Because edge modification problems are computationally difficult for most target graph classes, considerable attention has been devoted to inclusion-minimal edge modifications, which are usually polynomial-time computable and which can serve as an approximation of minimum cardinality edge modifications, albeit with no guarantee on the cardinality of the resulting modification set. Over the past fifteen

Rotation symmetric Boolean functions are potentially rich in functions of cryptographic significance. In this paper, a new construction of odd-variable rotation symmetric Boolean functions with optimal algebraic immunity is presented. By a direct calculation, the nonlinearity of the newly constructed functions is higher than the nonlinearities of all the known odd-variable rotation symmetric Boolean

The Maximum Vertex Coverage problem (abbreviated as MVC) is to maximum the number of edges covered by a set of vertices of size exactly K on a graph. This problem is the dual of the vertex cover problem and has attracted a lot of interests in the literature of approximation algorithm. So far, the best approximation factor for the MVC problem is 3/4, which is obtained using an LP-rounding method. The

Secret sharing allows a dealer to distribute a secret among a set of parties such that only authorized subsets, specified by an access structure, can reconstruct the secret. Sehrawat and Desmedt (COCOON 2020) introduced hidden access structures, that remain secret until some authorized subset of parties collaborate. However, their scheme assumes semi-honest parties and supports only restricted access

We study the decomposition of multivariate polynomials as sums of powers of linear forms. As one of our main results, we give a randomized algorithm for the following problem: given a homogeneous polynomial f(x1,…,xn) of degree 3, decide whether it can be written as a sum of cubes of linearly independent linear forms with complex coefficients. Compared to previous algorithms for the same problem, the

We introduce the class of modified Schelling games in which there are different types of agents who occupy the nodes of a location graph; agents of the same type are friends, and agents of different types are enemies. Every agent is strategic and jumps to empty nodes of the graph aiming to maximize her utility, defined as the ratio of her friends in her neighborhood over the neighborhood size including

High fault tolerance and reliability of multiprocessor systems, modeled by interconnection network, are of great significance to assess the flexibility and effectiveness of the systems. Connectivity is an important metric to evaluate the fault tolerance and reliability of interconnection networks. As classical connectivity is not suitable for such large scale systems, a novel and generalized connectivity

Hierarchical identity-based encryption (HIBE) can be extended to revocable HIBE (RHIBE) if a private key of a user can be revoked when the private key is revealed or expired. Previously, many selectively secure RHIBE schemes were proposed, but it is still unsolved problem to construct an adaptively secure RHIBE scheme. In this work, we propose two RHIBE schemes in composite-order bilinear groups and

We consider the scheduling model with two identical machines and jobs which arrive online in a list and are assigned to the machines with the objective of minimizing the makespan. Differently from the pure online version, we know in advance a lower bound and also an upper bound on the total size of all jobs. Our algorithm improves previous results on some interval of r, where r is the ratio of the

V-order is a total order on strings that determines an instance of Unique Maximal Factorization Families (UMFFs), a generalization of Lyndon words. The fundamental V-comparison of strings can be done in linear time and constant space. V-order has been proposed as an alternative to lexicographic order (lexorder) in the computation of suffix arrays and in the suffix-sorting induced by the Burrows-Wheeler

Magnetic Resonance Imaging (MRI) is a widely used medical diagnosis technique. However, the quality of MR image is affected by the noise which is caused by mechanical and environmental reasons during the MR image acquisition process. For decades, various kinds of methods including filtering approaches, transform domain approaches and statistical approaches have been applied to the MR image denoising

Smart contracts are currently en vogue, thanks to the infrastructure provided by the blockchain technology. However, their effective use requires that the textual (legalese) specification of the contract be accompanied by a precise computational definition of the actions leading to its satisfaction or breach, as well as of their admissible sequences. Insofar as contracts can be viewed as prescribing

