parameterized complexity of happy coloring problems abstract in a vertex colored graph an edge is happy if its endpoints have the same color similarly a vertex is happy if all its incident edges are happy motivated by the computation of homophily in social networks we consider the algorithmic aspects of the following maximum happy edges k mhe problem given a partially k colored graph g and an integer l find an extended full k coloring of g making at least l edges happy when we want to make l vertices happy on the same input the problem is known as maximum happy vertices k mhv we perform an extensive study into the complexity of the problems particularly from a parameterized viewpoint for every k 3 we prove both problems can be solved in time 2 n n o 1 moreover by combining this result with a linear vertex kernel of size k l for k mhe we show that the edge variant can be solved in time 2 l n o 1 in contrast we prove that the vertex variant remains w 1 hard for the natural parameter l however the problem does admit a kernel with o k 2 l 2 vertices for the combined parameter k l from a structural perspective we show both problems are fixed parameter tractable for treewidth and neighborhood diversity which can both be seen as sparsity and density measures of a graph finally we extend the known completeness results of the problems by showing they remain hard on bipartite graphs and split graphs on the positive side we show the vertex variant can be solved optimally in polynomial time for cographs

synchronization of arbitrarily switched boolean networks this paper investigates the complete synchronization problem for the drive response switched boolean networks sbns under arbitrary switching signals where the switching signals of the response sbn follow those generated by the drive sbn at each time instant first the definition of complete synchronization is introduced for the drive response sbns under arbitrary switching signals second the concept of switching reachable set starting from a given initial state set is put forward based on it a necessary and sufficient condition is derived for the complete synchronization of the drive response sbns last we give a simple algebraic expression for the switching reachable set in a given number of time steps and two computable algebraic criteria are obtained for the complete synchronization of the sbns a biological example is given to demonstrate the effectiveness of the obtained main results

on the complexity of some colorful problems parameterized by treewidth in this paper we study the complexity of several coloring problems on graphs parameterized by the treewidth of the graph 1 the list coloring problem takes as input a graph g together with an assignment to each vertex v of a set of colors c v the problem is to determine whether it is possible to choose a color for vertex v from the set of permitted colors c v for each vertex so that the obtained coloring of g is proper we show that this problem is w 1 hard parameterized by the treewidth of g the closely related precoloring extension problem is also shown to be w 1 hard parameterized by treewidth 2 an equitable coloring of a graph g is a proper coloring of the vertices where the numbers of vertices having any two distinct colors differs by at most one we show that the problem is hard for w 1 parameterized by the treewidth plus the number of colors we also show that a list based variation list equitable coloring is w 1 hard for forests parameterized by the number of colors on the lists 3 the list chromatic number g l g of a graph g is defined to be the smallest positive integer r such that for every assignment to the vertices v of g of a list l v of colors where each list has length at least r there is a choice of one color from each vertex list l v yielding a proper coloring of g we show that the problem of determining whether g l g

synchronization in an array of output coupled boolean networks with time delay this brief presents an analytical study of synchronization in an array of coupled deterministic boolean networks bns with time delay two kinds of models are considered in one model the outputs contain time delay while in another one the outputs do not one restriction in this brief is that the state delay and output delay are restricted to be equal by referring to the algebraic representations of logical dynamics and using the techniques of semitensor product of matrices some necessary and sufficient conditions are derived for the synchronization of delay coupled bns examples including a practical epigenetic example are given for illustration

the parameterised complexity of list problems on graphs of bounded treewidth we consider the parameterised complexity of several list problems on graphs with parameter treewidth or pathwidth in particular we show that list edge chromatic number and list total chromatic number are fixed parameter tractable parameterised by treewidth whereas list hamilton path is w1 hard even parameterised by pathwidth these results resolve two open questions of fellows fomin lokshtanov rosamond saurabh szeider and thomassen 2011

almost optimal lower bounds for problems parameterized by clique width we obtain asymptotically tight algorithmic bounds for max cut and edge dominating set problems on graphs of bounded clique width we show that on an n vertex graph of clique width t both problems 1 cannot be solved in time f t n o t for any function f of t unless exponential time hypothesis fails and 2 can be solved in time n o t

