super p restricted edge connectivity of line graphs super restricted connectivity and super restricted edge connectivity are more refined network reliability indices than connectivity and edge connectivity in this paper we first introduce the concepts of super restricted connectivity and super restricted edge connectivity and then give a property of graphs with equal p restricted edge connectivity and 1 p restricted connectivity applying this property we show a sufficient condition for a line graph to be super p restricted edge connected and a relationship between super 1 p restricted connected graphs and super p restricted edge connected graphs

fault tolerant hamiltonian laceability of balanced hypercubes the balanced hypercube as a new variant of hypercube has many desirable properties such as strong connectivity high regularity and symmetry the particular property of the balanced hypercube is that each processor has a backup processor sharing the same neighborhood a hamiltonian bipartite graph g v 0 v 1 e is said to be hamiltonian laceable if there is a hamiltonian path between any two vertices x v 0 and y v 1 it has been proved that the balanced hypercube bh n is hamiltonian laceable for all n 1 in this paper we have proved that after at most 2 n 2 faulty edges occur bh n remains hamiltonian laceable for all n 2 this result is optimal with respect to the number of faulty edges can be tolerated in bh n

matching preclusion for n dimensional torus networks abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings wang et al 13 proved that a class of n dimensional tours networks with even order are super matched later cheng et al 8 further showed that all n dimensional tours networks with even order are super matched in this paper we prove that all n dimensional torus networks with odd order are super matched if n 3 two dimensional torus networks with odd order is maximally matched except for c 3 c 3 our results are complementary to those of wang et al 13 and cheng et al 8

lms algorithms for tracking slow markov chains with applications to hidden markov estimation and adaptive multiuser detection this paper analyzes the tracking properties of the least mean squares lms algorithm when the underlying parameter evolves according to a finite state markov chain with infrequent jumps first using perturbed liapunov function methods mean square error estimates are obtained for the tracking error then using recent results on two time scale markov chains mean ordinary differential equation and diffusion approximation results are obtained it is shown that a sequence of the centered tracking errors converges to an ordinary differential equation moreover a suitably scaled sequence of the tracking errors converges weakly to a diffusion process it is also shown that iterate averaging of the tracking algorithm results in optimal asymptotic convergence rate in an appropriate sense two application examples analysis of the performance of an adaptive multiuser detection algorithm in a direct sequence code division multiple access ds cdma system and tracking analysis of the state of a hidden markov model hmm with infrequent jumps are presented

two disjoint cycle cover bipancyclicity of balanced hypercubes abstract a bipartite graph g is two disjoint cycle cover r1 r2 bipancyclic if for any even integer l satisfying r1 l r2 there exist two vertex disjoint cycles c1 and c2 in g such that v c 1 l and v c 2 v g l where v g denotes the number of vertices in g in this paper we study the two disjoint cycle cover bipancyclicity of the n dimensional balanced hypercube bhn which is a hypercube variant network and is superior to hypercube due to having a smaller diameter as a consequence we show that bhn is two disjoint cycle cover 4 2 2 n 1 bipancyclic for n 2

matching preclusion number in product graphs abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has no perfect matchings or almost perfect matchings for many interconnection networks the matching preclusion number is equal to the minimum degree of a vertex in the network and the sets of edges attaining the minimum are precisely those incident to a single vertex of minimum degree we say such networks are super matched in this paper we derive upper and lower bounds for the matching preclusion number for networks constructed using a variety of binary graph operations and give sufficient conditions for such networks to be super matched

strong matching preclusion for n dimensional torus networks the strong matching preclusion number of a graph is the minimum number of edges and or vertices whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings in 14 wang et al proved that c k c k is super strongly matched where k 3 is odd in this paper we show that c k 1 c k 2 c k n is super strongly matched where n 3 is an integer and k i 3 is an odd integer for each i 1 n our studies generalize the results of wang et al 14

strong matching preclusion of n k star graphs the strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings this is an extension of the matching preclusion problem that was introduced by park and ihm the generalized n k star graph was introduced to address scaling issues of the star graph and it has many desirable properties in this paper the goal is to find the strong matching preclusion number of n k star graphs and to categorize all optimal strong matching preclusion sets of these graphs since bipartite graphs generally have low strong matching preclusion numbers we assume that k n 2

weighted means in stochastic approximation of minima weighted averages of kiefer wolfowitz type procedures which are driven by larger step lengths than usual can achieve the optimal rate of convergence a priori knowledge of a lower bound on the smallest eigenvalue of the hessian matrix is avoided the asymptotic mean squared error of the weighted averaging algorithm is the same as would emerge using a newton type adaptive algorithm several different gradient estimates are considered one of them leads to a vanishing asymptotic bias this gradient estimate applied with the weighted averaging algorithm usually yields a better asymptotic mean squared error than applied with the standard algorithm

