A directed path in a digraph is proper if any two consecutive arcs on the path have distinct colors. An arc-colored digraph D is proper connected if for any two distinct vertices x and y of D, there are both proper (x,y)-directed paths and proper (y,x)-directed paths in D. The proper connection number pc→(D) of a digraph D is the minimum number of colors that can be used to make D proper connected

We revisit the Learning Sparse Parities with Noise (LSPN) problem on k out of n variables for k≪n, and present the following findings. 1. For true parity size k=nu for any 0

We present ⦇λ⦈, a calculus with special constructions for dealing with effects and handlers. This is an extension of the simply-typed λ-calculus (STLC). We enrich STLC with a type for representing effectful computations alongside with operations to create and process values of this type. The calculus is motivated by natural language modelling, and especially semantic representation. Traditionally,

We consider opinion diffusion on social graphs where agents hold opinions and where social pressure leads them to conform to the opinion manifested by the majority of their neighbors. Within this setting, we look for dynamics that allows us to maximize the diffusion of a target opinion given the initial opinions of all agents. In particular, we focus on the setting where more than two opinions are

There is a lot of research on probabilistic transition systems. There are not many studies in probabilistic process models. The lack of investigation into the interactive aspect of probabilistic processes is mainly due to the difficulty caused by the discrepancy between probabilistic choices and nondeterministic actions. The paper proposes a uniform approach to probabilistic process models and a bisimulation

The Fibonacci cube is the subgraph of the hypercube induced by the vertices whose binary string representations do not contain two consecutive 1s. These cubes was presented as an alternative interconnection network. In this paper, we calculate the number of induced paths and cycles of small length in Fibonacci cubes by using the recursive structure of these graphs.

A recent trend in algorithm design consists of augmenting classic data structures with machine learning models, which are better suited to reveal and exploit patterns and trends in the input data so to achieve outstanding practical improvements in space occupancy and time efficiency. This is especially known in the context of indexing data structures for big data where, despite few attempts in evaluating

In this paper, we propose an algorithm which approximates the Two-Sided Scaffold Filling problem to a better performance ratio of 1.4+ε. This is achieved through a deep investigation of the optimal solution structure of Two-Sided Scaffold Filling. We make use of a relevant graph aiming at a solution of a Two-Sided Scaffold Filling instance, and evaluate the optimal solution value by the number of connected

The Min Anonymous-Edge-Rotation problem asks for an input graph G and a positive integer k to find a minimum number of edge rotations that transform G into a graph such that for each vertex there are at least k−1 other vertices of the same degree (a k-degree-anonymous graph). In this paper, we prove that the Min Anonymous-Edge-Rotation problem is NP-hard even for k=n/q, where n is the order of a graph

The maximum/minimum bisection problems are, given an edge-weighted graph, to find a bipartition of the vertex set into two sets whose sizes differ by at most one, such that the total weight of edges between the two sets is maximized/minimized. Although these two problems are known to be NP-hard, there is an efficient algorithm for bounded-treewidth graphs. In particular, Jansen et al. (SIAM J. Comput

Given a graph G=(V,E) with a vertex ordering ≺, the fixed-order book thickness problem asks whether there is a page assignment σ such that 〈≺,σ〉 is a k-page book embedding of G. This problem is NP-complete even for any fixed k greater than 3. Recently, Bhore et al.(GD 2019; J. Graph Algorithms Appl. 2020) presented a parameterized algorithm with respect to the pathwidth κ of the vertex ordering. In

Prefetching constitutes a valuable tool toward the goal of efficient Web surfing. As a result, estimating the amount of resources that need to be preloaded during a surfer's browsing becomes an important task. In this regard, prefetching can be modeled as a two-player combinatorial game [Fomin et al., Theoretical Computer Science 2014], where a surfer and a marker alternately play on a given graph

A rectangular floorplan (RFP) is a partition of a rectangle R into rectangles R1,R2,…,Rn such that no four of them meet at a point. Rectangular floorplans find their applications in VLSI circuits floorplanning and architectural floorplanning. Let G represent the graph of a rectangular floorplan RFP1(n) and H be a subgraph of G, where n denotes the number of rectangles in RFP1(n). It is well known that

In this paper, we propose a simple and intuitive model to investigate the efficiency of the two-party election system, especially regarding the nomination process. Each of the two parties has its own candidates, and each of them brings utilities for the people including the supporters and non-supporters. In an election, each party nominates exactly one of its candidates to compete against the other

In this paper, we consider the submodular edge cover problem with submodular penalties. In this problem, we are given an undirected graph G=(V,E) with vertex set V and edge set E. Assume the covering cost function c:2E→R+ and the penalty function p:2V→R+ are both submodular with p non-decreasing, c(∅)=0 and p(∅)=0. The goal of the submodular edge cover problem with submodular penalties is to select

We study a revenue maximization problem in the context of social networks. Namely, we generalize a model introduced by Alon, Mansour, and Tennenholtz [2] that captures inequity aversion, i.e., it captures the fact that prices offered to neighboring nodes should not differ significantly. We first provide approximation algorithms for a natural class of instances, where the total revenue is the sum of