Research in the area of secure multi-party computation using a deck of playing cards, often called card-based cryptography, started from the introduction of the five-card trick protocol to compute the logical AND function by den Boer in 1989. Since then, many card-based protocols to compute various functions have been developed. In this paper, we propose two new protocols that securely compute the

A t/s-diagnosable system refers to such a system that all the faulty nodes of the system can be isolated within a set of size at most s in the presence of at most t faulty nodes. Moreover, it increases the allowed faulty nodes, hence enhancing the diagnosability of the system. We can find that the t/s-diagnosability of n-dimensional folded hypercube FQn has not been studied under the PMC model and

In this paper, we advocate the use of setwise contests for aggregating a set of input rankings into an output ranking. We propose a generalization of the Kemeny rule where one minimizes the number of k-wise disagreements instead of pairwise disagreements (one counts 1 disagreement each time the top choice in a subset of alternatives of cardinality at most k differs between an input ranking and the

The problem of dispersion of mobile robots on a graph asks that n robots initially placed arbitrarily on the nodes of an n-node anonymous graph, autonomously move to reach a final configuration where exactly each node has at most one robot on it. This problem is of significant interest due to its relationship to other fundamental robot coordination problems, such as exploration, scattering, load balancing

Given a vertex-colored graph, we say a path is a rainbow vertex path if all its internal vertices have distinct colors. The graph is rainbow vertex-connected if there is a rainbow vertex path between every pair of its vertices. In the Rainbow Vertex Coloring (RVC) problem we want to decide whether the vertices of a given graph can be colored with at most k colors so that the graph becomes rainbow vertex-connected

This work is devoted to the study of the Balanced Connected Subgraph Problem (BCS) from a complexity, inapproximability and approximation point of view. The input is a graph G=(V,E), with each vertex having been colored, “red” or “blue”; the goal is to find a maximum connected subgraph G′=(V′,E′) from G that is color-balanced (having exactly |V′|/2 red vertices and |V′|/2 blue vertices). This problem

A maximal repetition, or run, in a string, is a maximal periodic substring whose smallest period is at most half the length of the substring. In this paper, we consider runs that correspond to a path on a trie, or in other words, on a rooted edge-labeled tree where each edge is labeled with a single symbol, and the endpoints of the path must be a descendant/ancestor of the other. For a trie with n

The elegance of the single-pushout (SPO) approach to graph transformations arises from substituting total morphisms by partial ones in the underlying category. SPO's applicability depends on the durability of pushouts after this transition. There is a wide range of work on the question when pushouts exist in categories with partial morphisms starting with the pioneering work of Löwe and Kennaway and

An incidence of a graph G is a vertex-edge pair (v,e) such that the vertex v is incident with the edge e. A proper incidence k-coloring of a graph is a coloring of its incidences involving k colors so that two incidences (u,e) and (w,f) receive distinct colors if and only if u=w, or e=f, or uw∈{e,f}. In this paper, we present some idea of using the incidence coloring to model a kind of multi-frequency

The Maximum Weight Independent Set (MWIS) problem on finite undirected graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum weight sum. MWIS is one of the most investigated and most important algorithmic graph problems; it is well known to be NP-complete, and it remains NP-complete even under various strong restrictions such as for triangle-free graphs. Its complexity

We introduce the game influence, a scoring combinatorial game, played on a directed graph where each vertex is either colored black or white. The two players, Black and White, play alternately by taking a vertex of their color and all its successors (for Black) or all its predecessors (for White). The score of each player is the number of vertices he has taken. We prove that influence is a nonzugzwang

This paper concerns the behavior of an SINR diagram of wireless systems, composed of a set S of n stations embedded in Rd, when restricted to the corresponding Voronoi diagram imposed on S. The diagram obtained by restricting the SINR zones to their corresponding Voronoi cells is referred to hereafter as an SINR+Voronoi diagram. Uniform SINR diagrams, where all stations transmit with the same power