strong matching preclusion number of graphs abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings the strong matching preclusion number or simply smp number s m p g of a graph g is the minimum number of vertices and or edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings this is an extension of the matching preclusion problem and has been introduced by park and ihm in this paper we first study the smp number of some special graph classes and give some sharp upper and lower bounds of smp number next graphs with large and small smp number are characterized respectively in the end we investigate the nordhaus gaddum type relations on smp number

strong matching preclusion for k composition networks abstract let g 1 v 1 e 1 g 2 v 2 e 2 g k v k e k be k graphs and let f 1 v 1 v 2 f 2 v 2 v 3 f k 1 v k 1 v k f k v k v 1 be k bijections the k composition networks g induced by g 1 g 2 g k is the graph with v g t 1 k v g t and e g t 1 k e g t a t f t a t a t v g t and 1 t k many interconnection networks such as n dimensional torus networks recursive circulant graphs and cayley graphs on abelian groups generated by minimal generating sets are special k composition networks the strong matching preclusion number of a graph is the minimum number of edges and or vertices whose deletion results in the remaining graph has neither perfect matchings nor almost perfect matchings in this paper we study the strong matching preclusion number and strong matching preclusion sets for k composition networks with odd order our results generalize the main conclusion in 12

bipanconnectivity of balanced hypercubes the balanced hypercube proposed by wu and huang is a variant of the hypercube network in this paper paths of various lengths are embedded into balanced hypercubes a bipartite graph g is bipanconnected if for two arbitrary nodes x and y of g with distance d x y there exists a path of length l between x and y for every integer l with d x y l v g 1 and l d x y 0 mod 2 we prove that the n dimensional balanced hypercube bh n is bipanconnected for all n 1 this result is stronger than that obtained by xu et al which shows that the balanced hypercube is edge bipancyclic and hamiltonian laceable

edge pancyclicity and hamiltonian laceability of the balanced hypercubes abstract the balanced hypercube bh n is a variant of the hypercube q n huang and wu proved that bh n has better properties than q n with the same number of links and processors in particularly they showed that there exists a cycle of length 2 l in bh n for all l 2 l 2 n in this paper we improve this result by showing that bh n is edge pancyclic which means that for arbitrary edge e there exists a cycle of even length from 4 to 2 2 n containing e in bh n we also show that the balanced hypercubes are hamiltonian laceable

adaptive nonlinear filters for narrow band interference suppression in spread spectrum cdma systems this paper presents a novel nonlinear filter and parameter estimator for narrow band interference suppression in code division multiple access spread spectrum systems as in the article by rusch and poor 1994 the received sampled signal is modeled as the sum of the spread spectrum signal modeled as a finite state independently identically distributed i i d process here we generalize to a finite state markov chain narrow band interference modeled as a gaussian autoregressive process and observation noise modeled as a zero mean white gaussian process the proposed algorithm combines a recursive hidden markov model hmm estimator kalman filter kf and the recursive expectation maximization algorithm the nonlinear filtering techniques for narrow band interference suppression presented in rusch and poor and our proposed hmm kf algorithm have the same computational cost detailed simulation studies show that the hmm kf algorithm outperforms the filtering techniques in rusch and poor in particular significant improvements in the bit error rate and signal to noise ratio snr enhancement are obtained in low to medium snr furthermore in simulation studies we investigate the effect on the performance of the hmm kf and the approximate conditional mean acm filter in the paper by rusch and poor when the observation noise variance is increased as expected the performance of the hmm kf and acm algorithms worsen with increasing observation noise and number of users however hmm kf significantly outperforms acm in medium to high observation noise

on closed loop adaptive noise cancellation given the mean limit ordinary differential equation for the stochastic approximation defining the adaptive algorithm for a closed loop adaptive noise cancellation we characterize the limit points under appropriate conditions it is shown that as the dimension of the weight vector increases the sequence of corresponding limit points converges in the sense of l sub 2 to the infinite dimensional optimal weight vector also the limit point of the algorithm is nearly optimal if the dimension of the weight vector is large enough the gradient of the mean square error with respect to the weight vector evaluated at the limit goes to zero in l sub 1 and l sub 2 as the dimension increases as does the gradient with respect to the coefficients in the transfer function connecting the reference noise signal with the error output thus the algorithm is nearly a gradient descent algorithm and is error reducing for large enough dimension under broad conditions iterative averaging can be used to get a nearly optimal rate of convergence

adaptive step size algorithms for blind interference suppression in ds cdma systems this paper develops adaptive step size blind lms algorithms and adaptive forgetting factor blind rls algorithms for code aided suppression of multiple access interference mai and narrowband interference nbi in ds cdma systems these algorithms optimally adapt both the step size forgetting factor and the weight vector of the blind linear multiuser detector using the received measurements simulations are provided to compare the proposed algorithms with previously studied blind rls and blind lms algorithms they show that the adaptive step size blind lms algorithm and adaptive forgetting factor blind rls algorithm field significant improvements over the standard blind lms algorithm and blind rls algorithm in dynamic environments where the number of interferers are time varying

