on the complexity of finding chordless paths in bipartite graphs and some interval operators in graphs and hypergraphs in this paper we show that the problem of finding a chordless path between a vertex s and a vertex t containing a vertex v remains np complete in bipartite graphs thereby strengthening the previous results on the same problem we show a relation between this problem and two interval operators the simple path interval operator in hypergraphs and the even chorded path interval operator in graphs we show that the problem of computing the two mentioned intervals is np complete

mastrovito multiplier for general irreducible polynomials we present a new formulation of the mastrovito multiplication matrix for the field gf 2 sup m generated by an arbitrary irreducible polynomial we study in detail several specific types of irreducible polynomials e g trinomials all one polynomials and equally spaced polynomials and obtain the time and space complexity of these designs particular examples illustrating the properties of the proposed architecture are also given the complexity results established in this paper match the best complexity results known to date the most important new result is the space complexity of the mastrovito multiplier for an equally spaced polynomial which is found as m sup 2 spl delta xor gates and m sup 2 and gates where spl delta is the spacing factor

compact operators into the spaces of strongly c1 summable and bounded sequences abstract we establish the necessary and sufficient conditions for the entries of an infinite matrix to map any of the classical sequence spaces l p 1 p c 0 and c into the spaces w 0 w and w of all sequences that are strongly summable to zero strongly summable and strongly bounded by the cesaro method of order 1 we also give the representations of the general bounded linear operators from c into any of the spaces w 0 w and w and compute or estimate the hausdorff measure of noncompactness in each case finally we apply our results to characterise the compact linear operators between the spaces mentioned above and generalise two classical results by steinhaus 1911 5 maddox 1967 31 and cohen and dunford 1937 24

np hard graph problems and boundary classes of graphs any graph problem which is np hard in general graphs becomes polynomial time solvable when restricted to graphs in special classes when does a difficult problem become easy to answer this question we study the notion of boundary classes in the present paper we define this notion in its most general form describe several approaches to identify boundary classes and apply them to various graph problems

mastrovito form of non recursive karatsuba multiplier for all trinomials we present a new type of bit parallel non recursive karatsuba multiplier over gf 2 m generated by an arbitrary irreducible trinomial this design effectively exploits mastrovito approach and shifted polynomial basis spb to reduce the time complexity and karatsuba algorithm to reduce its space complexity we show that this type of multiplier is only one t x slower than the fastest bit parallel multiplier for all trinomials where t x is the delay of one 2 input xor gate meanwhile its space complexity is roughly 3 4 of those multipliers to the best of our knowledge it is the first time that our scheme has reached such a time delay bound this result outperforms previously proposed non recursive karatsuba multipliers

compactness by the hausdorff measure of noncompactness abstract in the present paper we establish some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain operators given by infinite matrices that map an arbitrary b k space into the sequence spaces c 0 c l and l 1 and into the matrix domains of triangles in these spaces furthermore by using the hausdorff measure of noncompactness we apply our results to characterize some classes of compact operators on the b k spaces

hybrid tractability of valued constraint problems the constraint satisfaction problem csp is a central generic problem in computer science and artificial intelligence it provides a common framework for many theoretical problems as well as for many real life applications valued constraint problems are a generalisation of the csp which allow the user to model optimisation problems considerable effort has been made in identifying properties which ensure tractability in such problems in this work we initiate the study of hybrid tractability of valued constraint problems that is properties which guarantee tractability of the given valued constraint problem but which do not depend only on the underlying structure of the instance such as being tree structured or only on the types of valued constraints in the instance such as submodularity we present several novel hybrid classes of valued constraint problems in which all unary constraints are allowed which include a machine scheduling problem constraint problems of arbitrary arities with no overlapping nogoods and the softalldiff constraint with arbitrary unary valued constraints an important tool in our investigation will be the notion of forbidden substructures

