minimum fill in inapproximability and almost tight lower bounds abstract given an n n sparse symmetric matrix with m nonzero entries performing gaussian elimination may turn some zeroes into nonzero values so called fill ins the minimum fill in problem asks whether it is possible to perform the elimination with at most k fill ins we exclude the existence of polynomial time approximation schemes for this problem assuming p np and the existence of 2 o n 1 time approximation schemes for any positive assuming the exponential time hypothesis we also give a 2 o k 1 2 n o 1 parameterized lower bound all these results come as corollaries of a new reduction from vertex cover to the minimum fill in problem which might be of its own interest all previous reductions for similar problems start from some kind of graph layout problems and hence have limited use in understanding their fine grained complexity

block recombination approach for subquadratic space complexity binary field multiplication based on toeplitz matrix vector product in this paper we present a new method for parallel binary finite field multiplication which results in subquadratic space complexity the method is based on decomposing the building blocks of the fan hasan subquadratic toeplitz matrix vector multiplier we reduce the space complexity of their architecture by recombining the building blocks in comparison to other similar schemes available in the literature our proposal presents a better space complexity while having the same time complexity we also show that block recombination can be used for efficient implementation of the ghash function of galois counter mode gcm

multiway splitting method for toeplitz matrix vector product computing the product of a toeplitz matrix and a vector arises in various applications including cryptography in this paper we consider toeplitz matrices and vectors with entries in hbox rlap i kern 2 0pt hbox f 2 for improved efficiency in such computations large toeplitz matrices and vectors are recursively split and special formulas with subquadratic arithmetic complexity are applied to this end we first present a formula for the five way splitting and then provide a generalization for the k way splitting where k is an arbitrary integer these formulas can be used to compute a toeplitz matrix vector product tmvp of size n with an arithmetic complexity of o n log k k k 1 2

parameterized and approximation complexity of partial vc dimension abstract we introduce the problem partial vc dimension that asks given a hypergraph h x e and integers k and l whether one can select a set c x of k vertices of h such that the set e c e e of distinct hyperedge intersections with c has size at least l the sets e c define equivalence classes over e partial vc dimension is a generalization of vc dimension which corresponds to the case l 2 k and of distinguishing transversal which corresponds to the case l e the latter is also known as test cover in the dual hypergraph we also introduce the associated fixed cardinality maximization problem max partial vc dimension that aims at maximizing the number of equivalence classes induced by a solution set of k vertices we study the algorithmic complexity of partial vc dimension and max partial vc dimension both on general hypergraphs and on more restricted instances in particular neighborhood hypergraphs of graphs

mixing and non mixing local minima of the entropy contrast for blind source separation in this paper both non mixing and mixing local minima of the entropy are analyzed from the viewpoint of blind source separation bss they correspond respectively to acceptable and spurious solutions of the bss problem the contribution of this work is twofold first a taylor development is used to show that the exact output entropy cost function has a non mixing minimum when this output is proportional to any of the non gaussian sources and not only when the output is proportional to the lowest entropic source second in order to prove that mixing entropy minima exist when the source densities are strongly multimodal an entropy approximator is proposed the latter has the major advantage that an error bound can be provided even if this approximator and the associated bound is used here in the bss context it can be applied for estimating the entropy of any random variable with multimodal density

excluded grid minors and efficient polynomial time approximation schemes two of the most widely used approaches to obtain polynomial time approximation schemes ptass on planar graphs are the lipton tarjan separator based approach and baker s approach in 2005 demaine and hajiaghayi strengthened both approaches using bidimensionality and obtained efficient polynomial time approximation schemes eptass for several problems including c onnected d ominating s et and f eedback v ertex s et in this work we unify the two strengthened approaches to combine the best of both worlds we develop a framework allowing the design of eptas on classes of graphs with the subquadratic grid minor sqgm property roughly speaking a class of graphs has the sqgm property if for every graph g from the class the fact that g contains no t t grid as a minor guarantees that the treewidth of g is subquadratic in t for example the class of planar graphs and more generally classes of graphs excluding some fixed graph as a minor have the sqgm property at the heart of our framework is a decomposition lemma stating that for most bidimensional problems on a graph class g with the sqgm property there is a polynomial time algorithm that given a graph g e g as input and an e 0 outputs a vertex set x of size e opt such that the treewidth of g x is f e here opt is the objective function value of the problem in question and f is a function depending only on e this allows us to obtain eptass on apex minor free graphs for all problems covered by the previous framework as well as for a wide range of packing problems partial covering problems and problems that are neither closed under taking minors nor contractions to the best of our knowledge for many of these problems including c ycle p acking f p acking f d eletion m ax l eaf s panning t ree or p artial r d ominating s et no eptass even on planar graphs were previously known we also prove novel excluded grid theorems in unit disk and map graphs without large cliques using these theorems we show that these classes of graphs have the sqgm property based on the developed framework we design eptass and subexponential time parameterized algorithms for various classes of problems on unit disk and map graphs

blind source separation by nonstationarity of variance a cumulant based approach blind separation of source signals usually relies either on the nongaussianity of the signals or on their linear autocorrelations a third approach was introduced by matsuoka et al 1995 who showed that source separation can be performed by using the nonstationarity of the signals in particular the nonstationarity of their variances in this paper we show how to interpret the nonstationarity due to a smoothly changing variance in terms of higher order cross cumulants this is based on the time correlation of the squares energies of the signals and leads to a simple optimization criterion using this criterion we construct a fixed point algorithm that is computationally very efficient

exact analysis of dodgson elections lewis carroll s 1876 voting system is complete for parallel access to np in 1876 lewis carroll proposed a voting system in which the winner is the candidate who with the fewest changes in voters preferences becomes a condorcet winner a candidate who beats all other candidates in pairwise majority rule elections bartholdi tovey and trick provided a lower bound np hardness on the computational complexity of determining the election winner in carroll s system we provide a stronger lower bound and an upper bound that matches our lower bound in particular determining the winner in carroll s system is complete for parallel access to np that is it is complete for theta 2 p for which it becomes the most natural complete problem known it follows that determining the winner in carroll s elections is not np complete unless the polynomial hierarchy collapses