conditional edge fault tolerant edge bipancyclicity of hypercubes the hypercube has been one of the most popular interconnection networks for parallel computer communication systems in this paper we assume that each node is incident with at least two fault free links under this assumption we show that every fault free edge lies on a fault free cycle of every even length from 6 to 2 n inclusive even if it has up to 2n 5 link faults the result is optimal with respect to the number of link faults tolerated

the balanced hypercube a cube based system for fault tolerant applications in this paper we present an interconnection structure called the balanced hypercube which is a variation of the standard hypercube with desirable properties of strong connectivity regularity and symmetry the proposed structure is a special type of load balanced graph designed to tolerate processor failure in balanced hypercubes each processor has a backup matching processor that shares the same set of neighboring nodes therefore tasks that run on a faulty processor can be reactivated in the backup processor to provide efficient system reconfiguration other properties of balanced hypercubes are examined it is also shown that odd dimensional balanced hypercubes have smaller diameters than that of standard hypercubes as an application of balanced hypercubes we show a fault tolerant embedding of rings in balanced hypercubes

on conditional diagnosability of the folded hypercubes the n dimensional folded hypercube fq n a variation of the hypercube proposed by ahmed et al a el amawy s latifi properties and performance of folded hypercubes ieee transactions on parallel and distributed systems 2 3 1991 31 42 is an n 1 regular n 1 connected graph conditional diagnosability a new measure of diagnosability introduced by lai et al pao lien lai jimmy j m tan chien ping chuang lih hsing hsu conditional diagnosability measures for large multiprocessor systems ieee transactions on computers 54 2 2005 165 175 can better measure the diagnosability of regular interconnection networks this paper determines that under pmc model the conditional diagnosability of fq n t c fq n is 4n 3 when n 5 or n 8 t c fq 3 3 t c fq 4 7

low complexity variable step size mechanisms for stochastic gradient algorithms in minimum variance cdma receivers in this paper the performance of blind adaptive receivers for direct sequence code division multiple access ds cdma systems that employ stochastic gradient sg algorithms with variable step size mechanisms is investigated two low complexity variable step size mechanisms are proposed for estimating the parameters of linear cdma receivers that operate with sg algorithms for multipath channels the novel adaptation mechanisms are also incorporated in the channel estimation algorithms whereas for the single path case the novel techniques are restricted to the linear receiver parameter vector estimation analytical expressions for the excess mean squared error mse are derived and a convergence analysis of the proposed adaptation techniques is carried out for both frequency selective and flat scenarios finally numerical experiments are presented for nonstationary environments showing that the new mechanisms achieve superior performance to previously reported methods at a reduced complexity

strong matching preclusion for augmented cubes the strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings the concept was introduced by park and son in this paper we study the strong matching preclusion problem for the augmented cube graphs as a result we find smp aqn and classify all optimal solutions

hamilton decompositions of regular expanders a proof of kelly s conjecture for large tournaments abstract a long standing conjecture of kelly states that every regular tournament on n vertices can be decomposed into n 1 2 edge disjoint hamilton cycles we prove this conjecture for large n in fact we prove a far more general result based on our recent concept of robust expansion and a new method for decomposing graphs we show that every sufficiently large regular digraph g on n vertices whose degree is linear in n and which is a robust outexpander has a decomposition into edge disjoint hamilton cycles this enables us to obtain numerous further results e g as a special case we confirm a conjecture of erd s on packing hamilton cycles in random tournaments as corollaries to the main result we also obtain several results on packing hamilton cycles in undirected graphs giving e g the best known result on a conjecture of nash williams we also apply our result to solve a problem on the domination ratio of the asymmetric travelling salesman problem which was raised e g by glover and punnen as well as alon gutin and krivelevich

stochastic approximation with averaging of the iterates optimal asymptotic rate of convergence for general processes consider the stochastic approximation algorithm x n 1 x n a n g x n xi n in an important paper polyak and juditsky siam j control optim 30 1992 pp 838 855 showed that loosely speaking if the coefficients a n go to zero slower than o 1 n then the averaged sequence sum nolimits i 1 n x i n converged to its limit at an optimum rate for any coefficient sequence the conditions were rather special and direct constructions were used here a rather simple proof is given that results of this type are generic to stochastic approximation and essentially hold any time that the classical asymptotic normality of the normalized and centered iterates holds considerable intuitive insight is provided into the procedure simulations have well borne out the importance of the method