systematic design of original and modified mastrovito multipliers for general irreducible polynomials this paper considers the design of bit parallel dedicated finite field multipliers using standard basis an explicit algorithm is proposed for efficient construction of mastrovito product matrix based on which we present a systematic design of mastrovito multiplier applicable to gf 2 sup m generated by an arbitrary irreducible polynomial this design effectively exploits the spatial correlation of elements in mastrovito product matrix to reduce the complexity using a similar methodology we propose a systematic design of modified mastrovito multiplier which is suitable for gf 2 sup m generated by high hamming weight irreducible polynomials for both original and modified mastrovito multipliers the developed multiplier architectures are highly modular which is desirable for vlsi hardware implementation applying the proposed algorithm and design approach we study the mastrovito multipliers for several special irreducible polynomials such as trinomial and equally spaced polynomial and the obtained complexity results match the best known results moreover we have discovered several new special irreducible polynomials which also lead to low complexity mastrovito multipliers

a linear recognition algorithm for cographs cographs are the graphs formed from a single vertex under the closure of the operations of union and complement another characterization of cographs is that they are the undirected graphs with no induced paths on four vertices cographs arise naturally in such application areas as examination scheduling and automatic clustering of index terms furthermore it is known that cographs have a unique tree representation called a cotree using the cotree it is possible to design very fast polynomial time algorithms for problems which are intractable for graphs in general such problems include chromatic number clique determination clustering minimum weight domination isomorphism minimum fill in and hamiltonicity in this paper we present a linear time algorithm for recognizing cographs and constructing their cotree representation

the strong perfect graph theorem a graph g is perfect if for every induced subgraph h the chromatic number of h equals the size of the largest complete subgraph of h and g is berge if no induced subgraph of g is an odd cycle of length at least five or the complement of one the strong perfect graph conjecture berge 1961 asserts that a graph is perfect if and only if it is berge a stronger conjecture was made recently by conforti cornu ejols and vuiskovi c that every berge graph either falls into one of a few basic classes or admits one of a few kinds of separation designed so that a minimum counterexample to berge s conjecture cannot have either of these properties in this paper we prove both of these conjectures

characterizing and bounding the imperfection ratio for some classes of graphs perfect graphs constitute a well studied graph class with a rich structure which is reflected by many characterizations with respect to different concepts perfect graphs are for instance precisely those graphs g where the stable set polytope stab g equals the fractional stable set polytope qstab g the dilation ratio rm min t rm qstab g subseteq t rm stab g of the two polytopes yields the imperfection ratio of g it is np hard to compute and for most graph classes it is even unknown whether it is bounded for graphs g such that all facets of stab g are rank constraints associated with antiwebs we characterize the imperfection ratio and bound it by 3 2 outgoing from this result we characterize and bound the imperfection ratio for several graph classes including near bipartite graphs and their complements namely quasi line graphs by means of induced antiwebs and webs respectively

packing and covering with linear programming a survey this paper considers the polyhedral results and the min max results on packing and covering problems of the decade since the strong perfect graph theorem published in 2006 the main such results are available for the packing problem however there are still important polyhedral questions that remain open for the covering problem the main questions are still open although there has been important progress we survey some of the main results with emphasis on those where linear programming and graph theory come together they mainly concern the covering of cycles or dicycles in graphs or signed graphs either with vertices or edges this includes the multicut and integral multiflow problems

on the switch markov chain for perfect matchings we study a simple markov chain the switch chain on the set of all perfect matchings in a bipartite graph this markov chain was proposed by diaconis graham and holmes as a possible approach to a sampling problem arising in statistics we ask for which hereditary classes of graphs is the markov chain ergodic and for which is it rapidly mixing we provide a precise answer to the ergodicity question and close bounds on the mixing question we show for the first time that the mixing time of the switch chain is polynomial in the case of monotone graphs a class that includes examples of interest in the statistical setting