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

inapproximability of maximal strip recovery in comparative genomics the first step of sequence analysis is usually to decompose two or more genomes into syntenic blocks that are segments of homologous chromosomes for the reliable recovery of syntenic blocks noise and ambiguities in the genomic maps need to be removed first maximal strip recovery msr is an optimization problem proposed by zheng zhu and sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities given d genomic maps as sequences of gene markers the objective of msr d is to find d subsequences one subsequence of each genomic map such that the total length of syntenic blocks in these subsequences is maximized for any constant d 2 a polynomial time 2d approximation for msr d was previously known in this paper we show that for any d 2 msr d is apx hard even for the most basic version of the problem in which all gene markers are distinct and appear in positive orientation in each genomic map moreover we provide the first explicit lower bounds on approximating msr d for all d 2 in particular we show that msr d is np hard to approximate within w d logd from the other direction we show that the previous 2d approximation for msr d can be optimized into a polynomial time algorithm even if d is not a constant but is part of the input we then extend our inapproximability results to several related problems including cmsr d d gap msr d and d gap cmsr d

on the complexity of the vector connectivity problem we study a relaxation of the vector domination problem called vector connectivity veccon given a graph g with a requirement r v for each vertex v veccon asks for a minimum cardinality set s of vertices such that every vertex v v s is connected to s via r v disjoint paths in the paper introducing the problem boros et al 4 gave polynomial time solutions for veccon in trees cographs and split graphs and showed that the problem can be approximated in polynomial time on n vertex graphs to within a factor of log n 2 leaving open the question of whether the problem is np hard on general graphs we show that veccon is apx hard in general graphs and np hard in planar bipartite graphs and in planar line graphs we also generalize the polynomial result for trees by solving the problem for block graphs

specializations and generalizations of the stackelberg minimum spanning tree game let be given a graph g v e whose edge set is partitioned into a set r of red edges and a set b of blue edges and assume that red edges are weighted and form a spanning tree of g then the stackelberg minimum spanning tree stackmst problem is that of pricing i e weighting the blue edges in such a way that the total weight of the blue edges selected in a minimum spanning tree of the resulting graph is maximized stackmst is known to be apx hard already when the number of distinct red edge weights is 2 in this paper we analyze some meaningful specializations and generalizations of stackmst which shed some more light on the computational complexity of the problem more precisely we first show that if g is restricted to be complete then the following holds i if there are only 2 distinct red edge weights then the problem can be solved optimally this contrasts with the corresponding apx hardness of the general problem ii otherwise the problem can be approximated within 7 4 for any 0 afterwards we define a natural extension of stackmst namely that in which blue edges are associated with a non negative activation cost and it is given a global activation budget that can be used and must not be exceeded in order to activate a subset of blue edges to be priced here after showing that the very same approximation ratio as that of the original problem can be achieved we prove that if the spanning tree of red edges can be rooted so as that any root leaf path contains at most h edges then the problem admits a 2 h approximation algorithm for any 0

on solving linear programs with the ordered weighted averaging objective abstract the problem of aggregating multiple criteria to form overall objective functions is of considerable importance in many disciplines the most commonly used aggregation is based on the weighted sum the ordered weighted averaging owa aggregation introduced by yager uses the weights assigned to the ordered values i e to the worst value the second worst and so on rather than to the specific criteria this allows to model various aggregation preferences preserving simultaneously the impartiality neutrality with respect to the individual criteria in this paper we analyze solution procedures for linear programs with the owa objective functions two alternative linear programming formulations are introduced and their computational efficiency is analyzed

nonorthogonal joint diagonalization by combining givens and hyperbolic rotations a new algorithm for computing the nonorthogonal joint diagonalization of a set of matrices is proposed for independent component analysis and blind source separation applications this algorithm is an extension of the jacobi like algorithm first proposed in the joint approximate diagonalization of eigenmatrices jade method for orthogonal joint diagonalization the improvement consists mainly in computing a mixing matrix of determinant one and columns of equal norm instead of an orthogonal mixing matrix this target matrix is constructed iteratively by successive multiplications of not only givens rotations but also hyperbolic rotations and diagonal matrices the algorithm performance evaluated on synthetic data compares favorably with existing methods in terms of speed of convergence and complexity

hard constraint satisfaction problems have hard gaps at location 1 an instance of the maximum constraint satisfaction problem max csp is a finite collection of constraints on a set of variables and the goal is to assign values to the variables that maximises the number of satisfied constraints max csp captures many well known problems such as maxk sat and max cut and is consequently np hard thus it is natural to study how restrictions on the allowed constraint types or constraint language affect the complexity and approximability of max csp the pcp theorem is equivalent to the existence of a constraint language for which max csp has a hard gap at location 1 i e it is np hard to distinguish between satisfiable instances and instances where at most some constant fraction of the constraints are satisfiable all constraint languages for which the csp problem i e the problem of deciding whether all constraints can be satisfied is currently known to be np hard have a certain algebraic property we prove that any constraint language with this algebraic property makes max csp have a hard gap at location 1 which in particular implies that such problems cannot have a ptas unless p np we then apply this result to max csp restricted to a single constraint type this class of problems contains for instance max cut and max dicut assuming p np we show that such problems do not admit ptas except in some trivial cases our results hold even if the number of occurrences of each variable is bounded by a constant finally we give some applications of our results

fast kernel based independent component analysis recent approaches to independent component analysis ica have used kernel independence measures to obtain highly accurate solutions particularly where classical methods experience difficulty for instance sources with near zero kurtosis fastkica fast hsic based kernel ica is a new optimization method for one such kernel independence measure the hilbert schmidt independence criterion hsic the high computational efficiency of this approach is achieved by combining geometric optimization techniques specifically an approximate newton like method on the orthogonal group with accurate estimates of the gradient and hessian based on an incomplete cholesky decomposition in contrast to other efficient kernel based ica algorithms fastkica is applicable to any twice differentiable kernel function experimental results for problems with large numbers of sources and observations indicate that fastkica provides more accurate solutions at a given cost than gradient descent on hsic comparing with other recently published ica methods fastkica is competitive in terms of accuracy relatively insensitive to local minima when initialized far from independence and more robust towards outliers an analysis of the local convergence properties of fastkica is provided