synchronization of boolean networks with time delays abstract this paper studies analytically synchronization of two deterministic boolean networks with time delays which are unidirectionally coupled in the drive response configuration necessary and sufficient conditions of synchronization are established based on the algebraic representations of logical dynamics in terms of the semi tensor product of matrices the synchronization conditions show that for drive response boolean networks different relations between the inherent state delay and the unidirectional coupling delay may result in distinct synchronization phenomena and both kinds of time delays that ensure synchronization if existent are not unique examples are worked out to illustrate the present results

the many facets of upper domination this paper studies upper domination i e the problem of computing the maximum cardinality of a minimal dominating set in a graph with respect to classical and parameterised complexity as well as approximability

system decomposition with respect to inputs for boolean control networks abstract in this paper the problem of system decomposition with respect to inputs is investigated for boolean control networks bcns first based on the linear representation of bcns some algebraic equivalent conditions for the decomposability are obtained second the concept of perfect equal vertex partition pevp is proposed for bcns a necessary and sufficient graphical condition for the decomposability i e the existence of a pevp is proposed third for calculating a pevp an algorithm called vertex set uniting algorithm vsua is designed finally a biological example is analyzed to show the effectiveness of the proposed method

use of the viterbi algorithm to compute error events of trellis phase coding in order of increasing distance the use of the viterbi algorithm to evaluate the minimum distance parameters of trellis phase codes is extended to evaluate distances and paths of error events other than the free distance event distances and paths are found for error events sequentially in order of increasing distance starting with the free distance event memory requirements increase slowly with the number of error events required the time taken to find the next error event increases slowly with the number of error events already found results of sample calculations and computation times are included

designing fpt algorithms for cut problems using randomized contractions we introduce a new technique for designing fixed parameter algorithms for cut problems called randomized contractions we apply our framework to obtain the first fixed parameter algorithms fpt algorithms with exponential speed up for the steiner cut and node multiway cut uncut problems we prove that the parameterized version of the unique label cover problem which is the base of the unique games conjecture can be solved in 2 o k 2 log sigma n 4 log n deterministic time even in the stronger vertex deletion variant where k is the number of unsatisfied edges and sigma is the size of the alphabet as a consequence we show that one can in polynomial time solve instances of unique games where the number of edges allowed not to be satisfied is upper bounded by o sqrt log n to optimality which improves over the trivial o 1 upper bound we prove that the steiner cut problem can be solved in 2 o k 2 log k n 4 log n deterministic time and tilde o 2 o k 2 log k n 2 random

a maximum principle for single input boolean control networks boolean networks have recently been attracting considerable interest as computational models for genetic and cellular networks we consider a mayer type optimal control problem for a single input boolean network and derive a necessary condition for a control to be optimal this provides an analog of pontryagin s maximum principle for single input boolean networks

extracting constrained 2 interval subsets in 2 interval sets 2 interval sets were used in s vialette pattern matching over 2 intervals sets in proc 13th annual symposium combinatorial pattern matching cpm 2002 in lecture notes in computer science vol 2373 springer verlag 2002 pp 53 63 s vialette on the computational complexity of 2 interval pattern matching theoret comput sci 312 2 3 2004 223 249 for establishing a general representation for macroscopic describers of rna secondary structures in this context we have a 2 interval for each legal local fold in a given rna sequence and a constrained pattern made of disjoint 2 intervals represents a putative rna secondary structure we focus here on the problem of extracting a constrained pattern in a set of 2 intervals more precisely given a set of 2 intervals and a model r describing if two disjoint 2 intervals in a solution can be in precedence order be allowed to nest and or be allowed to cross we consider the problem of finding a maximum cardinality subset of disjoint 2 intervals such that any two 2 intervals in agree with r the different combinations of restrictions on model r alter the computational complexity of the problem and need to be examined separately in this paper we improve the time complexity of s vialette on the computational complexity of 2 interval pattern matching theoret comput sci 312 2 3 2004 223 249 for model r by giving an optimal o nlogn time algorithm where n is the cardinality of the 2 interval set we also give a graph like relaxation for model r that is solvable in time finally we prove that the considered problem is np complete for model r even for same length intervals and give a fixed parameter tractability result based on the crossing structure of