Notions of guardedness serve to delineate admissible recursive definitions in various settings in a compositional manner. In recent work, we have introduced an axiomatic notion of guardedness in symmetric monoidal categories, which serves as a unifying framework for various examples from program semantics, process algebra, and beyond. In the present paper, we propose a generic metalanguage for guarded

Let Gn be an n-dimensional recursive network. A set F⊂V(Gn) (resp. F⊂E(Gn)) is called a t-embedded vertex cut (resp. t-embedded edge cut) of Gn if Gn−F is disconnected and each vertex of which lies in a t-dimensional subnetwork of Gn−F. The t-embedded vertex connectivity ζt(Gn) (resp. t-embedded edge connectivity ηt(Gn)) of Gn is the minimum cardinality over all t-embedded vertex cuts (resp. t-embedded

Context-free grammars are not able to capture cross-serial dependencies occurring in some natural languages. To overcome this issue, Seki et al. introduced a generalization called m-multiple context-free grammars (m-MCFGs), which deal with m-tuples of strings. We show that m-MCFGs are capable of comparing the number of consecutive occurrences of at most 2m different letters. In particular, the language

Given a graph G of n vertices and an integer k, the Dual Coloring problem determines if G is (n−k)-colorable, i.e., if we can color vertices of G with at most n−k colors so that every vertex obtains exactly one color and every two adjacent vertices have different colors. We derive a kernelization for the Dual Coloring problem with respect to the parameter k. In particular, for any fixed ϵ>0, our kernelization

In social advertising, the social platform host may run marketing campaigns for multiple competing clients simultaneously. In this case, each client comes up with a budget and an influence spread requirement. The host runs campaigns by allocating a set of seed nodes for each client. If the influence spread triggered by a seed set meets the requirement, the host can earn the budget from the corresponding

We initiate the systematic algorithmic study for gerrymandering over graphs that was recently introduced by Cohen-Zemach, Lewenberg and Rosenschein. Namely, we study a strategic procedure for a political districting designer to draw electoral district boundaries so that a particular target candidate can win in an election. We focus on the existence of such a strategy under the plurality voting rule

Time-evolving or temporal graphs gain more and more popularity when exploring complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one studies the different (time) layers of a temporal graph (effectively meaning that the edge set may change over time, but the vertex set remains unchanged), and one searches for

We give an improved lower bound of 10/3 on the competitive ratio for the exploration of an undirected, edge-weighted graph with a single agent that needs to return to the starting location after visiting all vertices. We assume that the agent has full knowledge of all edges incident to visited vertices, and, in particular, vertices have unique identifiers. Our bound improves a lower bound of 2.5 by

We consider the problem of collectively delivering a package from a specified source to a designated target location in a graph, using multiple mobile agents. Each agent starts from some vertex of the graph; it can move along the edges of the graph and can pick up the package from a vertex and drop it in another vertex during the course of its movement. However, each agent has limited energy budget

The study of the degree sequences of k-uniform hypergraphs, usually called k-sequences, has been a longstanding open problem for the case of k>2, and the corresponding decision version was proved to be NP-complete recently in 2018 [15]. The problem can be formalized as follows: Given a non decreasing sequence of positive integers π=(d1,d2,…,dn), can π be the degree sequence of a k-uniform simple hypergraph

We investigate a two player scenario, in which a decision maker locates some facilities in a network, while a second player, called the interdictor, may disrupt the infrastructure by deleting some edges in the network in order to worsen the first player's objective value. For the case that the locational decision is assessed with the covering objective function, we show that the problem of the interdictor

Snoopy is a powerful modelling and simulation tool for various types of Petri nets, which have been applied to a wide range of biochemical reaction networks. We present an enhanced version of Snoopy, now supporting coloured and uncoloured stochastic, continuous and hybrid Petri Nets with fuzzy kinetic parameters. Colour helps to cope with modelling challenges imposed by larger and more complex networks

Given a graph G=(V,E), a subset S⊆V(G) is said to be a feedback vertex set of G if G−S is a forest. In the Feedback Vertex Set (FVS) problem, we are given an undirected graph G, and a positive integer k, the question is whether there exists a feedback vertex set of size at most k. In this paper, we study three variants of the FVS problem: Unrestricted Fair FVS, Restricted Fair FVS, and Relaxed Fair

We address in this paper the two-machine open shop problem with set-up time considerations to build schedules that minimize the overall completion time, known as the makespan. In the model we are considering, the set-up, handled by a single server, consists of a preparation phase separated from the processing phase. Once the server completes the preparation of a job, it becomes again available for

We consider the classical problems (Edge) Steiner Tree and Vertex Steiner Tree after restricting the input to some class of graphs characterized by a small set of forbidden induced subgraphs. We show a dichotomy for the former problem restricted to (H1,H2)-free graphs and a dichotomy for the latter problem restricted to H-free graphs. We find that there exists an infinite family of graphs H such that