The red-blue median problem considers a set of red facilities, a set of blue facilities, and a set of clients located in some metric space. The goal is to open kr red facilities and kb blue facilities such that the sum of the distance from each client to its nearest opened facility is minimized, where kr, kb≥0 are two given integers. Designing approximation algorithms for this problem remains an active

Universal locally testable codes (universal-LTCs), recently introduced in our companion paper (CJTCS, 2018), are codes that admit local tests for membership in numerous subcodes, allowing for testing properties of the encoded message. Unfortunately, universal-LTCs suffer strong limitations, which motivate us to initiate, in this work, the study of the “NP analogue” of these codes, wherein the testing

Recently, an innovative hypercube-variant network called bicube, denoted as BQn, has been proposed to possess both short diameter and symmetry advantages. Unlike other existing hypercube-variant networks, they lose their symmetry in pursuit of short diameters. For solving the problems of fault-tolerant transmission and secure message distribution in a reliable network, one solution suggested a dual-CIST

Abstract interpretation was proposed for predicting changes of reaction networks with partial kinetic information in systems biology. This requires to compute the set of difference abstractions of a system of linear equations under nonlinear constraints. We present the first practical algorithm that can compute the difference abstractions of linear equation systems exactly. We also present a new heuristics

We show that the CNF satisfiability problem can be solved in O⁎(1.2226m) time, where m is the number of clauses in the formula, improving the known upper bounds O⁎(1.234m) given by Yamamoto 15 years ago and O⁎(1.239m) given by Hirsch 22 years ago. By using an amortized technique and careful case analysis, we successfully avoid the bottlenecks in previous algorithms and get the improvement.

This paper investigates a novel RSA-like cryptosystem proposed by Murru-Saettone. This cryptosystem is constructed from a cubic field connected to the cubic Pell equation and Redei rational functions. The scheme is claimed to be secure against the Wiener-type attack. However, in this paper, we show a Wiener-type attack that can recover the secret key from the continued fraction constructed from public

The Nearest neighbour search (NNS) is a fundamental problem in many application domains dealing with multidimensional data. In a concurrent setting, where dynamic modifications are allowed, a linearizable implementation of the NNS is highly desirable. This paper introduces the LockFree-kD-tree (LFkD-tree ): a lock-free concurrent kD-tree, which implements an abstract data type (ADT) that provides the

In this paper, we propose the notion of adaptive all-but-one lossy trapdoor functions (aABO-LTFs), a variant of all-but-one lossy trapdoor functions. An aABO-LTF is parameterised by a set of branches. Given the lossy branch, the function statistically loses the information of its inputs. Given injective branches, the function is injective, and there is a trapdoor that enables efficient function inversion

In this paper, we study the problem of finding read-once refutations (ROR) of linear feasibility in a specialized class of constraint systems called UTVPI+ constraint systems (UCS+). The refutations in this paper are analyzed using the ADD inference rule. Recall that a Unit Two Variable per Inequality (UTVPI) constraint is a constraint of the form ai⋅xi+aj⋅xj≤b, where b∈Z, and ai,aj∈{0,1,−1}. A conjunction

The block reversal of a word is a generalization of the concept of reversal of a word where in place of reversing individual letters, we take the blocks of the word in the reverse order. Since there can be multiple ways in which a word can be divided into blocks, the block reversal of a word forms a set. We study some properties of the block reversal of a word. We characterize words that have the same

This paper introduces a new communication abstraction, called Set-Constrained Delivery Broadcast (SCD-broadcast), whose aim is to provide its users with an appropriate abstraction level when they have to implement objects or distributed tasks in an asynchronous message-passing system prone to process crash failures. This abstraction allows each process to broadcast messages and deliver a sequence of

Consider n identical relocatable sensors, with sensing range r and visibility range 2r, initially placed at arbitrary positions on a line segment barrier; each sensor can detect the presence of an intruder in its sensing range, and is said to cover the portion of the barrier that intersects with its sensing range. Sensors operate in Look-Compute-Move cycles: in a cycle a sensor determines the positions