a refined complexity analysis of degree anonymization in graphs motivated by a strongly growing interest in graph anonymization we study the np hard degree anonymity problem asking whether a graph can be made k anonymous by adding at most a given number of edges herein a graph is k anonymous if for every vertex in the graph there are at least k 1 other vertices of the same degree our algorithmic results shed light on the performance quality of a popular heuristic due to liu and terzi acm sigmod 2008 in particular we show that the heuristic provides optimal solutions if many edges need to be added based on this we develop a polynomial time data reduction yielding a polynomial size problem kernel for degree anonymity parameterized by the maximum vertex degree in terms of parameterized complexity analysis this result is in a sense tight since we also show that the problem is already np hard for h index three implying np hardness for smaller parameters such as average degree and degeneracy

brief paper controllability of boolean control networks via the perron frobenius theory boolean control networks bcns are recently attracting considerable interest as computational models for genetic and cellular networks addressing control theoretic problems in bcns may lead to a better understanding of the intrinsic control in biological systems as well as to developing suitable protocols for manipulating biological systems using exogenous inputs we introduce two definitions for controllability of a bcn and show that a necessary and sufficient condition for each form of controllability is that a certain nonnegative matrix is irreducible or primitive respectively our analysis is based on a result that may be of independent interest namely a simple algebraic formula for the number of different control sequences that steer a bcn between given initial and final states in a given number of time steps while avoiding a set of forbidden states

brief paper an integer programming approach to optimal control problems in context sensitive probabilistic boolean networks a boolean network is one of the models of biological networks such as gene regulatory networks and has been extensively studied in particular a probabilistic boolean network pbn is well known as an extension of boolean networks but in the existing methods to solve the optimal control problem of pbns it is necessary to compute the state transition diagram with 2 n nodes for a given pbn with n states to avoid this computation an integer programming based approach is proposed for a context sensitive pbn cs pbn which is a general form of pbns in the proposed method a cs pbn is transformed into a linear system with binary variables and the optimal control problem is reduced to an integer linear programming problem by a numerical example the effectiveness of the proposed method is shown

optimal control of boolean control networks in this paper we address the optimal control problem for boolean control networks bcns we first consider the problem of finding the input sequences that minimize a given cost function over a finite time horizon the problem solution is obtained by means of a recursive algorithm that represents the analogue for bcns of the difference riccati equation for linear systems we prove that a significant number of optimal control problems for bcns can be easily reframed into the present setup in particular the cost function can be adjusted so as to include penalties on the switchings provided that we augment the size of the bcn state variable in the second part of the paper we address the infinite horizon optimal control problem and we provide necessary and sufficient conditions for the problem solvability the solution is obtained as the limit of the solution over the finite horizon 0 t and it is always achieved in a finite number of steps finally the average cost problem over the infinite horizon investigated in optimal control of logical control networks y zhao ieee trans autom control vol 56 no 8 pp 1766 1776 aug 2011 is addressed by making use of the results obtained in the previous sections

filtering for nonlinear genetic regulatory networks with stochastic disturbances in this paper the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition the stochastic perturbation is in the form of a scalar brownian motion and the time delays exist in both the translation process and the feedback regulation process the purpose of the addressed filtering problem is to estimate the true concentrations of the mrna and protein specifically we are interested in designing a linear filter such that in the presence of time delays stochastic disturbances as well as sector nonlinearities the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta by using the linear matrix inequality lmi technique sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model and the filter gain is then characterized in terms of the solution to an lmi which can be easily solved by using standard software packages a simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

incremental list coloring of graphs parameterized by conservation incrementally k list coloring a graph means that a graph is given by adding vertices step by step and for each intermediate step we ask for a vertex coloring such that each vertex has one of the colors specified by its associated list containing some of in total k colors we introduce the conservative version of this problem by adding a further parameter c n specifying the maximum number of vertices to be recolored between two subsequent graphs differing by one vertex the conservation parameter c models the natural quest for a modest evolution of the coloring in the course of the incremental process instead of performing radical changes we show that even on bipartite graphs the problem is np hard for k 3 and w 1 hard for an unbounded number of colors when parameterized by c in contrast also on general graphs the problem becomes fixed parameter tractable with respect to the combined parameter k c we prove that the problem has an exponential size kernel with respect to k c and there is no polynomial size kernel unless np conp poly furthermore we investigate the parameterized complexity on various subclasses of perfect graphs we show fixed parameter tractability for the combined parameter treewidth and number k of colors finally we provide empirical findings on the practical relevance of our approach in terms of an effective graph coloring heuristic