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

on the approximability of single machine scheduling with precedence constraints we consider the single machine scheduling problem to minimize the weighted sum of completion times under precedence constraints in a series of recent papers it was established that this scheduling problem is a special case of minimum weighted vertex cover in this paper we show that the vertex cover graph associated with the scheduling problem is exactly the graph of incomparable pairs defined in the dimension theory of partial orders exploiting this relationship allows us to present a framework for obtaining 2 2 f approximation algorithms provided that the set of precedence constraints has fractional dimension of at most f our approach yields the best known approximation ratios for all previously considered special classes of precedence constraints and it provides the first results for bounded degree and orders of interval dimension 2 on the negative side we show that the addressed problem remains np hard even when restricted to the special case of interval orders furthermore we prove that the general problem if a fixed cost present in all feasible schedules is ignored becomes as hard to approximate as vertex cover we conclude by giving the first inapproximability result for this problem showing under a widely believed assumption that it does not admit a polynomial time approximation scheme

np completeness and apx completeness of restrained domination in graphs let g v e be a simple graph a vertex set email protected v is a restrained dominating set if every vertex not in s is adjacent to a vertex in s and to a vertex in v s in this paper we investigate the np completeness of the restrained domination problem in planar graphs and split graphs meanwhile it is proved that the restrained domination problem is apx complete for bounded degree graphs

the within strip discrete unit disk cover problem we present a study of the within strip discrete unit disk cover wsdudc problem which is a restricted version of the discrete unit disk cover dudc problem for the wsdudc problem there exists a set of points and a set of unit disks in the plane and the points and disk centres are conned to a strip of xed height an optimal solution to the wsdudc problem is a set of disks of minimum cardinality that covers all points in the input set we describe a range of approximation algorithms for the problem including 4 and 3 approximate algorithms which apply for strips of height 2 p 2 3 0 94 and 0 8 units respectively as well as a general scheme for any strip with less than unit height we prove that the wsdudc problem is np complete on strips of any xed height which is our most interesting result from a theoretical standpoint the result is also quite surprising since a number of similar problems are tractable on strips of xed height finally we discuss how these results may be applied to known dudc approximation algorithms

completeness in approximation classes we introduce a formal framework for studying approximation properties of np optimization npo problems the classes we consider are those appearing in the literature namely the class of approximable problems within a constant e apx the class of problems having a polynomial time approximation scheme pas and the class of problems having a fully polynomial time approximation scheme fpas we define natural approximation preserving reductions and obtain completeness results for these classes a complete problem in a class can not have stronger approximation properties unless p np we also show that the degree structure of npo allows intermediate degrees that is if p np there are problems which are neither complete nor belong to a lower class

improved approximation algorithms for capacitated facility location problems in a surprising result korupolu plaxton and rajaraman 13 showed that a simple local search heuristic for the capacitated facility location problem cflp in which the service costs obey the triangle inequality produces a solution in polynomial time which is within a factor of 8 e of the value of an optimal solution by simplifying their analysis we are able to show that the same heuristic produces a solution which is within a factor of 6 1 e of the value of an optimal solution our simplified analysis uses the supermodularity of the cost function of the problem and the integrality of the transshipment polyhedron additionally we consider the variant of the cflp in which one may open multiple copies of any facility using ideas from the analysis of the local search heuristic we show how to turn any approximation algorithm for this variant into a polynomial time algorithm which at an additional cost of twice the optimum of the standard cflp opens at most one additional copy of any facility this allows us to transform a recent 2 approximation algorithm of mahdian ye and zhang 17 that opens many additional copies of facilities into a polynomial time algorithm which only opens one additional copy and has cost no more than four times the value of the standard cflp

local convergence analysis of fastica and related algorithms the fastica algorithm is one of the most prominent methods to solve the problem of linear independent component analysis ica although there have been several attempts to prove local convergence properties of fastica rigorous analysis is still missing in the community the major difficulty of analysis is because of the well known sign flipping phenomenon of fastica which causes the discontinuity of the corresponding fastica map on the unit sphere in this paper by using the concept of principal fiber bundles fastica is proven to be locally quadratically convergent to a correct separation higher order local convergence properties of fastica are also investigated in the framework of a scalar shift strategy moreover as a parallelized version of fastica the so called qr fastica algorithm which employs the qr decomposition gram schmidt orthonormalization process instead of the polar decomposition is shown to share similar local convergence properties with the original fastica

on the hardness of approximating minimization problems we prove results indicating that it is hard to compute efficiently good approximate solutions to the graph coloring set covering and other related minimization problems specifically there is an e 0 such that graph coloring cannot be approximated with ratio n e unless p np set covering cannot be approximated with ratio c log n for any c 1 4 unless np is contained in dtime n poly log n similar results follow for related problems such as clique cover fractional chromatic number dominating set and others

a sort jacobi algorithm for semisimple lie algebras the classical jacobi algorithm is extended to an unified lie algebraic approach the conventional jacobi algorithm minimize the distance to diagonality they reduce the off norm i e the sum of squares of off diagonal entries sorting the diagonal elements after each step would accelerate the convergence but there are difficulties to apply this sorting to the off norm that has to minimize using the gradient flow of a trace function it r w brockett dynamical systems that sort lists diagonalize matrices and solve linear programming problems linear algebra appl 146 79 91 1991 zbl 0719 90045 as a more appropriate distance measure matrices can be diagonalized and the eigenvalues can be simultaneously sorted in this paper the sort jacobi algorithm is extended to a large class of structured matrices besides the semisimple lie algebra cases such as e g the symmetric hermitian and skew symmetric eigenvalue problem and the real and complex singular value decomposition par the local quadratic convergence of the sort jacobi method is proved for the regular case but not for the case in which the eigenvalues or singular values occur in clusters for these more complicated irregular problem a future publication is announced par the results are illustrated considering the lie algebra of derivations of the complex octonions

finding a collective set of items we consider the following problem there is a set of items e g movies and a group of agents e g passengers on a plane each agent has some intrinsic utility for each of the items our goal is to pick a set of k items that maximize the total derived utility of all the agents i e in our example we are to pick k movies that we put on the plane s entertainment system however the actual utility that an agent derives from a given item is only a fraction of its intrinsic one and this fraction depends on how the agent ranks the item among the chosen available ones we provide a formal specification of the model and provide concrete examples and settings where it is applicable we show that the problem is hard in general but we show a number of tractability results for its natural special cases

some apx completeness results for cubic graphs four fundamental graph problems minimum vertex cover maximum independent set minimum dominating set and maximum cut are shown to be apx complete even for cubic graphs therefore unless p np these problems do not admit any polynomial time approximation scheme on input graphs of degree bounded by three