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

note on matching preclusion number of random graphs abstract a perfect matching in a graph is a set of edges such that every vertex is incident with exactly one edge in this set the matching preclusion number of an even graph g denoted by m p g is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching in this paper we study the matching preclusion number of random graphs and prove that if n is even and p log n log log n n then asymptotically almost surely m p g n p g n p

fault hamiltonicity and fault hamiltonian connectivity of the arrangement graphs the arrangement graph a sub n k is a generalization of the star graph there are some results concerning fault hamiltonicity and fault hamiltonian connectivity of the arrangement graph however these results are restricted in some particular cases and thus are less completed we improve these results and obtain a stronger and simpler statement let n k spl ges 2 and f spl sube v a sub n k spl cup e a sub n k we prove that a sub n k f is hamiltonian if f spl les k n k 2 and a sub n k f is hamiltonian connected if f spl les k n k 3 these results are optimal

iterate averaging sign algorithms for adaptive filtering with applications to blind multiuser detection motivated by the developments on iterate averaging of recursive stochastic approximation algorithms and asymptotic analysis of sign error algorithms for adaptive filtering this work develops two stage sign algorithms for adaptive filtering the proposed algorithms are based on constructions of a sequence of estimates using large step sizes followed by iterate averaging our main effort is devoted to improving the performance of the algorithms by establishing asymptotic normality of a suitably scaled sequence of the estimation errors the asymptotic covariance is calculated and shown to be the smallest possible hence the asymptotic efficiency or asymptotic optimality is obtained then variants of the algorithm including sign regressor procedures and constant step algorithms are studied the minimal window width of averaging is also dealt with finally iterate averaging algorithms for blind multiuser detection in direct sequence code division multiple access ds cdma systems are proposed and developed and numerical examples are examined

hamiltonian cycle embedding for fault tolerance in balanced hypercubes abstract the balanced hypercube bh n defined by wu and huang is a variant of the hypercube network yang proposed that fault tolerance of balanced hypercube bh n is an important issue in parallel computing which needs further study yang 2010 24 in this paper we prove that there exists a fault free hamiltonian path between any two adjacent vertices in bh n with 2 n 2 faulty edges as a corollary we derive that for any fault free edge e there exists a fault free hamiltonian cycle containing e in bh n with 2 n 2 faulty edges which is optimal in the sense of the number of faulty edges

fault tolerant strong menger edge connectivity and 3 extra edge connectivity of balanced hypercubes abstract a connected graph g is called strongly menger edge connected if for any two distinct vertices x y of g there are min deg g x deg g y edge disjoint paths between x and y the g g 0 extra edge connectivity of the connected graph g denoted by g g is the minimal cardinality of a set of edges of g if exists whose deletion disconnects g and each remaining component contains more than g vertices in this paper we show that the n dimensional balanced hypercube b h n which is a variant of hypercube q n is still strongly menger edge connected even when there are 2 n 4 faulty vertices resp 2 n 2 faulty edges for n 2 moreover under the restricted condition that each vertex has at least two fault free edges we show that b h n is still strongly menger edge connected even when there are 6 n 8 faulty edges for n 2 these results are all optimal with respect to the maximum number of tolerated edge faults furthermore we showed that the 3 extra edge connectivity of b h n is 8 n 8 for n 2

on reliability of the folded hypercubes in this paper we explore the 2 extra connectivity and 2 extra edge connectivity of the folded hypercube fq n we show that k 2 fq n 3n 2 for n 8 and l 2 fq n 3n 1 for n 5 that is for n 8 resp n 5 at least 3n 2 vertices resp 3n 1 edges of fq n are removed to get a disconnected graph that contains no isolated vertices resp edges when the folded hypercube is used to model the topological structure of a large scale parallel processing system these results can provide more accurate measurements for reliability and fault tolerance of the system

conditional matching preclusion for the arrangement graphs the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex recently the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex it is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost perfect matchings in this paper we find this number and classify all optimal sets for the arrangement graphs one of the most popular interconnection networks

how does a stochastic optimization approximation algorithm adapt to a randomly evolving optimum root with jump markov sample paths stochastic optimization approximation algorithms are widely used to recursively estimate the optimum of a suitable function or its root under noisy observations when this optimum or root is a constant or evolves randomly according to slowly time varying continuous sample paths in comparison this paper analyzes the asymptotic properties of stochastic optimization approximation algorithms for recursively estimating the optimum or root when it evolves rapidly with nonsmooth jump changing sample paths the resulting problem falls into the category of regime switching stochastic approximation algorithms with two time scales motivated by emerging applications in wireless communications and system identification we analyze asymptotic behavior of such algorithms our analysis assumes that the noisy observations contain a nonsmooth jump process modeled by a discrete time markov chain whose transition frequency varies much faster than the adaptation rate of the stochastic optimization algorithm using stochastic averaging we prove convergence of the algorithm rate of convergence of the algorithm is obtained via bounds on the estimation errors and diffusion approximations remarks on improving the convergence rates through iterate averaging and limit mean dynamics represented by differential inclusions are also presented