controllability of probabilistic boolean control networks based on transition probability matrices in this paper we propose a new approach to investigate the controllability and reachability of probabilistic boolean control networks pbcns with forbidden states we first give a simple algebraic formula for the transition probability between two states in a given number of time step while avoiding a set of forbidden states then we construct the controllability matrix based on a new operator and some necessary and sufficient conditions are obtained for the controllability and reachability of pbcns a numerical example is given to illustrate the efficiency of the obtained results

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

parameterized complexity of critical node cuts we consider the following graph cut problem called critical node cut cnc given a graph g on n vertices and two positive integers k and x determine whether g has a set of k vertices whose removal leaves g with at most x connected pairs of vertices we analyze this problem in the framework of parameterized complexity that is we are interested in whether or not this problem is solvable in f n o 1 time i e whether or not it is fixed parameter tractable for various natural parameters we consider four such parameters the size k of the required cut the upper bound x on the number of remaining connected pairs the lower bound y on the number of connected pairs to be removed the treewidth w of g we determine whether or not cnc is fixed parameter tractable for each of these parameters we determine this also for all possible aggregations of these four parameters apart from w k moreover we also determine whether or not cnc admits a polynomial kernel for all these parameterizations that is whether or not there is an algorithm that reduces each instance of cnc in polynomial time to an equivalent instance of size o 1 where is the given parameter

boolean dynamics of networks with scale free topology the dynamics of boolean networks with scale free topology are studied the existence of a phase transition from ordered to chaotic dynamics governed by the value of the scale free exponent of the network is shown analytically by analyzing the overlap between two distinct trajectories the phase diagram shows that the phase transition occurs for values of the scale free exponent in the open interval 2 2 5 since the boolean networks under study are directed graphs the scale free topology of the input connections and that of the output connections are studied separately ultimately these two topologies are shown to be equivalent a numerical study of the attractor structure of the configuration space reveals that this structure is similar in both networks with scale free topologies and networks with homogeneous random topologies however an important result of this work is that the fine tuning usually required to achieve stability in the dynamics of networks with homogeneous random topologies is no longer necessary when the network topology is scale free finally based on the results presented in this work it is hypothesized that the scale free topology favors the evolution and adaptation of network functioning from a biological perspective

increasing the minimum degree of a graph by contractions abstract the degree contractibility problem is to test whether a given graph g can be modified to a graph of minimum degree at least d by using at most k contractions we prove the following three results first degree contractibility is np complete even when d 14 second it is fixed parameter tractable when parameterized by k and d third it is w 1 hard when parameterized by k we also study its variant where the input graph is weighted i e has some edge weighting and the contractions preserve these weights the weighted degree contractibility problem is to test if a weighted graph g can be contracted to a weighted graph of minimum weighted degree at least d by using at most k weighted contractions we show that this problem is np complete and that it is fixed parameter tractable when parameterized by k in addition we pinpoint a relationship with the problem of finding a minimal edge cut of maximum size in a graph and study the parameterized complexity of this problem and its variants

fixed parameter tractability and completeness i basic results for many fixed parameter problems that are trivially soluable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as k feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is soluable in time bounded by a polynomial of degree c where c is a constant independent of k we establish the main results of a completeness program which addresses the apparent fixed parameter intractability of many parameterized problems in particular we define a hierarchy of classes of parameterized problems fpt subseteq w 1 subseteq w 2 subseteq cdots subseteq w sat subseteq w p and identify natural complete problems for w t for t geq 2 in other papers we have shown many problems complete for w 1 dominating set is shown to be complete for w 2 and thus is not fixed parameter tractable unless independent set clique irredundant set and many other natural problems in w 2 are also fixed parameter tractable we also give a compendium of currently known hardness results as an appendix