performance analysis of the strong uncorrelating transformation in blind separation of complex valued sources the strong uncorrelating transformation sut is an effective tool for blind separation of complex valued independent sources commonly applied to the spatial sample autocovariance and pseudo autocovariance matrices of the observed mixtures in this work we analyze the performance in terms of the resulting interference to source ratio isr of sut based blind separation of general wide sense stationary complex valued sources based on a small errors analysis we derive explicit expressions for the attainable isr in terms of the temporal correlations and pseudo correlations of the sources we demonstrate by simulation that the empirical performance closely follows our analytic prediction at moderate to long observation lengths an important implication ensuing from our analysis is that a rectilinear maximally improper source can be perfectly separated from all the other nonrectilinear sources

on the approximability of dodgson and young elections the voting rules proposed by dodgson and young are both designed to find an alternative closest to being a condorcet winner according to two different notions of proximity the score of a given alternative is known to be hard to compute under either rule in this paper we put forward two algorithms for approximating the dodgson score a combinatorial greedy algorithm and an lp based algorithm both of which yield an approximation ratio of h m 1 where m is the number of alternatives and h m 1 is the m 1 st harmonic number we also prove that our algorithms are optimal within a factor of 2 unless problems in np have quasi polynomial time algorithms despite the intuitive appeal of the greedy algorithm we argue that the lp based algorithm has an advantage from a social choice point of view further we demonstrate that computing any reasonable approximation of the ranking produced by dodgson s rule is np hard this result provides a complexity theoretic explanation of sharp discrepancies that have been observed in the social choice theory literature when comparing dodgson elections with simpler voting rules finally we show that the problem of calculating the young score is np hard to approximate by any factor this leads to an inapproximability result for the young ranking

on approximating restricted cycle covers a cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle an l cycle cover is a cycle cover in which the length of every cycle is in the set l the weight of a cycle cover of an edge weighted graph is the sum of the weights of its edges we come close to settling the complexity and approximability of computing l cycle covers on the one hand we show that for almost all l computing l cycle covers of maximum weight in directed and undirected graphs is mathsf apx hard most of our hardness results hold even if the edge weights are restricted to zero and one on the other hand we show that the problem of computing l cycle covers of maximum weight can be approximated within a factor of 2 for undirected graphs and within a factor of 8 3 in the case of directed graphs this holds for arbitrary sets l

blind separation of noncircular correlated sources using gaussian entropy rate we introduce a new blind source separation bss algorithm for correlated noncircular sources that uses only second order statistics and fully takes the correlation structure into account we propose a parametric entropy rate estimator that uses a widely linear autoregressive ar model for the sources and derive the bss algorithm by minimizing the mutual information of separated time series we compare the performance of the new algorithm with competing algorithms and demonstrate its superior separation performance as well as its effectiveness in separation of non gaussian sources when the identification conditions are met

fpt approximation schemes for maximizing submodular functions we investigate the existence of approximation algorithms for maximization of submodular functions that run in a fixed parameter tractable fpt time given a non decreasing submodular set function v 2 x r v 2 x r the goal is to select a subset s of k elements from x such that v s v s is maximized we identify three properties of set functions referred to as p separability properties and we argue that many real life problems can be expressed as maximization of submodular p separable functions with low values of the parameter p we present fpt approximation schemes for the minimization and maximization variants of the problem for several parameters that depend on characteristics of the optimized set function such as p and k

blind separation of instantaneous mixtures of nonstationary sources most source separation algorithms are based on a model of stationary sources however it is a simple matter to take advantage of possible nonstationarities of the sources to achieve separation this paper develops novel approaches in this direction based on the principles of maximum likelihood and minimum mutual information these principles are exploited by efficient algorithms in both the off line case via a new joint diagonalization procedure and in the on line case via a newton like procedure some experiments showing the good performance of our algorithms and evidencing an interesting feature of our methods are presented their ability to achieve a kind of super efficiency the paper concludes with a discussion contrasting separating methods for non gaussian and nonstationary models and emphasizing that as a matter of fact what makes the algorithms work is strictly speaking not the nonstationarity itself but rather the property that each realization of the source signals has a time varying envelope

a new concept for separability problems in blind source separation the goal of blind source separation bss lies in recovering the original independent sources of a mixed random vector without knowing the mixing structure a key ingredient for performing bss successfully is to know the indeterminacies of the problem that is to know how the separating model relates to the original mixing model separability for linear bss comon 1994 showed using the darmois skitovitch theorem that the linear mixing matrix can be found except for permutation and scaling in this work a much simpler direct proof for linear separability is given the idea is based on the fact that a random vector is independent if and only if the hessian of its logarithmic density resp characteristic function is diagonal everywhere this property is then exploited to propose a new algorithm for performing bss furthermore first ideas of how to generalize separability results based on hessian diagonalization to more complicated nonlinear models are studied in the setting of postnonlinear bss

semitotal domination new hardness results and a polynomial time algorithm for graphs of bounded mim width abstract a semitotal dominating set of a graph g with no isolated vertex is a dominating set d of g such that every vertex in d is within distance two of another vertex in d the minimum size t 2 g of a semitotal dominating set of g is squeezed between the domination number g and the total domination number t g semitotal dominating set is the problem of finding given a graph g a semitotal dominating set of g of size t 2 g in this paper we continue the systematic study on the computational complexity of this problem when restricted to special graph classes in particular we show that it is solvable in polynomial time for the class of graphs of bounded mim width by a reduction to total dominating set and we provide several approximation lower bounds for subclasses of subcubic graphs moreover we obtain complexity dichotomies in monogenic classes for the decision versions of semitotal dominating set and total dominating set finally we show that it is np complete to recognise the graphs such that t 2 g t g and those such that g t 2 g even if restricted to be planar and with maximum degree at most 4 and we provide forbidden induced subgraph characterisations for the graphs hereditarily satisfying either of these two equalities

comments on multiway splitting method for toeplitz matrix vector product we propose block decompositions for the toeplitz matrix vector product tmvp using the k way splitting method presented in the above paper as a result we show that the space complexity for tmvp can be improved

approximation algorithms for metric facility location and k median problems using the primal dual schema and lagrangian relaxation we present approximation algorithms for the metric uncapacitated facility location problem and the metric k median problem achieving guarantees of 3 and 6 respectively the distinguishing feature of our algorithms is their low running time o m log m and o m log m l log n respectively where n and m are the total number of vertices and edges in the underlying complete bipartite graph on cities and facilities the main algorithmic ideas are a new extension of the primal dual schema and the use of lagrangian relaxation to derive approximation algorithms