the theory of d sequences and powers of ideals in this paper we study the question of finding depth r i given an ideal i in a commutative ring this problem is difficult in general even for simple examples depth r z can be difficult to compute brodmann has shown that for any commutative noetherian ring depth r z become stable for large n finding this value however is quite hard this problem originally arose through consideration of the following example suppose k is a field and x xij is an n

low complexity variable forgetting factor mechanism for blind adaptive constrained constant modulus algorithms in this paper we propose a novel low complexity variable forgetting factor vff mechanism for blind adaptive constrained constant modulus ccm recursive least squares rls algorithms applied to linear interference suppression in direct sequence code division multiple access ds cdma systems the proposed variable forgetting factor mechanism employs an updated component related to the time average of the constant modulus cm cost function to automatically adjust the forgetting factor in order to ensure good tracking of the interference and the channel convergence and tracking analyses are carried out analytical expressions for predicting the mean squared error of the proposed adaptation technique are obtained simulation results are presented for nonstationary environments and show that the proposed variable forgetting factor mechanism achieves superior performance to previously reported methods at a reduced complexity

liaison equivalence classes we will work in ip n 2 over an algebraically closed field the notion of liaison among subvarieties of ip was introduced in 3 we will consider here liaison in codimension two generalizing results in 4 recall therefore that two subschemes v 1 v 2 of ip that are locally cohenmacaulay and equidimensional of codimension two are said to be linked algebraically via the complete intersection x of two hypersurfaces denoted v l v z via x if d e v j x v r o v x t j they are said to be linked geometrically if i 1 and v2 in the above definition have no components in common according to 4 theorem 1 7 the two notions of linkage generate the same equivalence relation among those subschemes v which are also generically locally complete intersections we will hence consider only algebraic linkage

strongly menger edge connectedness and strongly menger vertex connectedness of regular networks abstract let f be a conditional faulty edge set of a graph g here the condition imposed on f is g f r for some fixed integer r the graph g is called f strongly menger edge connected of order r if each pair of distinct vertices u and v are connected by min deg g f u deg g f v edge disjoint paths in g f where deg g f u and deg g f v are the degrees of u and v in g f respectively a graph g is t strongly menger edge connected of order r if g is f strongly menger edge connected of order r for every f e g with f t one can consider the vertex version in an analogous way there are a number of papers with results for r 2 for several popular classes of interconnection network in this paper we develop a unified approach by considering various sufficient conditions of a regular graph to be f strongly menger edge connected of order r and the corresponding vertex version as corollaries several results on fundamental classes of interconnection networks are presented including new results as well as strengthening of existing results such as the one given by qiao and yang 2017 20

strong matching preclusion for torus networks the torus network is one of the most popular interconnection network topologies for massively parallel computing systems strong matching preclusion that additionally permits more destructive vertex faults in a graph is a more extensive form of the original matching preclusion that assumes only edge faults in this paper we establish the strong matching preclusion number and all minimum strong matching preclusion sets for bipartite torus networks and 2 dimensional nonbipartite torus networks

averaging procedures in adaptive filtering an efficient approach an averaging procedure for adaptive filtering is developed in contrast to the traditional approach two sequences x sub n and x sub n are constructed where x sub n is the arithmetic average of x sub n the authors show that the algorithm so designed has optimal rate of convergence therefore the averaging approach is asymptotically efficient

stochastic approximation with averaging and feedback rapidly convergent on line algorithms consider the stochastic approximation x sub n 1 x sub n a sub n g x sub n spl xi sub n where 0 0 the averaging method is essentially off line in the sense that the actual sa iterate x sub n is not influenced by the averaging in many applications x sub n itself is of greatest interest since that is the operating parameter this paper deals with the problem of stochastic approximation with averaging and with appropriate feedback of the averages into the original algorithm it is shown both mathematically and via simulation that it works very well and has numerous advantages it is a clear improvement over the system x sub n by itself it is fairly robust and quite often it is much preferable to the use of the above averages without feedback the authors deal in particular with linear algorithms of the type appearing in parameter estimators adaptive noise cancellers channel equalizers adaptive control and similar applications the main development is for the constant parameter case because of its importance in applications but analogous results hold for the case where a sub n spl rarr 0

conditional matching preclusion for hypercube like interconnection networks the conditional matching preclusion number of a graph with n vertices is the minimum number of edges whose deletion results in a graph without an isolated vertex that does not have a perfect matching if n is even or an almost perfect matching if n is odd we develop some general properties on conditional matching preclusion and then analyze the conditional matching preclusion numbers for some hl graphs hypercube like interconnection networks