on the parameterized complexity of some optimization problems related to multiple interval graphs we show that for any constant t 2 k independent set and k dominating set in t track interval graphs are w 1 hard this settles an open question recently raised by fellows hermelin rosamond and vialette we also give an fpt algorithm for k clique in t interval graphs parameterized by both k and t with running time max t o k 2 o k l o g k poly n where n is the number of vertices in the graph this slightly improves the previous fpt algorithm by fellows hermelin rosamond and vialette finally we use the w 1 hardness of k independent set in t track interval graphs to obtain the first parameterized intractability result for a recent bioinformatics problem called maximal strip recovery msr we show that msr d is w 1 hard for any constant d 4 when the parameter is either the total length of the strips or the total number of adjacencies in the strips or the number of strips in the solution

shortest color spanning intervals abstract given a set of n points on a line where each point has one of k colors and given an integer s i 1 for each color i 1 i k the problem shortest color spanning t intervals scsi t aims at finding t intervals to cover at least s i points of each color i such that the maximum length of the intervals is minimized chen and misiolek introduced the problem scsi 1 and presented an algorithm running in o n time if the input points are sorted khanteimouri et al gave an o n 2 log n time algorithm for the special case of scsi 2 with s i 1 for all colors i in this paper we present an improved algorithm with running time of o n 2 for scsi 2 with arbitrary s i 1 we also obtain some interesting results for the general problem scsi t from the negative direction we show that approximating scsi t within any ratio is np hard when t is part of the input is w 2 hard when t is the parameter and is w 1 hard with both t and k as parameters moreover the np hardness and the w 2 hardness with parameter t hold even if s i 1 for all i from the positive direction we show that scsi t with s i 1 for all i is fixed parameter tractable with k as the parameter and admits an exact algorithm running in o 2 k n max k log n time

sampled data synchronization control of dynamical networks with stochastic sampling this technical note is concerned with the sampled data synchronization control problem for a class of dynamical networks the sampling period considered here is assumed to be time varying that switches between two different values in a random way with given probability the addressed synchronization control problem is first formulated as an exponentially mean square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays mpids and the sector bounded nonlinearities sbns then a novel lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean square stable both gronwall s inequality and jenson integral inequality are utilized to substantially simplify the derivation of the main results subsequently a set of sampled data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software finally a numerical simulation example is employed to show the effectiveness of the proposed sampled data synchronization control scheme

input state incidence matrix of boolean control networks and its applications the input state incidence matrix of a control boolean network is proposed it is shown that this matrix contains complete information of the input state mapping using it an easily verifiable necessary and sufficient condition for the controllability of a boolean control network is obtained the corresponding control which drives a point to a given reachable point is designed moreover certain topological properties such as the fixed points and cycles of a boolean control network are investigated then as another application a sufficient condition for the observability is presented finally the results are extended to mix valued logical control systems

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

global h_ infty pinning synchronization of complex networks with sampled data communications this paper investigates the global h infty pinning synchronization problem for a class of complex networks with aperiodic samplings combined with the writinger based integral inequality a new less conservative criterion is presented to guarantee the global pinning synchronization of the complex network furthermore a novel condition is proposed under which the complex network is globally pinning synchronized with a given h infty performance index it is shown that the h infty performance index gamma has a positive correlation with the upper bound of the sampling intervals finally the validity and the advantage of the theoretic results obtained are verified by means of the applications in chua s circuit and pendulum

