the network is not fully connected which is a reasonable assumption in practice achievability schemes from graph theoretic and interference alignment perspectives are proposed together with outer bounds built upon generator sequence the concept of compound channel settings and the relation to index coding we characterize the symmetric dof for the so called regular networks with constant number of interfering links and identify the sufficient and or necessary conditions for the arbitrary network topologies to achieve a certain amount of symmetric dof

energy function based approaches to graph coloring we describe an approach to optimization based on a multiple restart quasi hopfield network where the only problem specific knowledge is embedded in the energy function that the algorithm tries to minimize we apply this method to three different variants of the graph coloring problem the minimum coloring problem the spanning subgraph k coloring problem and the induced subgraph k coloring problem though hopfield networks have been applied in the past to the minimum coloring problem our encoding is more natural and compact than almost all previous ones in particular we use k state neurons while almost all previous approaches use binary neurons this reduces the number of connections in the network from nk sup 2 to n sup 2 asymptotically and also circumvents a problem in earlier approaches that of multiple colors being assigned to a single vertex experimental results show that our approach compares favorably with other algorithms even nonneural ones specifically developed for the graph coloring problem

symplectic groupoids and poisson manifolds on definit la notion de groupoide symplectique on donne la variete de poisson de ce groupoide symplectique on presente une construction

deformations of holomorphic pseudo symplectic poisson manifolds abstract we prove unobstructed deformations for compact kahlerian even dimensional poisson manifolds whose poisson tensor degenerates along a divisor with mild singularities examples include hilbert schemes of del pezzo surfaces

a post optimization method for the routing and wavelength assignment problem applied to scheduled lightpath demands we consider here a np hard problem related to the routing and wavelength assignment rwa problem in optical networks dealing with scheduled lightpath demands slds an sld is a connection demand between two nodes of the network during a certain time given a set of slds we want to assign a lightpath i e a routing path and a wavelength to each sld so that the total number of required wavelengths is minimized the constraints are the following a same wavelength must be assigned all along the edges of the routing path of any sld at any time a given wavelength on a given edge of the network cannot be used to satisfy more than one sld to solve this problem we design a post optimization method improving the solutions provided by a heuristic the experimental results show that this post optimization method is quite efficient to reduce the number of necessary wavelengths

interference networks with no csit impact of topology we consider partially connected k user interference networks where the transmitters have no knowledge about the channel gain values but they are aware of network topology we introduce several linear algebraic and graph theoretic concepts to derive new topology based outer bounds and inner bounds on the symmetric degrees of freedom of these networks we evaluate our bounds for two classes of networks to demonstrate their tightness for most networks in these classes quantify the gain of our inner bounds over benchmark interference management strategies and illustrate the effect of network topology on these gains

on codimension 1 del pezzo foliations on varieties with mild singularities in this paper we extend to the singular setting the theory of fano foliations developed in our previous paper araujo and druel adv math 238 70 118 2013 a mathbb q fano foliation on a complex projective variety x is a foliation fancyscript f subsetneq t x whose anti canonical class k fancyscript f is an ample mathbb q cartier divisor in the spirit of kobayashi ochiai theorem we prove that under some conditions the index i fancyscript f of a mathbb q fano foliation is bounded by the rank r of fancyscript f and classify the cases in which i fancyscript f r next we consider mathbb q fano foliations fancyscript f for which i fancyscript f r 1 these are called del pezzo foliations we classify codimension 1 del pezzo foliations on mildly singular varieties

multiple pickup and delivery traveling salesman problem with last in first out loading and distance constraints abstract we extend the traveling salesman problem with pickup and delivery and lifo loading tsppdl by considering two additional factors namely the use of multiple vehicles and a limitation on the total distance that a vehicle can travel both of these factors occur commonly in practice we call the resultant problem the multiple pickup and delivery traveling salesman problem with lifo loading and distance constraints mtsppd ld this paper presents a thorough preliminary investigation of the mtsppd ld we propose six new neighborhood operators for the problem that can be used in search heuristics or meta heuristics we also devise a two stage approach for solving the problem where the first stage focuses on minimizing the number of vehicles required and the second stage minimizes the total travel distance we consider two possible approaches for the first stage simulated annealing and ejection pool and two for the second stage variable neighborhood search and probabilistic tabu search our computational results serve as benchmarks for future researchers on the problem

morita equivalence of poisson manifolds poisson manifolds are the classical analogue of associative algebras for poisson manifolds symplectic realizations play a similar role as representations do for associative algebras in this paper the notion of morita equivalence of poisson manifolds a classical analogue of morita equivalence of algebras is introduced and studied it is proved that morita equivalent poisson manifolds have equivalent categories of complete symplectic realizations for certain types of poisson manifolds the geometric invariants of morita equivalence are also investigated