list matrix partitions of chordal graphs it is well known that a clique with k 1 vertices is the only minimal obstruction to k colourability of chordal graphs a similar result is known for the existence of a cover by l cliques both of these problems are in fact partition problems restricted to chordal graphs the first seeks partitions into k independent sets and the second is equivalent to finding partitions into l cliques in an earlier paper we proved that a chordal graph can be partitioned into k independent sets and l cliques if and only if it does not contain an induced disjoint union of l 1 cliques of size k 1 a linear time algorithm for finding such partitions can be derived from the proof in this paper we expand our focus and consider more general partitions of chordal graphs for each symmetric matrix m over 0 1 the m partition problem seeks a partition of the input graph into independent sets cliques or arbitrary sets with certain pairs of sets being required to have no edges or to have all edges joining them as encoded in the matrix m moreover the vertices of the input chordal graph can be equipped with lists restricting the parts to which a vertex can be placed such list partitions generalize list colourings and list homomorphisms and arise frequently in the theory of graph perfection we show that many m partition problems that are np complete in general become solvable in polynomial time for chordal graphs even in the presence of lists on the other hand we show that there are m partition problems without lists that remain np complete for chordal graphs it is not known whether or not each list m partition problem is np complete or polynomial but it has been shown that each is np complete or quasi polynomial no log n for chordal graphs even this quasi dichotomy is not known but we do identify large families of matrices m for which dichotomy or at least quasi dichotomy holds we also discuss forbidden subgraph characterizations of graphs admitting an m partition such characterizations have recently been investigated for partitions of perfect graphs and we focus on highlighting the improvements one can obtain for the class of chordal rather than just perfect graphs

montgomery multiplier and squarer for a class of finite fields montgomery multiplication in gf 2 sup m is defined by a x b x r sup 1 x mod f x where the field is generated by a root of the irreducible polynomial f x a x and b x are two field elements in gf 2 sup m and r x is a fixed field element in gf 2 sup m in this paper first a slightly generalized montgomery multiplication algorithm in gf 2 sup m is presented then by choosing r x according to f x we show that efficient architectures of bit parallel montgomery multiplier and squarer can be obtained for the fields generated with an irreducible trinomial complexities of the montgomery multiplier and squarer in terms of gate counts and time delay of the circuits are investigated and found to be as good as or better than that of previous proposals for the same class of fields

bit serial and bit parallel montgomery multiplication and squaring over gf 2 m multiplication and squaring are main finite field operations in cryptographic computations and designing efficient multipliers and squarers affect the performance of cryptosystems in this paper we consider the montgomery multiplication in the binary extension fields and study different structures of bit serial and bit parallel multipliers for each of these structures we study the role of the montgomery factor and then by using appropriate factors propose new architectures specifically we propose two bit serial multipliers for general irreducible polynomials and then derive bit parallel montgomery multipliers for two important classes of irreducible polynomials in this regard first we consider trinomials and provide a way for finding efficient montgomery factors which results in a low time complexity then we consider type ii irreducible pentanomials and design two bit parallel multipliers which are comparable to the best finite field multipliers reported in the literature moreover we consider squaring using this family of irreducible polynomials and show that this operation can be performed very fast with the time complexity of two xor gates

parameterized complexity of vertex deletion into perfect graph classes vertex deletion problems are at the heart of parameterized complexity for a graph class f the f deletion problem takes as input a graph g and an integer k the question is whether it is possible to delete at most k vertices from g such that the resulting graph belongs to f whether perfect deletion is fixed parameter tractable and whether chordal deletion admits a polynomial kernel when parameterized by k have been stated as open questions in previous work we show that perfect deletion and weakly chordal deletion are w 2 hard when parameterized by k in search of positive results we study a restricted variant of the f deletion problem in this restricted variant the deleted vertices must be taken from a specified set x and we parameterize by x we show that for perfect deletion and weakly chordal deletion although this restriction immediately ensures fixed parameter tractability it is not enough to yield polynomial kernels unless np conp poly on the positive side for chordal deletion the restriction enables us to obtain a kernel with o x 4 vertices

low complexity bit parallel multiplier for gf 2 sup m defined by all one polynomials using redundant representation this paper presents a new bit parallel multiplier for the finite field gf 2 sup m defined by an irreducible all one polynomial in order to reduce the complexity of the multiplier we introduce a redundant representation and use the well known multiplication method proposed by karatsuba the main idea is to combine the redundant representation and the karatsuba method to design an efficient bit parallel multiplier as a result the proposed multiplier requires about 25 percent fewer and xor gates than the previously proposed multipliers using an all one polynomial while it has almost the same time delay as the previously proposed ones