new algorithms for maximum disjoint paths based on tree likeness we study the classical mathsf np hard problems of finding maximum size subsets from given sets of k terminal pairs that can be routed via edge disjoint paths maxedp or node disjoint paths maxndp in a given graph the approximability of maxedp maxndp is currently not well understood the best known lower bound is 2 varomega sqrt log n assuming mathsf np not subseteq mathsf dtime n mathcal o log n this constitutes a significant gap to the best known approximation upper bound of mathcal o sqrt n due to chekuri et al theory comput 2 137 146 2006 and closing this gap is currently one of the big open problems in approximation algorithms in their seminal paper raghavan and thompson combinatorica 7 4 365 374 1987 introduce the technique of randomized rounding for lps their technique gives an mathcal o 1 approximation when edges or nodes may be used by mathcal o left log n log log n right paths in this paper we strengthen the fundamental results above we provide new bounds formulated in terms of the feedback vertex set number r of a graph which measures its vertex deletion distance to a forest in particular we obtain the following results for maxedp we give an mathcal o sqrt r log k r approximation algorithm up to a logarithmic factor our result strengthens the best known ratio mathcal o sqrt n due to chekuri et al as r le n further we show how to route varomega text opt pairs with congestion bounded by mathcal o log kr log log kr strengthening the bound obtained by the classic approach of raghavan and thompson for maxndp we give an algorithm that gives the optimal answer in time k r mathcal o r cdot n this is a substantial improvement on the run time of 2 kr mathcal o r cdot n which can be obtained via an algorithm by scheffler we complement these positive results by proving that maxedp is mathsf np hard even for r 1 and maxndp is mathsf w 1 hard when r is the parameter this shows that neither problem is fixed parameter tractable in r unless mathsf fpt mathsf w 1 and that our approximability results are relevant even for very small constant values of r

complete synchronization of boolean networks we examine complete synchronization of two deterministic boolean networks bns coupled unidirectionally in the drive response configuration a necessary and sufficient criterion is presented in terms of algebraic representations of bns as a consequence we show that complete synchronization can occur only between two conditionally identical bns when the transition matrix of the drive network is nonsingular two examples are worked out to illustrate the obtained results

a new approximation to the symbol error probability for coded modulation schemes with maximum likelihood sequence detection the power efficiency of coded modulation schemes in additive white gaussian noise depends on the signal space distribution of their most common error events symbol error probability calculation allowing for the pairwise interaction of these error events is discussed two optimality criteria are considered for detectors the first minimizes the probability of symbol error for each symbol decision this is called the symbol to symbol detector the second which is superior is the maximum likelihood sequence detector mlsd a lower bound for the symbol to symbol detector and an approximation to the mlsd symbol error probability are described the theoretical performance difference between these two detectors is given the results are more accurate than minimum squared euclidean distance predictions especially at low and intermediate signal to noise ratios the mlsd symbol error probability approximation is obtained for considerably less cost than computer simulation and gives more insight into the signal space structure of the scheme being analyzed numerical results are presented for a continuous phase modulation cpm example

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

subset feedback vertex set on graphs of bounded independent set size abstract the weighted subset feedback vertex set problem is a generalization of the classical feedback vertex set problem and asks for a vertex set of minimum weight size that intersects all cycles containing a vertex of a predescribed set of vertices although subset feedback vertex set and feedback vertex set exhibit different computational complexity on split graphs no similar characterization is known on other classes of graphs towards the understanding of the complexity difference between the two problems it is natural to study the importance of structural graph parameters here we consider graphs of bounded independent set number for which it is known that weighted feedback vertex set can be solved in polynomial time we provide a dichotomy result with respect to the size of a maximum independent set in particular we show that weighted subset feedback vertex set can be solved in polynomial time for graphs with 3 whereas we prove that the problem remains np hard for graphs with 4 moreover we show that the unweighted subset feedback vertex set problem can be solved in polynomial time on graphs of bounded independent set number by giving an algorithm with running time n o to complement our results we demonstrate how our ideas can be extended to other terminal set problems on graphs of bounded independent set size node multiway cut is a terminal set problem that asks for a vertex set of minimum size that intersects all paths connecting any two terminals based on our findings for subset feedback vertex set we settle the complexity of node multiway cut as well as its variants where nodes are weighted and or the terminals are deletable for every value of the given independent set number

on the computational complexity of 2 interval pattern matching problems the focus of this paper is on the computational complexity of pattern matching problems over set of 2 intervals these problems occur in the context of molecular biology when a structured pattern i e a rna secondary structure given in the form of a 2 interval pattern has to be found in a sequence database we show that finding a 2 interval pattern in a set of 2 intervals is a np complete problem even if no 2 interval of the pattern precedes the other but can be solved in polynomial time for several interesting special cases in particular it is shown that the pseudo knot free rna secondary structure case is polynomial time solvable in our 2 interval formalism also we investigate the computational complexity of finding the longest 2 interval pattern in a set of 2 intervals and prove several np completeness results as well as polynomial time solvable special cases