independent component analysis and simultaneous third order tensor diagonalization comon s 1994 well known scheme for independent component analysis ica is based on the maximal diagonalization in a least squares sense of a higher order cumulant tensor in a previous paper we proved that for fourth order cumulants the computation of an elementary jacobi rotation is equivalent to the computation of the best rank 1 approximation of a fourth order tensor in this paper we show that for third order tensors the computation of an elementary jacobi rotation is again equivalent to a best rank 1 approximation however here it is a matrix that has to be approximated this favorable computational load makes it attractive to do something third order like for fourth order cumulant tensors as well we show that simultaneous optimal diagonalization of third order tensor slices of the fourth order cumulant is a suitable strategy this simultaneous third order tensor diagonalization approach stotd is similar in spirit to the efficient jade algorithm

finding approximate and constrained motifs in graphs one of the most relevant topics in the analysis of biological networks is the identification of functional motifs inside a network a recent approach introduced in literature called graph motif represents the network as a vertex colored graph and the motif m as a multiset of colors an occurrence of a motif m in a vertex colored graph g is a connected induced subgraph of g whose vertex set is colored exactly as m in this paper we investigate three different variants of the graph motif problem the first two variants minimum adding motif min add graph motif and minimum substitution motif min sub graph motif deal with approximate occurrences of a motif in the graph while the third variant constrained graph motif cgm constrains the motif to contain a given set of vertices we investigate the computational and parameterized complexity of the three problems we show that min add graph motifand min sub graph motifare both np hard even when m is a set and the graph is a tree with maximum degree 4 in which each color appears at most twice then we show that min sub graph motifis fixed parameter tractable when parameterized by the size of m finally we consider the parameterized complexity of the cgmproblem we give a fixed parameter algorithm for graphs of bounded treewidth and show that the problem is w 2 hard when parameterized by m even if the input graph has diameter 2

blind source separation using second order cyclostationary statistics this paper studies the blind source separation bss problem with the assumption that the source signals are cyclostationary identifiability and separability criteria based on second order cyclostationary statistics socs alone are derived the identifiability condition is used to define an appropriate contrast function an iterative algorithm ath2 is derived to minimize this contrast function this algorithm separates the sources even when they do not have distinct cycle frequencies

the learnability of voting rules scoring rules and voting trees are two broad and concisely representable classes of voting rules scoring rules award points to alternatives according to their position in the preferences of the voters while voting trees are iterative procedures that select an alternative based on pairwise comparisons in this paper we investigate the pac learnability of these classes of rules we demonstrate that the class of scoring rules as functions from preferences into alternatives is efficiently learnable in the pac model with respect to voting trees while in general a learning algorithm would require an exponential number of samples we show that if the number of leaves is polynomial in the size of the set of alternatives then a polynomial training set suffices we apply these results in an emerging theory automated design of voting rules by learning

the l diversity problem tractability and approximability publishing personal data without giving up privacy is becoming an increasingly important problem in different fields in the last years different interesting approaches have been proposed i e k anonymity and l diversity given an input table these approaches partition its rows so that the computed partition satisfies some constraint in order to prevent the inference of the individuals the data belong to then the rows in a same set of the partition are related to the same rows by suppressing some of their entries here we focus on the l diversity problem where the attributes of the input table are distinguished in sensitive attributes and quasi identifier attributes the goal is to partition the rows of the input table so that each set c of the partition contains at most 1l c rows having a specific value in the sensitive attribute and the number of suppressions is minimized in this paper we investigate the approximation and parameterized complexity ofl diversity first we prove that the problem is not approximable within factor clnl for some constant c 0 even if the input table consists of only two columns and that the problem is apx hard even if l 4 and the input table contains exactly three columns then we give an approximation algorithm of factor m where m 1 is the number of columns in the input table when the sensitive attribute ranges over an alphabet of constant size concerning the parameterized complexity we prove that the problem is w 1 hard when parameterized by the cost bound by l and by the size of the alphabet then we prove that the problem admits a fixed parameter algorithm when both the maximum number of different values in a column and the number of columns are parameters

a novel parameterised approximation algorithm for minimum vertex cover parameterised approximation is a relatively new but growing field of interest it merges two ways of dealing with np hard optimisation problems namely polynomial approximation and exact parameterised exponential time algorithms we exemplify this idea by designing and analysing parameterised approximation algorithms for minimum vertex cover more specifically we provide a simple algorithm that works on any approximation ratio of the form 2l 1l 1 l 1 2 and has complexity that outperforms previously published algorithms based on sophisticated exact parameterised algorithms in particular for l 1 factor 1 5 approximation our algorithm runs in time o 1 0883 k where parameter k 23 t and t is the size of a minimum vertex cover additionally we present an improved polynomial time approximation algorithm for graphs of average degree at most four and a limited number of vertices with degree less than two

graph orientation with splits abstract the minimum maximum outdegree problem mmo is to assign a direction to every edge in an input undirected edge weighted graph so that the maximum weighted outdegree taken over all vertices becomes as small as possible in this paper we introduce a new variant of mmo called the p split minimum maximum outdegree problem p split mmo in which one is allowed to perform a sequence of p split operations on the vertices before orienting the edges for some specified non negative integer p and study its computational complexity

hardness of approximating flow and job shop scheduling problems we consider several variants of the job shop problem that is a fundamental and classical problem in scheduling the currently best approximation algorithms have worse than logarithmic performance guarantee but the only previously known inapproximability result says that it is np hard to approximate job shops within a factor less than 5 4 closing this big approximability gap is a well known and long standing open problem this article closes many gaps in our understanding of the hardness of this problem and answers several open questions in the literature it is shown the first nonconstant inapproximability result that almost matches the best known approximation algorithm for acyclic job shops the same bounds hold for the general version of flow shops where jobs are not required to be processed on each machine similar inapproximability results are obtained when the objective is to minimize the sum of completion times it is also shown that the problem with two machines and the preemptive variant with three machines have no ptas

fast and robust fixed point algorithms for independent component analysis independent component analysis ica is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible we use a combination of two different approaches for linear ica comon s information theoretic approach and the projection pursuit approach using maximum entropy approximations of differential entropy we introduce a family of new contrast functions for ica these contrast functions enable both the estimation of the whole decomposition by minimizing mutual information and estimation of individual independent components as projection pursuit directions the statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model and it is shown how to choose contrast functions that are robust and or of minimum variance finally we introduce simple fixed point algorithms for practical optimization of the contrast functions