edge fault tolerant edge bipancyclicity of balanced hypercubes abstract the balanced hypercube bh n is a variant of hypercube q n hao et al 2014 showed that there exists a fault free hamiltonian path between any two adjacent vertices in bh n with 2 n 2 faulty edges cheng et al 2015 proved that bh n is 6 edge bipancyclic after 2 n 3 faulty edges occur for all n 2 in this paper we improve these two results by demonstrating that bh n is 6 edge bipancyclic even when there exist 2 n 2 faulty edges for all n 2 our result is optimal with respect to the maximum number of tolerated edge faults

reliability analysis of twisted cubes connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model let g v e g v e be a connected graph a connected graph g is called supper resp super if every minimum vertex cut edge cut of g is the set of neighbors of some vertex in g let f v f v be a vertex set f is called extra cut if g f g f is not connected and each component of g f g f has more than k vertices the extraconnectivity k g k g is the cardinality of the minimum extra cuts a r component cut of g is a set s of vertices g s g s has at least r components r component connectivity c r g c r g of g is the size of the smallest r component cut the r component edge connectivity c r g c r g can be defined similarly in this paper we determine the r component edge connectivity of twisted cubes tn n t n n for small r and we also prove other properties of tn n t n n

hamiltonian paths passing through prescribed edges in balanced hypercubes abstract the balanced hypercube was proposed as a novel interconnection network for large scale parallel systems it is known that the balanced hypercube is edge bipancyclic given a set of edges p with p n 1 and two vertices x and y in different bipartite sets we show that there exists a hamiltonian path from x to y passing through p in b h n if and only if p is a linear forest and neither x nor y is an internal vertex of p and x and y are not end vertices of a component of p simultaneously consequently the balanced hypercube contains a hamiltonian cycle passing through a set p of at most n prescribed edges if and only if p is a linear forest moreover our result improves some known results

matching preclusion for balanced hypercubes matching preclusion is a measure of robustness in the event of edge failure in interconnection networks the matching preclusion number of a graph g is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching or an almost perfect matching and the conditional matching preclusion number of g is the minimum number of edges whose deletion leaves the resulting graph with no isolated vertices and without a perfect matching or an almost perfect matching in this paper we consider balanced hypercubes we obtain that an n dimension balanced hypercube bh n has the matching preclusion number 2n and mainly prove that for the balanced hypercube bh n each matching preclusion set of cardinality 2n is trivial and the conditional matching preclusion number of balanced hypercube is 4n 2 whenever n 2

strong matching preclusion the matching preclusion problem introduced by brigham et al r c brigham f harary e c violin and j yellen perfect matching preclusion congressus numerantium 174 2005 185 192 studies how to effectively make a graph have neither perfect matchings nor almost perfect matchings by deleting as small a number of edges as possible extending this concept we consider a more general matching preclusion problem called the strong matching preclusion in which deletion of vertices is additionally permitted we establish the strong matching preclusion number and all possible minimum strong matching preclusion sets for various classes of graphs

general multilevel adaptations for stochastic approximation algorithms of robbins monro and polyak ruppert type in this article we present and analyse new multilevel adaptations of classical stochastic approximation algorithms for the computation of a zero of a function f d rightarrow mathbb r d defined on a convex domain d subset mathbb r d which is given as a parameterised family of expectations the analysis of the error and the computational cost of our method is based on similar assumptions as used in giles oper res 56 3 607 617 2008 for the computation of a single expectation additionally we essentially only require that f satisfies a classical contraction property from stochastic approximation theory under these assumptions we establish error bounds in pth mean for our multilevel robbins monro and polyak ruppert schemes that decay in the computational time as fast as the classical error bounds for multilevel monte carlo approximations of single expectations known from giles oper res 56 3 607 617 2008 our approach is universal in the sense that having multilevel implementations for a particular application at hand it is straightforward to implement the corresponding stochastic approximation algorithm

averaged stochastic gradient algorithms for adaptive blind multiuser detection in ds cdma systems in this paper we present a blind adaptive gradient bag algorithm for code aided suppression of multiple access interference mai and narrow band interference nbi in direct sequence code division multiple access ds cdma systems this bag algorithm is based on the concept of accelerating the convergence of a stochastic gradient algorithm by averaging this ingenious concept of averaging was invented by polyak and juditsky 1992 this paper examines its application to blind multiuser detection and nbi suppression in ds cdma systems we prove that bag has identical convergence and tracking properties to recursive least squares lms but has a computational cost similar to the least mean squares lms algorithm i e an order of magnitude lower computational cost than rls simulations are used to compare our averaged gradient algorithm with the blind lms and lms schemes

linearly many faults in dual cube like networks the dual cubes were introduced as a better interconnection network than the hypercubes for large scale distributed memory multiprocessors in this paper we introduce a generalization of these networks called dual cube like networks which preserve the basic structure of dual cubes and retain many of its topological properties we investigate structural properties of these networks beyond simple measures such as connectivity we prove that if up to kn k k 1 2 vertices are deleted from a dual cube like n regular network then the resulting graph will either be connected or will have a large component and small components having at most k 1 vertices in total and this result is sharp for k n as an application we derive additional results such as the cyclic vertex connectivity and the restricted vertex connectivity of these networks