synchronization for the realization dependent probabilistic boolean networks this paper investigates the synchronization problem for the realization dependent probabilistic boolean networks pbns coupled unidirectionally in the drive response configuration the realization of the response pbn is assumed to be uniquely determined by the realization signal generated by the drive pbn at each discrete time instant first the drive response pbns are expressed in their algebraic forms based on the semitensor product method and then a necessary and sufficient condition is presented for the synchronization of the pbns second by resorting to a newly defined matrix operator the reachable set from any initial state is expressed by a column vector consequently an easily computable algebraic criterion is derived assuring the synchronization of the drive response pbns finally three illustrative examples are employed to demonstrate the applicability and usefulness of the developed theoretical results

the complexity of dominating set in geometric intersection graphs abstract we study the parameterized complexity of the dominating set problem in geometric intersection graphs in one dimension we investigate intersection graphs induced by translates of a fixed pattern q that consists of a finite number of intervals and a finite number of isolated points we prove that dominating set on such intersection graphs is polynomially solvable whenever q contains at least one interval and whenever q contains no intervals and for any two point pairs in q the distance ratio is rational the remaining case where q contains no intervals but does contain an irrational distance ratio is shown to be np complete and contained in fpt when parameterized by the solution size in two and higher dimensions we prove that dominating set is contained in w 1 for intersection graphs of semi algebraic sets with constant description complexity so far this was only known for unit squares finally we establish w 1 hardness for a large class of intersection graphs

kernel bounds for path and cycle problems connectivity problems like k path and k disjoint paths relate to many important milestones in parameterized complexity namely the graph minors project color coding and the recent development of techniques for obtaining kernelization lower bounds this work explores the existence of polynomial kernels for various path and cycle problems by considering nonstandard parameterizations we show polynomial kernels when the parameters are a given vertex cover a modulator to a cluster graph or a promised max leaf number we obtain lower bounds via cross composition e g for hamiltonian cycle and related problems when parameterized by a modulator to an outerplanar graph

parameterized complexity of min power multicast problems in wireless ad hoc networks power assignment in wireless ad hoc networks can be seen as a family of problems in which the task is to find in a given power requirement network a minimum power communication subnetwork that satisfies a given connectivity constraint these problems have been extensively studied from the viewpoint of approximation heuristic linear programming etc in this paper we add a new facet by initiating a systematic parameterized complexity study of three types of power assignment problems related to multicast min power single source h multicast min power strongly connected h multicast and min power multi source h multicast we investigate their parameterized complexities with respect to the number of terminals and the number of senders we show that a min power single source h multicast is fixed parameter tractable with respect to the number of terminals and achieve several parameterized hardness results

symbol error probability bounds for coherently viterbi detected continuous phase modulated signals recently the minimum euclidean distance and bandwidth properties of continuous phase modulated cpm signals have been considered it has also been shown that for rational modulation indexes a state description of these signals is possible and that the viterbi algorithm va can be used for demodulation in this paper the performance analysis of cpm systems is extended to obtain bounds on the symbol error probability when the va is used the calculation of these bounds is based on the transfer function technique which has been generalized from numerical comparisons of the upper and lower bounds it is concluded that the minimum euclidean distance is a good performance measure for a broad class of cpm signals even when the symbol error probability is as large as 10 2

separation and synchronization of piecewise linear chaotic systems in this paper a topic regarding the synchronization of chaotic systems is dealt with the case of separation and synchronization of many chaotic signals generated by different chaotic circuits and combined together is examined in particular an observer based strategy has been adopted and an approach for the simultaneous stabilization of many luenberger observers has been investigated to face the problem of separation and synchronization the design strategy is based on linear matrix inequalities lmis indeed the lmi problem is referred to have a solution if a dual optimization problem admits a solution in our case the feasibility condition if it does exist allows us to establish that the separation and synchronization problem for the chosen circuit admits a solution some numerical simulations are reported further results refer to an experimental circuit showing the suitability of the approach furthermore the use of the proposed scheme to transmit two or more information masked into two or more multiplexed chaotic signals and the design of suitable parameters through the introduced technique based on lmis are discussed