comparing incomplete sequences via longest common subsequence abstract inspired by scaffold filling a recent approach for genome reconstruction from incomplete data we consider a variant of the well known longest common subsequence problem for the comparison of two sequences the new problem called longest filled common subsequence aims to compare a complete sequence with an incomplete one i e with some missing elements longest filled common subsequence lfcs given a complete sequence a an incomplete sequence b and a multiset m of symbols missing in b asks for a sequence b obtained by inserting the symbols of m into b so that b induces a common subsequence with a of maximum length we investigate the computational and approximation complexity of the problem and we show that it is np hard and apx hard when a contains at most two occurrences of each symbol and we give a polynomial time algorithm when the input sequences are over a constant size alphabet we give a 3 5 approximation algorithm for the longest filled common subsequence problem finally we present a fixed parameter algorithm for the problem when it is parameterized by the number of symbols inserted in b that match symbols of a

on the tractability of finding disjoint clubs in a network abstract we study a variant of the problem of finding a collection of disjoint s clubs in a given network given a graph the problem asks whether there exists a collection of at most r disjoint s clubs that covers at least k vertices of the network an s club is a connected graph that has diameter bounded by s for a positive integer s we demand that each club is non trivial that is it has order at least t 2 for some positive integer t we prove that the problem is apx hard even when the input graph has bounded degree s 2 t 3 and r v moreover we show that the problem is polynomial time solvable when s 4 t 3 and r v and when s 3 t 2 and r v finally for s 2 we present a fixed parameter algorithm for the problem when parameterized by the number of covered vertices

complexity analysis of p 3 convexity problems on bounded degree and planar graphs this paper studies new complexity aspects of p 3 convexity restricted to planar graphs with bounded maximum degree more specifically we are interested in identifying either a minimum p 3 geodetic set or a minimum p 3 hull set of such graphs from which the whole vertex set of g is obtained either after one or sufficiently many iterations respectively each iteration adds to a set s all vertices of v g s with at least two neighbors in s in this paper it is shown that a minimum p 3 hull set of a graph g can be found in polynomial time when g n g c for some constant c deciding if there is a p 3 hull set of size at most k in a given graph remains np complete even for planar graphs with maximum degree four and surprisingly as well as rather counterintuitively it is np complete to decide if there is a p 3 hull set of size at most k in a graph with maximum degree three though one can determine a minimum p 3 hull set in polynomial time not only for cubic graphs but also for graphs with minimum feedback vertex set of bounded size and no vertices of degree two concerning p 3 geodetic sets the problem of deciding if there is a p 3 geodetic set of size at most k in a planar graph with maximum degree three is proved to be np complete finally from a parameterized point of view we observe that finding a p 3 geodetic set of size at most k where k is the parameter is w2 hard however when considering the maximum degree as an additional parameter this problem becomes fixed parameter tractable

mutual information approach to blind separation of stationary sources this paper presents a unified approach to the problem of blind separation of sources based on the concept of mutual information this concept is applied to the whole source sequences as stationary processes and thus provides a universal contrast applicable to both the instantaneous and convolutive mixture cases for practical implementation we introduce several degraded forms of this contrast computable from a finite dimensional distribution of the reconstructed source processes only from them we derive several sets of estimating equations generalizing those considered earlier

primal dual rnc approximation algorithms for set cover and covering integer programs we build on the classical greedy sequential set cover algorithm in the spirit of the primal dual schema to obtain simple parallel approximation algorithms for the set cover problem and its generalizations our algorithms use randomization and our randomized voting lemmas may be of independent interest fast parallel approximation algorithms were known before for set cover though not for the generalizations considered in this paper

hardness results and approximation algorithms for weighted paired domination in graphs let g v e be a simple graph without isolated vertices a vertex set s v is a paired dominating set if every vertex in v s has a neighbor in s and the induced subgraph g s has a perfect matching in this paper we investigate the approximation hardness of paired domination in graphs for weighted paired domination an approximation algorithm in general graphs and an exact dynamic programming style algorithm in trees are also given

the label cut problem with respect to path length and label frequency given a graph with labels defined on edges and a source sink pair s t the label s t cut problem asks for a minimum number of labels such that the removal of edges with these labels disconnects s and t similarly the global label cut problem asks for a minimum number of labels to disconnect g itself for these two problems we identify two useful parameters i e l max the maximum length of any s t path only applies to label s t cut and f max the maximum number of appearances of any label in the graph applies to the two problems we show that l max 2 and f max 2 are two complexity thresholds for label s t cut furthermore we give i an o c k time parameterized algorithm for label s t cut with l max bounded from above where parameter k is the number of labels in a solution and c is a constant with l max 1 c l max ii a combinatorial l max approximation algorithm for label s t cut and iii a polynomial time exact algorithm for global label cut with f max bounded from above we give an fpt algorithm for label s t cut in a special case we give a pure combinatorial approximation algorithm for label s t cut we give a polynomial time exact algorithm for global label cut in a special case

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

on simultaneous diagonalization of one hermitian and one symmetric form abstract it is remarked that if a b m n c a a t and b b t b positive definite there exists a nonsingular matrix u such that 1 t bu i and 2 u t au is a diagonal matrix with nonnegative entries some related actions of the real orthogonal group and equations involving the unitary group are studied

volterra filtering and higher order whiteness some properties of volterra filtering are established finite order finite horizon volterra filtering is investigated as well as its asymptotic properties next the concepts of volterra unpredictability and uninterpolability lead to generalizations of the notion of white noise to higher orders these generalizations are introduced and relations are established between them

parameterized computational complexity of dodgson and young elections abstract we show that the two np complete problems of dodgson score and young score have differing computational complexities when the winner is close to being a condorcet winner on the one hand we present an efficient fixed parameter algorithm for determining a condorcet winner in dodgson elections by a minimum number of switches in the votes on the other hand we prove that the corresponding problem for young elections where one has to delete votes instead of performing switches is w 2 complete in addition we study dodgson elections that allow ties between the candidates and give fixed parameter tractability as well as w 2 completeness results depending on the cost model for switching ties