progress on perfect graphs a graph is perfect if for every induced subgraph the chromatic number is equal to the maximum size of a complete subgraph the class of perfect graphs is important for several reasons for instance many problems of interest in practice but intractable in general can be solved efficiently when restricted to the class of perfect graphs also the question of when a certain class of linear programs always have an integer solution can be answered in terms of perfection of an associated graph

perfectness is an elusive graph property a graph property is called elusive or evasive if every algorithm for testing this property has to read in the worst case n choose 2 entries of the adjacency matrix of the given graph several graph properties have been shown to be elusive e g planarity or k colorability a famous conjecture of karp says that every nontrivial monotone graph property is elusive we prove that a nonmonotone but hereditary graph property is elusive perfectness

a chinese remainder theorem approach to bit parallel gf 2 n polynomial basis multipliers for irreducible trinomials we show that the step modulo the degree n field generating irreducible polynomial in the classical definition of the gf 2 n multiplication operation can be avoided this leads to an alternative representation of the finite field multiplication operation combining this representation and the chinese remainder theorem we design bit parallel gf 2 n multipliers for irreducible trinomials u n u k 1 on gf 2 where 1 for some values of n our architectures have the same time complexity as the fastest bit parallel multipliers the quadratic multipliers but their space complexities are reduced take the special irreducible trinomial u 2k u k 1 for example the space complexity of the proposed design is reduced by about 1 8 while the time complexity matches the best result our experimental results show that among the 539 values of n such that 4 and x n x k 1 is irreducible over gf 2 for some k in the range 1 the proposed multipliers beat the current fastest parallel multipliers for 290 values of n when n 1 3 le k le n 2 they have the same time complexity but the space complexities are reduced by 8 4 percent on average

regular inference as vertex coloring abstract this paper is concerned with the problem of supervised learning of deterministic finite state automata in the technical sense of identification in the limit from complete data by finding a minimal dfa consistent with a sample we solve this problem by translating it in its entirety to a vertex coloring problem essentially such a problem consists of two types of constraints that restrict the hypothesis space inequivalence and equivalence constraints the inequivalence constraints translate to the vertex coloring problem in a very natural way the equivalence constraints however greatly complicate the translation to vertex coloring in previous coloring based translations these were therefore encoded either dynamically by modifying the vertex coloring instance on the fly or by encoding them as satisfiability problems we provide the first translation that encodes both types of constraints together in a pure vertex coloring instance and prove the correctness of the construction the coloring approach offers many opportunities for applying insights from combinatorial optimization and graph theory to regular inference we immediately obtain new complexity bounds as well as a family of new learning algorithms which can be used to obtain exact hypotheses as well as fast approximations we also demonstrate that satisfying all inequivalence constraints in regular inference and vertex coloring are in some sense equally hard this immediately implies that regular inference is not approximable within s 1 s being the cardinality of the sample for any 1 2 unless p np it also indicates that solving only for inequivalence constraints is easier than the full regular inference problem

parallel multipliers based on special irreducible pentanomials the state of the art galois field gf 2 sup m multipliers offer advantageous space and time complexities when the field is generated by so special irreducible polynomial to date the best complexity results have been obtained when the irreducible polynomial is either a trinomial or an equally spaced polynomial esp unfortunately there exist only a few irreducible esps in the range of interest for most of the applications e g error correcting codes computer algebra and elliptic curve cryptography furthermore it is not always possible to find an irreducible trinomial of degree m in this range for those cases where neither an irreducible trinomial nor an irreducible esp exists the use of irreducible pentanomials has been suggested irreducible pentanomials are abundant and there are several eligible candidates for a given m we promote the use of two special types of irreducible pentanomials we propose new mastrovito and dual basis multiplier architectures based on these special irreducible pentanomials and give rigorous analyses of their space and time complexity

mastrovito multiplier for all trinomials an efficient algorithm for the multiplication in gf 2 sup m was introduced by mastrovito the space complexity of the mastrovito multiplier for the irreducible trinomial x sup m x 1 was given as m sup 2 1 xor and m sup 2 and gales in this paper we describe an architecture based on a new formulation of the multiplication matrix and show that the mastrovito multiplier for the generating trinomial x sup m x sup n 1 where m spl ne 2n also requires m sup 2 1 xor and m sup 2 and gates however m sup 2 x sup m 2 xor gates are sufficient when the generating trinomial is of the form x sup m x sup m 2 1 for an even m we also calculate the time complexity of the proposed mastrovito multiplier and give design examples for the irreducible trinomials x sup 7 x sup 4 1 and x sup 6 x sup 3 1