on the np completeness of the perfect matching free subgraph problem given a bipartite graph g u v e such that u v and every edge is labelled true or false or both the perfect matching free subgraph problem is to determine whether or not there exists a subgraph of g containing for each node u of u either all the edges labelled true or all the edges labelled false incident to u and which does not contain a perfect matching this problem arises in the structural analysis of differential algebraic systems the purpose of this paper is to show that this problem is np complete we show that the problem is equivalent to the stable set problem in a restricted case of tripartite graphs then we show that the latter remains np complete in that case we also prove the np completeness of the related minimum blocker problem in bipartite graphs with perfect matching

various cycles embedding in faulty balanced hypercubes consider the balanced hypercube bh n with f e 2 n 3 faulty edges prove that every edge of bh n f e lies on fault free cycles of even lengths from 6 to 22n prove that the lower limit of the length 6 is sharp quite a lot of interconnection networks are served as the underlying topologies of large scale multiprocessor systems the hypercube is one of the most popular interconnection networks in this paper we consider the balanced hypercube which is a variant of the hypercube huang and wu showed that the balanced hypercube has better properties than hypercube with the same number of links and processors let f e be the set of faulty edges in an n dimensional balanced hypercube bh n where n 2 in this paper we consider bh n with f e 2 n 3 faulty edges and prove that every fault free edge lies on a fault free cycle of every even length from 6 to 2 2 n in bh n f e furthermore we prove that the lower limit of the length 6 is sharp by giving a counter example

analysis of adaptive step size sa algorithms for parameter tracking we present proofs and data for adaptive step size algorithms for tracking time varying parameters when recursive stochastic approximation type algorithms are used a classical problem in adaptive control and communication theory concerns the tracking of the best fit of a given form when the statistics or the parameters change slowly a major and yet unresolved problem has been the choice of the step sizes in the tracking algorithm an algorithm for adapting the step size using the same system measurements which are used for the tracking was suggested by benveniste and various examples worked out by brossier the numerical results were very encouraging but proofs were lacking these proofs are supplied here together with supporting numerical data the proofs are based on recent results in stochastic approximation the adaptive step size technique works very well indeed much supporting analysis is presented particularly concerning the interpretation of certain stationary processes as stationary pathwise derivatives finite difference forms are also treated these are mathematically simpler and can be applied to a wide variety of systems even when the system is not well modeled the data shows that they work well

a note on generalized matching preclusion in bipartite graphs abstract for a graph with an even number of vertices the matching preclusion number is the minimum number of edges whose deletion results in a graph with no perfect matchings the conditional matching preclusion number introduced as an extension of the matching preclusion number has the additional requirement that the resulting graph have no isolated vertices in bipartite graphs the edge sets that achieve these minimum numbers can be construed in terms of obstruction sets of vertices from this perspective the generalized matching preclusion problem was developed the matching preclusion number of order a is the minimum number of edges whose deletion results in a graph with no perfect matchings and no obstruction sets with fewer than a vertices in this paper we extend known sufficient conditions regarding the matching preclusion and conditional matching preclusion numbers orders 1 and 2 respectively to give sufficient conditions for the matching preclusion problem of order a for any positive integer a

matching preclusion number of graphs abstract the matching preclusion number of a graph g denoted by mp g is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings in this paper we first give some sharp upper and lower bounds of matching preclusion number next graphs with large and small matching preclusion number are characterized respectively in the end we investigate some extremal problems and the nordhaus gaddum type relations on matching preclusion number

path embedding in faulty hypercubes abstract there are some interesting results concerning longest paths or even cycles embedding in faulty hypercubes this paper considers the embeddings of paths of all possible lengths between any two fault free vertices in faulty hypercubes let fv respectively fe denote the number of faulty vertices respectively edges in an n dimensional hypercube qn we prove that there exists a fault free path of length l between any two distinct fault free vertices u and v in qn with f v f e n 2 for each l satisfying d q n u v 2 l 2 n 2 f v 1 and 2 l d q n u v the bounds on path length l and faulty set size f v f e for a successful embedding are tight that is the result does not hold if l d q n u v 2 or l 2 n 2 f v 1 or f v f e n 2 moreover our result improves some known results

fault tolerance of locally twisted cubes abstract let g v e be a connected graph and p be graph theoretic property a network is often modeled by a graph g v e one fundamental consideration in the design of networks is reliability the connectivity is an important parameter to measure the fault tolerance and reliability of network the conditional connectivity g p or g p is the minimum cardinality of a set of edges or vertices if it exists whose deletion disconnects g and each remaining component has property p let f be a vertex set or edge set of g and p be the property of with at least k components then we have the k component connectivity c k g and the k component edge connectivity c k g in this paper we determine the k component edge connectivity of locally twisted cubes ltqn for small k and we also prove other properties of ltqn