controllability and observability of boolean control networks with time variant delays in states this brief investigates the controllability and observability of boolean control networks with not necessarily bounded time variant delays in states after a brief introduction to converting a boolean control network to an equivalent discrete time bilinear dynamical system via the semi tensor product of matrices the system is split into a finite number of subsystems constructed forest with no time delays by using the idea of splitting time that is proposed in this brief then the controllability and observability of the system are investigated by verifying any so called controllability constructed path and any so called observability constructed paths in the above forest respectively which generalize some recent relevant results matrix test criteria for the controllability and observability are given the corresponding control design algorithms based on the controllability theorems are given we also show that the computing complexity of our algorithm is much less than that of the existing algorithms

fixed parameter tractability and completeness ii on completeness for w 1 abstract for many fixed parameter problems that are trivially solvable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is solvable in time bounded by a polynomial of degree c where c is a constant independent of k in a previous paper the w hierarchy of parameterized problems was defined and complete problems were identified for the classes w t for t 2 our main result shows that independent set is complete for w 1

parameterized complexity in multiple interval graphs domination partition separation irredundancy we show that the problem k dominating set and its several variants including k connected dominating set k independent dominating set and k dominating clique when parameterized by the solution size k are w 1 hard in either multiple interval graphs or their complements or both on the other hand we show that these problems belong to w 1 when restricted to multiple interval graphs and their complements this answers an open question of fellows et al in sharp contrast we show that d distance k dominating set for d 2 is w 2 complete in multiple interval graphs and their complements we also show that k perfect code and d distance k perfect code for d 2 are w 1 complete even in unit 2 track interval graphs in addition we present various new results on the parameterized complexities of k vertex clique partition and k separating vertices in multiple interval graphs and their complements and present a very simple alternative proof of the w 1 hardness of k irredundant set in general graphs

set stability and set stabilization of boolean control networks based on invariant subsets this study addresses the set stability of boolean networks bns and set stabilization of boolean control networks bcns set stability determines whether a bn converges to a given subset whereas set stabilizability addresses the issue of whether a bcn can be stabilized to a given subset many problems can be viewed as special cases of set stability and set stabilization including synchronization partial stability and partial stabilization problems the concepts of invariant subset and control invariant subset are introduced then algorithms for the largest invariant subset and the largest control invariant subset contained in a given subset are proposed based on the invariant subsets obtained the necessary and sufficient conditions for set stability and set stabilizability are established and formulae are provided to calculate the shortest transient periods for respective initial states a design procedure is proposed for finding all the time optimal set stabilizers finally an example is used to show the application of the proposed results to the synchronization problem of bns

mim width iii graph powers and generalized distance domination problems abstract we generalize the family of problems and locally checkable vertex partition problems to their distance versions which naturally captures well known problems such as distance r dominating set and distance r independent set we show that these distance problems are in xp parameterized by the structural parameter mim width and hence polynomial time solvable on graph classes where mim width is bounded and quickly computable such as k trapezoid graphs dilworth k graphs circular permutation graphs interval graphs and their complements convex graphs and their complements k polygon graphs circular arc graphs complements of d degenerate graphs and h graphs if given an h representation we obtain these results by showing that taking any power of a graph never increases its mim width by more than a factor of two to supplement these findings we show that many classes of problems are w 1 hard parameterized by mim width solution size we show that powers of graphs of tree width w 1 or path width w and powers of graphs of clique width w have mim width at most w these results provide new classes of bounded mim width we prove a slight strengthening of the first statement which implies that surprisingly leaf power graphs which are of importance in the field of phylogenetic studies have mim width at most 1

synchronization of kauffman networks we analyze the synchronization transition for a pair of coupled identical kauffman networks in the chaotic phase the annealed model for kauffman networks shows that synchronization appears through a transcritical bifurcation and provides an approximate description for the whole dynamics of the coupled networks we show that these analytical predictions are in good agreement with numerical results for sufficiently large networks and study finite size effects in detail preliminary analytical and numerical results for partially disordered networks are also presented