cycle transversals in perfect graphs and cographs a cycle transversal or feedback vertex set of a graph g is a subset t v g such that t v c 0 for every cycle c of g this work considers the problem of finding special cycle transversals in perfect graphs and cographs we prove that finding a minimum cycle transversal t in a perfect graph g is np hard even for bipartite graphs with maximum degree four since g t is acyclic this result implies that finding a maximum acyclic induced subgraph of a perfect graph is also np hard other special properties of t are considered a clique stable respectively cycle transversal or simply cct sct respectively is a cycle transversal which is a clique stable set respectively recognizing graphs which admit a cct can be done in polynomial time however no structural characterization of such graphs is known even for perfect graphs we characterize cographs with cct in terms of forbidden induced subgraphs and describe their structure this leads to linear time recognition of cographs with cct we also prove that deciding whether a perfect graph admits an sct is np complete we characterize cographs with sct in terms of forbidden induced subgraphs this characterization also leads to linear time recognition

fast bit parallel gf 2 sup n multiplier for all trinomials based on a new representation of gf 2 sup n we present two multipliers for all irreducible trinomials space complexities of the multipliers match the best results the time complexity of one multiplier is t sub a 1 log sub 2 n t sub x for all irreducible trinomials where t sub a and t sub x are the delay of one 2 input and and xor gates respectively

applications of measure of noncompactness in operators on the spaces sα s0α s c α lpα abstract in this paper we characterize some operators and matrix transformations in the sequence spaces s s 0 s c l p moreover using the hausdorff measure of noncompactness necessary and sufficient conditions are formulated for a linear operator between the mentioned spaces to be compact among other things some results of cohen and dunford are recovered

reconfiguration of colorable sets in classes of perfect graphs abstract a set of vertices in a graph is c colorable if the subgraph induced by the set has a proper c coloring in this paper we study the problem of finding a step by step transformation called a reconfiguration sequence between two c colorable sets in the same graph this problem generalizes the well studied independent set reconfiguration problem as the first step toward a systematic understanding of the complexity of this general problem we study the problem on classes of perfect graphs we first focus on interval graphs and give a combinatorial characterization of the distance between two c colorable sets this gives a linear time algorithm for finding an actual shortest reconfiguration sequence for interval graphs since interval graphs are exactly the graphs that are simultaneously chordal and co comparability we then complement the positive result by showing that even deciding reachability is pspace complete for chordal graphs and for co comparability graphs the hardness for chordal graphs holds even for split graphs we also consider the case where c is a fixed constant and show that in such a case the reachability problem is polynomial time solvable for split graphs but still pspace complete for co comparability graphs the complexity of this case for chordal graphs remains unsettled as by products our positive results give the first polynomial time solvable cases split graphs and interval graphs for feedback vertex set reconfiguration

a novel architecture for galois fields gf 2 m multipliers based on mastrovito scheme in this paper a new gf 2m multiplier for standard basis representation is developed the proposed multiplier implements the mastrovito multiplication scheme and can be designed for every field gf 2m a minimum area implementation of the first block of mastrovito multiplier and a high speed delay driven tree architecture for the second block of the mastrovito multiplier are employed in the new circuit multiplier complexity and delay are analytically evaluated for many polynomial classes timing and area occupation performances of the proposed multiplier are also calculated for many fields used in reed solomon codes applications and compared with those of previously proposed solutions the comparison shows that the proposed multiplier outperforms previous architectures for every considered gf 2m field the effectiveness of the proposed solution in a real application is verified by implementing in a 0 25 mum cmos technology the key equation solving block of a 255 239 reed solomon decoder the use of the proposed multiplier in this application results in a substantial speed improvement without any penalty in the silicon area occupation