acceleration of stochastic approximation by averaging a new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated convergence with probability one is proved for a variety of classical optimization and identification problems it is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence

matching preclusion and conditional matching preclusion problems for the folded petersen cube the matching preclusion number of an even graph is the minimum number of edges whose deletion results in a graph that has no perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex recently the conditional matching preclusion number of an even graph was introduced to look for obstruction sets beyond those induced by a single vertex it is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices and no perfect matchings in this paper we study this problem for the folded petersen cube fpq n k via some matching preclusion and conditional matching preclusion results of the cartesian products of graphs

budget dependent convergence rate of stochastic approximation convergence rate results are derived for a stochastic optimization problem where a performance measure is minimized with respect to a vector parameter t assuming that a gradient estimator is available and that both the bias and the variance of the estimator are known functions of the budget devoted to its computation the gradient estimator is employed in conjunction with a stochastic approximation sa algorithm our interest is to figure out how to allocate the total available computational budget to the successive sa iterations the effort is devoted to solving the asymptotic version of this problem by finding the convergence rate of sa toward the optimizer first as a function of the number of iterations and then as a function of the total computational effort as a result the optimal rate of increase of the computational budget per iteration can be found explicit expressions for the case where the computational budget devoted to an iteration is a polynomial in the iteration number and where the bias and variance of the gradient estimator are polynomials of the computational budget are derived applications include the optimization of steady state simulation models with likelihood ratio perturbation analysis or finite difference gradient estimators optimization of infinite horizon models with discounting optimization of functions of several expectations and so on several examples are discussed our results readily generalize to general root finding problems

fractional matching preclusion of product networks abstract the matching preclusion number of a graph introduced in 2 as a fault analysis is the minimum number of edges whose deletion leaves a resulting graph that has neither perfect matchings nor almost perfect matchings as a generalization liu and liu 14 recently introduced the concept of fractional matching preclusion number the fractional matching preclusion number of graph is the minimum number of edges whose deletion results in a graph that has no fractional perfect matching if the sets of edges of the graph attaining the minimum are precisely those incident to a single vertex of minimum degree we say such graph is fractional super matched in this paper the upper and lower bounds for the fractional matching preclusion number for cartesian product direct product strong product and lexicographic product are obtained and we give sufficient conditions for such graphs to be fractional super matched

stochastic optimization by simulation numerical experiments with the m m 1 queue in steady state this paper gives numerical illustrations of the behavior of stochastic approximation combined with different derivative estimation techniques to optimize a steady state system it is a companion paper to l ecuyer and glynn 1993 which gives convergence proofs for most of the variants experimented here the numerical experiments are made with a simple m m 1 queue which while simple serves to illustrate the basic convergence properties and possible pitfalls of the various techniques

edge fault tolerance of super edge connectivity for three families of interconnection networks let g v e be a connected graph g is said to be super edge connected or super l for short if every minimum edge cut of g isolates one of the vertex of g a graph g is called m super l if for any edge set s e g with s

fault tolerant path embedding in folded hypercubes with both node and edge faults the folded hypercube fq n is a well known variation of the hypercube structure fq n is superior to q n in many measurements such as diameter fault diameter connectivity and so on let email protected fq n resp email protected fq n denote the set of faulty nodes resp faulty edges in fq n in the case that all nodes in fq n are fault free it has been shown that fq n contains a fault free path of length 2 n 1 resp 2 n 2 between any two nodes of odd resp even distance if email protected fq n n 1 where n 1 is odd and fq n contains a fault free path of length 2 n 1 between any two nodes if email protected fq n n 2 where n 2 is even in this paper we extend the above result to obtain two further properties which consider both node and edge faults as follows 1 fq n contains a fault free path of length at least 2 n 2 email protected fq n 1 resp 2 n 2 email protected fq n 2 between any two fault free nodes of odd resp even distance if email protected fq n email protected fq n n 1 where n 1 is odd 2 fq n contains a fault free path of length at least 2 n 2 email protected fq n 1 between any two fault free nodes if email protected fq n email protected fq n n 2 where n 2 is even

conditional matching preclusion sets abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex in this paper we look for obstruction sets beyond these sets we introduce the conditional matching preclusion number of a graph it is the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost perfect matchings we find this number and classify all optimal sets for several basic classes of graphs

rates of convergence of adaptive step size of stochastic approximation algorithms we propose a new adaptive algorithm with decreasing step size for stochastic approximations the use of adaptive algorithms in various applications is widely spread across fields such as system identification and adaptive control we analyze the rate of convergence of the proposed algorithms an averaging algorithm on its optimality of the rate of convergence is used to control the step sizes our proofs are based on recent results in stochastic approximations and gaussian approximation theorem