Cops and Robbers games have been studied for the last few decades in computer science and mathematics. As in general pursuit evasion games, pursuers (cops) seek to capture evaders (robbers); however, players move in turn and are constrained to move on a discrete structure, usually a graph, and know the exact location of their opponent. In 2017, Bonato and MacGillivray [2] presented a general characterization

The graph search problem is the problem of searching for a mobile evader in a dark cave by a group of mobile searchers, where the cave is modeled by an undirected connected graph G. An offline and centralized version of the graph search problem is formalized as a pebble game on G, and has been extensively investigated under the name of the edge search problem. By es(G) we denote the number of pebbles

Chemical reaction networks are a popular formalism for modeling biological processes which supports both a deterministic and a stochastic interpretation based on ordinary differential equations and continuous-time Markov chains, respectively. In most cases, these models do not enjoy analytical solution, thus typically requiring expensive computational methods based on numerical solvers or stochastic

In the allocation problem, asynchronous processors must partition a set of items so that each processor leaves knowing all items exclusively allocated to it. We introduce a new variant of the allocation problem called the assignment problem, in which processors might leave having only partial knowledge of their assigned items. The missing items in a processor's assignment must eventually be announced

As a kind of important soft clustering model, the fuzzy C-means method is widely applied in many fields. In this method, instead of the strict distributive ability in the classical k-means method, all the sample points are endowed with degrees of membership to each center to depict the fuzzy clustering. In this paper, we show that the fuzzy C-means++ algorithm, which introduces the k-means++ algorithm

Calculating the “distance” between two given objects with respect to a designated “editing” operation is a hot research area in bioinformatics, where the “distance” is always defined as the minimum number of the “editing” operations required to transform one object into the other one. One of the famous problems in the area is the Minimum Common String Partition problem, which is the simplified variant

The concept of k-spectrum for genomes is here investigated as a basic tool to analyze genomes. Related spectral notions based on k-mers are introduced with some related mathematical properties which are relevant for informational analysis of genomes. Procedures to generate spectral segmentations of genomes are provided and are tested (under several values of length k for k-mers) on cases of real genomes

Let S be a set of positive integers, and let D be a set of integers larger than 1. The game is an impartial combinatorial game introduced by Sopena (2016), which is played with a single pile of tokens. In each turn, a player can subtract s∈S from the pile, or divide the size of the pile by d∈D, if the pile size is divisible by d. Sopena partially analyzed the games with S=[1,t−1] and D={d} for d≢1(modt)

A subset M⊆E of edges of a graph G=(V,E) is called a matching if no two edges of M share a common vertex. An edge e∈E is said to dominate itself and all other edges adjacent to it. A matching M in a graph G=(V,E) is called a dominating induced matching (d.i.m.) if every edge of G is dominated by edges of M exactly once. The dominating induced matching decide (DIM-Decide) problem asks whether a graph

Rough set theory is a granular computing tool used to deal with ambiguity and uncertainty in information systems. However, many optimization problems in rough sets, such as attribute reduction, are NP-hard problems, and most of the algorithms for these problems are greedy. As a complex mathematical structure, matroids provide a powerful tool for solving combinatorial optimization problems related to

Firing Squad Synchronisation on Cellular Automata is the dynamical synchronisation of finitely many cells without any prior knowledge of their range. This can be conceived as a signal with an infinite speed. Most of the proposed constructions naturally translate to the continuous setting of signal machines and generate fractal figures with an accumulation on a horizontal line, i.e. synchronously, in

Given a set F of k disjoint monotone orthogonal polygons with a total of m vertices, we present bounds on the number of vertex guards required to guard the free space and the boundaries of the polygons in F when the range of vision of each guard is bounded by 180∘ (the region in front of the guard). When the orthogonal polygons are axis aligned we prove that m2+⌊k4⌋+4 vertex guards are always sufficient