matrix transformations and compact operators on some new mth order difference sequences abstract we define some new sets of sequences the m th order differences of which are bounded convergent and convergent to zero and apply the general methods in e malkowsky v rakocevic on matrix domains of triangles appl math comput 189 2 2007 1146 1163 to give schauder bases for the latter two determine their duals and characterize matrix transformations on them our results generalize those in b de malafosse the banach algebra s and applications acta sci math szeged 70 1 2 2004 125 145 and improve those in e malkowsky s d parashar matrix transformations in spaces of bounded and convergent difference sequences of order m analysis 17 1997 87 97 we also establish identities and estimates for the hausdorff measure of non compactness of matrix operators from our spaces into the spaces of bounded convergent and null sequences and characterize the respective classes of compact operators some of these results generalize those in e malkowsky v rakocevic the measure of non compactness of linear operators between spaces of m th order difference sequences stud sci math hungar 33 1999 381 391

fixed parameter algorithms for cochromatic number and disjoint rectangle stabbing via iterative localization given a permutation p of 1 n and a positive integer k can p be partitioned into at most k subsequences each of which is either increasing or decreasing we give an algorithm with running time 2 o k 2 l o g k n o 1 that solves this problem thereby showing that it is fixed parameter tractable this np complete problem is equivalent to deciding whether the cochromatic number of a given permutation graph on n vertices is at most k our algorithm solves in fact a more general problem within the mentioned running time it decides whether the cochromatic number of a given perfect graph on n vertices is at most k to obtain our result we use a combination of two well known techniques within parameterized algorithms iterative compression and greedy localization consequently we name this combination iterative localization we further demonstrate the power of this combination by giving an algorithm with running time 2 o k 2 l o g k nlogn that decides whether a given set of n non overlapping axis parallel rectangles can be stabbed by at most k of a given set of horizontal and vertical lines

hausdorff measure of noncompactness of certain matrix operators on the sequence spaces of generalized means abstract in the present paper we derive some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain matrix operators on the sequence spaces of generalized means further by applying the hausdorff measure of noncompactness we obtain the necessary and sufficient conditions for such operators to be compact

measure of noncompactness of matrix operators on some difference sequence spaces of weighted means for a sequence x x k we denote the difference sequence by dx x k x k 1 let u u k k 0 and v v k k 0 be the sequences of real numbers such that u k 0 v k 0 for all email protected n the difference sequence spaces of weighted means l u v d are defined as l u v d x x k w x email protected where l c c 0 and and the matrix w w n k is defined by w n k u n v k v k 1 kn in this paper we establish some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain matrix operators on l u v d further we characterize some classes of compact operators on these spaces by using the hausdorff measure of noncompactness

lovasz schrijver sdp operator near perfect graphs and near bipartite graphs we study the lovasz schrijver lift and project operator mathrm text ls ls based on the cone of symmetric positive semidefinite matrices applied to the fractional stable set polytope of graphs the problem of obtaining a combinatorial characterization of graphs for which the mathrm text ls ls operator generates the stable set polytope in one step has been open since 1990 we call these graphs mathrm text ls ls perfect in the current contribution we pursue a full combinatorial characterization of mathrm text ls ls perfect graphs and make progress towards such a characterization by establishing a new close relationship among mathrm text ls ls perfect graphs near bipartite graphs and a newly introduced concept of full support perfect graphs

applications of measures of noncompactness to the infinite system of differential equations in lp spaces abstract in this paper we apply the technique of measures of noncompactness to the theory of infinite system of differential equations in the banach sequence spaces l p 1 p our aim is to present some existence results for infinite system of differential equations formulated with the help of measures of noncompactness

banach algebras of matrix transformations between some sequence spaces related to λ strong convergence and boundedness we study the spaces c 0 l c l and c l of sequences that are l strongly convergent to zero l strongly convergent and l strongly bounded and the related spaces v 0 l and v l in particular we give the characterizations of several classes of matrix transformations between those spaces furthermore we use our results to prove that the classes of matrix transformations from v l c l and c l into themselves are banach algebras as an application of our results we establish an estimate for the hausdorff measure of noncompactness of matrix operators that map c l into itself give a characterization of the subclass of compact operators and a sufficient condition for those operators to be fredholm