independent component analysis based on nonparametric density estimation in this paper we introduce a novel independent component analysis ica algorithm which is truly blind to the particular underlying distribution of the mixed signals using a nonparametric kernel density estimation technique the algorithm performs simultaneously the estimation of the unknown probability density functions of the source signals and the estimation of the unmixing matrix following the proposed approach the blind signal separation framework can be posed as a nonlinear optimization problem where a closed form expression of the cost function is available and only the elements of the unmixing matrix appear as unknowns we conducted a series of monte carlo simulations involving linear mixtures of various source signals with different statistical characteristics and sample sizes the new algorithm not only consistently outperformed all state of the art ica methods but also demonstrated the following properties 1 only a flexible model capable of learning the source statistics can consistently achieve an accurate separation of all the mixed signals 2 adopting a suitably designed optimization framework it is possible to derive a flexible ica algorithm that matches the stability and convergence properties of conventional algorithms 3 a nonparametric approach does not necessarily require large sample sizes in order to outperform methods with fixed or partially adaptive contrast functions

max ones generalized to larger domains we study a family of problems called maximum solution where the objective is to maximize a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints when the domain is boolean i e restricted to 0 1 the maximum solution problem is identical to the well studied max ones problem and the approximability is completely understood for all restrictions on the underlying constraints s khanna m sudan l trevisan and d p williamson siam j comput 30 2001 pp 1863 1920 we continue this line of research by considering domains containing more than two elements we present two main results a complete classification for the approximability of all maximal constraint languages over domains of cardinality at most 4 and a complete classification of the approximability of the problem when the set of allowed constraints contains all permutation constraints under the assumption that a conjecture due to szczepara minimal clones generated by groupoids ph d thesis universite de montreal montreal qc 1996 holds we give a complete classification for all maximal constraint languages these classes of languages are well studied in universal algebra and computer science they have for instance been considered in connection with machine learning and constraint satisfaction our results are proved by using algebraic results from clone theory and the results indicate that this approach is very powerful for classifying the approximability of certain optimization problems

finding a potential community in networks abstract an independent 2 clique of a graph is a subset of vertices that is an independent set and such that any two vertices inside have a common neighbor outside in this paper we study the complexity of finding an independent 2 clique of maximum size in several graph classes and we compare it with the complexity of maximum independent set we prove that this problem is np hard on apex graphs apx hard on line graphs not n 1 2 approximable on bipartite graphs and not n 1 approximable on split graphs while it is polynomial time solvable on graphs of bounded degree and their complements graphs of bounded treewidth planar graphs c 3 c 6 free graphs threshold graphs interval graphs and cographs

the complexity and approximability of finding maximum feasible subsystems of linear relations we study the combinatorial problem which consists given a system of linear relations of finding a maximum feasible subsystem that is a solution satisfying as many relations as possible the computational complexity of this general problem named max fls is investigated for the four types of relations and various constrained versions of max fls where a subset of relations must be satisfied or where the variables take bounded discrete values are also considered we establish the complexity of solving these problems optimally and whenever they are intractable we determine their degree of approximability max fls with or relations is np hard even when restricted to homogeneous systems with bipolar coefficients whereas it can be solved in polynomial time for relations with real coefficients the various np hard versions of max fls belong to different approximability classes depending on the type of relations and the additional constraints we show that the range of approximability stretches from apx complete problems which can be approximated within a constant but not within every constant unless p np to npo pb complete ones that are as hard to approximate as all np optimization problems with polynomially bounded objective functions while max fls with equations and integer coefficients cannot be approximated within pe for some e 0 where p is the number of relations the same problem over gf q for a prime q can be approximated within q but not within qe for some e 0 max fls with strict or nonstrict inequalities can be approximated within 2 but not within every constant factor our results also provide strong bounds on the approximability of two variants of max fls with and relations that arise when training perceptrons which are the building blocks of artificial neural networks and when designing linear classifiers

algorithmic aspects of semitotal domination in graphs abstract for a graph g v e a set d v is called a semitotal dominating set of g if d is a dominating set of g and every vertex in d is within distance 2 of another vertex of d the minimum semitotal domination problem is to find a semitotal dominating set of minimum cardinality given a graph g and a positive integer k the semitotal domination decision problem is to decide whether g has a semitotal dominating set of cardinality at most k the semitotal domination decision problem is known to be np complete for general graphs in this paper we show that the semitotal domination decision problem remains np complete for planar graphs split graphs and chordal bipartite graphs we give a polynomial time algorithm to solve the minimum semitotal domination problem in interval graphs we show that the minimum semitotal domination problem in a graph with maximum degree admits an approximation algorithm that achieves the approximation ratio of 2 3 ln 1 showing that the problem is in the class log apx we also show that the minimum semitotal domination problem cannot be approximated within 1 ln v for any 0 unless np dtime v o log log v finally we prove that the minimum semitotal domination problem is apx complete for bipartite graphs with maximum degree 4

a fast algorithm for joint diagonalization with non orthogonal transformations and its application to blind source separation a new efficient algorithm is presented for joint diagonalization of several matrices the algorithm is based on the frobenius norm formulation of the joint diagonalization problem and addresses diagonalization with a general non orthogonal transformation the iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer the algorithm s efficiency stems from the special approximation of the cost function resulting in a sparse block diagonal hessian to be used in the computation of the quasi newton update step extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods the results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state of the art joint diagonalization algorithms the practical use of our algorithm is shown for blind source separation problems

computing a small agreeable set of indivisible items abstract we study the problem of assigning a small subset of indivisible items to a group of agents so that the subset is agreeable to all agents meaning that all agents value the subset as least as much as its complement for an arbitrary number of agents and items we derive a tight worst case bound on the number of items that may need to be included in such a set we then present polynomial time algorithms that find an agreeable set whose size matches the worst case bound when there are two or three agents we also show that finding small agreeable sets is possible even when we only have access to the agents preferences on single items furthermore we investigate the problem of efficiently computing an agreeable set whose size approximates the size of the smallest agreeable set for any given instance we consider two well known models for representing the preferences of the agents the value oracle model and additive utilities and establish tight bounds on the approximation ratio that can be obtained by algorithms running in polynomial time in each of these models

the approximability of max csp with fixed value constraints in the maximum constraint satisfaction problem max csp one is given a finite collection of possibly weighted constraints on overlapping sets of variables and the goal is to assign values from a given finite domain to the variables so as to maximize the number or the total weight for the weighted case of satisfied constraints this problem is np hard in general and therefore it is natural to study how restricting the allowed types of constraints affects the approximability of the problem in this article we show that any max csp problem with a finite set of allowed constraint types which includes all fixed value constraints i e constraints of the form x e a is either solvable exactly in polynomial time or else is apx complete even if the number of occurrences of variables in instances is bounded moreover we present a simple description of all polynomial time solvable cases of our problem this description relies on the well known algebraic combinatorial property of supermodularity