Let G=(V(G),E(G)) be a simple connected graph. For any two distinct vertices u and v, d(u,v) represents the distance between u and v. Suppose k be any positive integer with 1⩽k⩽diam(G), where the diam(G) represents the diameter of G. A radio k-labeling of G is a mapping f:V(G)→{0,1,2,…} such that |f(u)−f(v)|⩾k+1−d(u,v) for each pair of distinct vertices u and v of G. The absolute difference of the

The logic of DNA molecules is explained as a consequence of their main functions: efficiently duplicating polymers conveying enormous quantities of biological information with minimal spatial occupancy. An abstract model is provided, where monomers are represented by triangles, that was materialized by means of a 3D printer.

The competitive facility location problem is the problem of determining facility locations involving multiple players to optimize their various gains. The Voronoi game is a competitive facility location problem on a given arena played by two players, the server and the adversary. The players alternately take turns, one or more times, to place their facilities in the arena with a predetermined set of

A subset M⊆E of edges of a graph G=(V,E) is called a matching if no two edges of M share a common vertex. A matching M in a graph G is called a uniquely restricted matching if, G[V(M)], the subgraph of G induced by the set of M-saturated vertices of G contains exactly one perfect matching. A uniquely restricted matching M is maximal if M is not properly contained in any uniquely restricted matching

Spiking neural P systems with rules on synapses (RSSNP systems) are a class of computation models which are inspired by the information processing and communication manner of neurons. In this work, we consider labelled RSSNP systems (lRSSNP systems), where each rule is assigned either with a label chosen from an alphabet Σ or with the empty label λ. A string over an alphabet is accepted by an lRSSNP

A family of Markov blankets, if learned purely as a set of subsets of variables, may not be consistent with any Bayesian network. This inconsistency may have a negative impact on Markov blanket-based structure learning. In this paper, we propose checking Markov blanket consistency using graph morality. We define an alternative concept of moral graph – weak recursive simpliciality – without relying

We study rainbow-free colourings of k-uniform hypergraphs; that is, colourings that use k colours but with the property that no hyperedge attains all colours. We show that p⁎=(k−1)(ln⁡n)/n is the threshold function for the existence of a rainbow-free colouring in a random k-uniform hypergraph.

LPN (learning parity with noise) problem is a good candidate for post-quantum cryptography which enjoys simplicity and suitability for weak-power devices. Döttling et al. (ASIACRYPT 2012) initiated the first secure public key encryption (PKE) under the low-noise LPN assumption. Kiltz et al. (PKC 2014) proposed a simpler and more efficient scheme using double-trapdoor technique from the same assumption

Functional encryption (FE), which provides fine-grained access control on encrypted data, is becoming a new hot spot in the field of cryptography. It especially shows great feasibility to construct indistinguishability obfuscation and reuseable garbled circuits. Recent applications, such as outsourcing computation, searchable encryption and so on, suggest that FE has unlimited possibilities. Furthermore

An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic edge coloring conjecture by Fiamčik (1978) and Alon, Sudakov and Zaks (2001) states that every simple graph with maximum degree Δ is acyclically edge (Δ+2)-colorable. Despite many milestones, the conjecture remains open even for planar graphs. In this paper, we confirm affirmatively

Balanced Stable Marriage (BSM) is a central optimization version of the classic Stable Marriage (SM) problem. We study BSM from the viewpoint of Parameterized Complexity. Informally, the input of BSM consists of n men, n women, and an integer k. Each person a has a (sub)set of acceptable partners, A(a), whom a ranks strictly; we use pa(b) to denote the position of b∈A(a) in a's preference list. The

The complexity classes PPA-k, k≥2, have recently emerged as the main candidates for capturing the complexity of important problems in fair division, in particular Alon's Necklace-Splitting problem with k thieves. Indeed, the problem with two thieves has been shown complete for PPA = PPA-2. In this work, we present structural results which provide a solid foundation for the further study of these classes