kernels for below upper bound parameterizations of the hitting set and directed dominating set problems in the hitting set problem we are given a collection f of subsets of a ground set v and an integer p and asked whether v has a p element subset that intersects each set in f we consider two parameterizations of hitting set below tight upper bounds p m k and p n k in both cases k is the parameter we prove that the first parameterization is fixed parameter tractable but has no polynomial kernel unless conp np poly the second parameterization is w 1 complete but the introduction of an additional parameter the degeneracy of the hypergraph h v f makes the problem not only fixed parameter tractable but also one with a linear kernel here the degeneracy of h v f is the minimum integer d such that for each x v the hypergraph with vertex set v x and edge set containing all edges of f without vertices in x has a vertex of degree at most d in nonblocker directed nonblocker we are given an undirected graph a directed graph g on n vertices and an integer k and asked whether g has a set x of n k vertices such that for each vertex y x there is an edge arc from a vertex in x to y nonblocker can be viewed as a special case of directed nonblocker replace an undirected graph by a symmetric digraph dehne et al proc sofsem 2006 proved that nonblocker has a linear order kernel we obtain a linear order kernel for directed nonblocker

contraction and deletion blockers for perfect graphs and h free graphs abstract we study the following problem for given integers d k and graph g can we reduce some fixed graph parameter of g by at least d via at most k graph operations from some fixed set s as parameters we take the chromatic number clique number and independence number and as operations we choose edge contraction ec and vertex deletion vd we determine the complexity of this problem for s ec and s vd and for a number of subclasses of perfect graphs we use these results to determine the complexity of the problem for s ec and s vd and restricted to h free graphs

on matrix domains of triangles we prove some general results for the determination of the duals of and the characterisations of matrix transformations on matrix domains of arbitrary triangles in fk spaces our results contain almost all recently published ones as special cases we also study the measure of noncompactness of several matrix transformations in particular we obtain some known results of sember give the corrected version of a recent result by djolovic and study compact operators on some spaces of altay basar and mursaleen

colorings of hypergraphs perfect graphs and associated primes of powers of monomial ideals abstract there is a natural one to one correspondence between squarefree monomial ideals and finite simple hypergraphs via the cover ideal construction let h be a finite simple hypergraph and let j j h be its cover ideal in a polynomial ring r we give an explicit description of all associated primes of r j s for any power j s of j in terms of the coloring properties of hypergraphs arising from h we also give an algebraic method for determining the chromatic number of h proving that it is equivalent to a monomial ideal membership problem involving powers of j our work yields two new purely algebraic characterizations of perfect graphs independent of the strong perfect graph theorem the first characterization is in terms of the sets ass r j s while the second characterization is in terms of the saturated chain condition for associated primes

permanents pfaffian orientations and even directed circuits given a 0 1 square matrix a when can some of the 1 s be changed toi1 s in such a way that the permanent of a equals the determinant of the modifled matrix when does a real square matrix have the property that every real matrix with the same sign pattern that is the corresponding entries either have the same sign or are both zero is nonsingular when is a hypergraph with n vertices and n hyperedges minimally nonbipartite when does a bipartite graph have a pfa an orientation given a digraph does it have no directed circuit of even length given a digraph does it have a subdivision with no even directed circuit it is known that all of the above problems are equivalent we prove a structural characterization of the feasible instances which implies a polynomial time algorithm to solve all of the above problems the structural characterization says roughly speaking that a bipartite graph has a pfa an orientation if and only if it can be obtained by piecing together in a specifled way planar bipartite graphs and one sporadic nonplanar bipartite graph

bit parallel finite field multiplier and squarer using polynomial basis bit parallel finite field multiplication using polynomial basis can be realized in two steps polynomial multiplication and reduction modulo the irreducible polynomial in this article we present an upper complexity bound for the modular polynomial reduction when the field is generated with an irreducible trinomial closed form expressions for the coefficients of the product are derived in term of the coefficients of the multiplicands the complexity of the multiplier architectures and their critical path length are evaluated and they are comparable to the previous proposals for the same class of fields an analytical form for bit parallel squaring operation is also presented the complexities for bit parallel squarer are also derived when an irreducible trinomial is used consequently it is argued that to solve multiplicative inverse using polynomial basis can be at least as good as using a normal basis