a coordinate descent algorithm for complex joint diagonalization under hermitian and transpose congruences abstract this paper deals with the problem of joint complexmatrix diagonalization by considering both the hermitian andtranspose congruences we address the general case where thesearched diagonalizing matrix is apriori nonunitary based onthe minimization of a quadratic criterion we propose a ex ible algorithm in the sense that it allows to directly consider arectangular diagonalizing matrix and to take into considerationboth the hermitian and transpose congruences within the sameframework the proposed algorithm is a coordinate descentalgorithm that is based on an approximate criterion leading to theanalytical derivation of the minima arguments computer simu lations are drawn to illustrate the usefulness and performancesof the algorithm and a comparison to state of the art algorithmsis presented finally an application to independent componentanalysis based on fourth order statistics is also presented index terms blind source separation complex symmetric ma trices hermitian matrices independent component analysis jointdiagonalization

complexity issues in color preserving graph embeddings in the context of comparative analysis of protein protein interaction graphs we use a graph based formalism to detect the preservation of a given protein complex pattern graph in the protein protein interaction graph target graph of another species with respect to w r t orthologous proteins we give an efficient exponential time randomized algorithm in case the occurrence of the pattern graph in the target graph is required to be exact for approximate occurrences we prove a tight inapproximability result and give four approximation algorithms that deal with bounded degree graphs small ortholog numbers linear forests and very simple yet hard instances respectively

ruling out ptas for graph min bisection dense k subgraph and bipartite clique assuming that np not subseteq cap epsilon 0 bptime 2 n epsilon we show that graph min bisection dense k subgraph and bipartite clique have no polynomial time approximation scheme ptas we give a reduction from the minimum distance of code mdc problem starting with an instance of mdc we build a quasi random probabilistically checkable proof pcp that suffices to prove the desired inapproximability results in a quasi random pcp the query pattern of the verifier looks random in a certain precise sense among the several new techniques we introduce the most interesting one gives a way of certifying that a given polynomial belongs to a given linear subspace of polynomials as is important for our purpose the certificate itself happens to be another polynomial and it can be checked probabilistically by reading a constant number of its values

complex random vectors and ica models identifiability uniqueness and separability in this paper the conditions for identifiability separability and uniqueness of linear complex valued independent component analysis ica models are established these results extend the well known conditions for solving real valued ica problems to complex valued models relevant properties of complex random vectors are described in order to extend the darmois skitovich theorem for complex valued models this theorem is used to construct a proof of a theorem for each of the above ica model concepts both circular and noncircular complex random vectors are covered examples clarifying the above concepts are presented

blind source separation via generalized eigenvalue decomposition in this short note we highlight the fact that linear blind source separation can be formulated as a generalized eigenvalue decomposition under the assumptions of non gaussian non stationary or non white independent sources the solution for the unmixing matrix is given by the generalized eigenvectors that simultaneously diagonalize the covariance matrix of the observations and an additional symmetric matrix whose form depends upon the particular assumptions the method critically determines the mixture coefficients and is therefore not robust to estimation errors however it provides a rather general and unified solution that summarizes the conditions for successful blind source separation to demonstrate the method which can be implemented in two lines of matlab code we present results for artificial mixtures of speech and real mixtures of electroencephalography eeg data showing that the same sources are recovered under the various assumptions

on the hardness of finding near optimal multicuts in directed acyclic graphs abstract given an edge weighted di graph and a list of source sink pairs of vertices of this graph the minimum multicut problem consists in selecting a minimum weight set of edges or arcs whose removal leaves no path from each source to the corresponding sink this is a well known np hard problem and improving several previous results we show that it remains apx hard in unweighted directed acyclic graphs dag even with only two source sink pairs this is also true if we remove vertices instead of arcs

a dynamic programming approach for a class of robust optimization problems common approaches to solve a robust optimization problem decompose the problem into a master problem mp and adversarial separation problems aps mp contains the original robust constraints however written only for finite numbers of scenarios additional scenarios are generated on the fly by solving the aps we consider in this work the budgeted uncertainty polytope from bertsimas and sim widely used in the literature and propose new dynamic programming algorithms to solve the aps that are based on the maximum number of deviations allowed and on the size of the deviations our algorithms can be applied to robust constraints that occur in various applications such as lot sizing tsp with time windows scheduling problems and inventory routing problems among many others we show how the simple version of the algorithms leads to a fptas when the deterministic problem is convex we assess numerically our approach on a lot sizing problem showing a comparison with the classical mip reformulation of the ap

non orthogonal joint diagonalization in the least squares sense with application in blind source separation approximate joint diagonalization of a set of matrices is an essential tool in many blind source separation bss algorithms a common measure of the attained diagonalization of the set is the weighted least squares wls criterion however most well known algorithms are restricted to finding an orthogonal diagonalizing matrix relying on a whitening phase for the nonorthogonal factor often such an approach implies unbalanced weighting which can result in degraded performance we propose an iterative alternating directions algorithm for minimizing the wls criterion with respect to a general not necessarily orthogonal diagonalizing matrix under some mild assumptions we prove weak convergence in the sense that the norm of parameters update is guaranteed to fall below any arbitrarily small threshold within a finite number of iterations we distinguish between hermitian and symmetrical problems using bss simulations results we demonstrate the improvement in estimating the mixing matrix resulting from the relaxation of the orthogonality restriction

uniqueness analysis of non unitary matrix joint diagonalization matrix joint diagonalization mjd is a powerful approach for solving the blind source separation bss problem it relies on the construction of matrices which are diagonalized by the unknown demixing matrix their joint diagonalizer serves as a correct estimate of this demixing matrix only if it is uniquely determined thus a critical question is under what conditions is a joint diagonalizer unique in the present work we fully answer this question about the identifiability of mjd based bss approaches and provide a general result on uniqueness conditions of matrix joint diagonalization it unifies all existing results which exploit the concepts of non circularity non stationarity non whiteness and non gaussianity as a corollary we propose a solution for complex bss which can be formulated in closed form in terms of an eigen and a singular value decomposition of two matrices

high order contrasts for independent component analysis this article considers high order measures of independence for the independent component analysis problem and discusses the class of jacobi algorithms for their optimization several implementations are discussed we compare the proposed approaches with gradient based techniques from the algorithmic point of view and also on a set of biomedical data