Given n data points in Rd, an appropriate edge-weighted graph connecting the data points finds application in solving clustering, classification, and regression problems. The graph proposed by Daitch, Kelner and Spielman (ICML 2009) can be computed by quadratic programming and hence in polynomial time. While a more efficient algorithm would be preferable, replacing quadratic programming is challenging

We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of n data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the actual value, and we may allow an error threshold in the sorting. The goal is to find a nearly-sorted permutation by performing a minimum-cost set of queries. We show that

A new metric parameter for a graph, Helly-gap, is introduced. A graph G is called α-weakly-Helly if any system of pairwise intersecting disks in G has a nonempty common intersection when the radius of each disk is increased by an additive value α. The minimum α for which a graph G is α-weakly-Helly is called the Helly-gap of G and denoted by α(G). The Helly-gap of a graph G is characterized by distances

A graph is fan-crossing free if it has a drawing in the plane so that each edge is crossed by independent edges, that is the crossing edges have distinct vertices. On the other hand, it is fan-crossing if the crossing edges have a common vertex, so that they form a fan. Both are prominent examples for beyond-planar graphs. Further well-known beyond-planar classes are the k-planar, k-gap-planar, quasi-planar

The theory of finite automata and rational semiring elements is reconsidered in the setting of summation semirings, traditionally known as Σ-semirings. These generalise complete semirings by allowing infinite sums to be defined just for selected families of elements. A relation of the presented approach to the theory of finite automata over partial Conway semirings is discussed. Equivalence of finite

Occurrences of a factor w in an infinite uniformly recurrent sequence u can be encoded by an infinite sequence over a finite alphabet. This sequence is usually denoted du(w) and called the derived sequence to w in u. If w is a prefix of a fixed point u of a primitive substitution φ, then by Durand's result from 1998, the derived sequence du(w) is fixed by a primitive substitution ψ as well. For a non-prefix

It is important to find ride matches for individuals who participate in ridesharing quickly, and it is equally important to minimize the number of drivers to serve all individuals and minimize the total travel distance of the vehicles. This paper considers the following ridesharing problem: given a set of trips, each trip consists of an individual, a vehicle of the individual and some requirements

The problem of partitioning a large complex network equitably into sparse modules with given rules can be modeled by the equitable list d-degenerate coloring of graphs. This paper establishes theoretical results on such a coloring based on a newly proposed conjecture which states that every graph G is equitably d-degenerate k-colorable and equitably k-choosable for every integer k≥(Δ(G)+1)/(d+1). This

The concept of proxy re-encryption (PRE) dates back to the work of Blaze, Bleumer, and Strauss in 1998. PRE offers delegation of decryption rights, i.e., it securely enables the re-encryption of ciphertexts from one key to another, without relying on trusted parties. PRE allows a semi-trusted third party termed as a “proxy” to securely divert encrypted files of user A (delegator) to user B (delegatee)

The classical Erdös-Gallai theorem (1960) kicked off the study of graph realizability by characterizing degree sequences. We extend this line of research by investigating realizability of directed acyclic graphs (DAGs) given a sequence of tuples each containing multiple node properties including the degree, reachability value (number of nodes reachable from a given node), depth and height of a node

We provide a reformulation and a formalization of the classical result by Juhani Karhumäki characterizing intersections of two languages of the form {x,y}⁎∩{u,v}⁎. We use the terminology of morphisms which allows to formulate the result in a shorter and more transparent way, and we formalize the result in the proof assistant Isabelle/HOL.

Given a (finite or infinite) subset X of the free monoid A⁎ over a finite alphabet A, the rank of X is the minimal cardinality of a set F such that X⊆F⁎. We say that a submonoid M generated by k elements of A⁎ is k-maximal if there does not exist another submonoid generated by at most k words containing M. We call a set X⊆A⁎ primitive if it is the basis of a |X|-maximal submonoid. This definition encompasses

For graphs F, G and H, let F→(G,H) signify that any red/blue edge coloring of F contains either a red G or a blue H. The Ramsey number R(G,H) is defined to be the minimum r such that Kr→(G,H), and the star-critical Ramsey number RS(G,H) is defined to be the maximum t such that Kr∖K1,t→(G,H), where r=R(G,H). In this note, we shall determine RS(Bn,Cm) for almost same orders.

The touring rays problem, which is also known as the traveling salesman problem for rays in the plane, asks to compute the shortest (closed) route that tours or intersects n given rays. We show that it can be reduced to the problem of computing a shortest route that intersects a set of ray-segments, inside a circle; at least one endpoint of every ray-segment is on the circle. Moreover, computing the

For a rational number r such that 1

A factor C of a string S is called a cover of S, if each position of S is contained in an occurrence of C. Breslauer (1992) [3] proposed a well-known O(n)-time algorithm that computes the shortest cover of every prefix of a string of length n. We show an O(nlog⁡n)-time and O(n)-space algorithm that computes the shortest cover of every cyclic shift of a string of length n and an O(n)-time algorithm

We give approximation algorithms for matching two sets of line segments in constant dimension. We consider several versions of the problem: Hausdorff distance, bottleneck distance and largest common subset. We study these similarity measures under several sets of transformations: translations in arbitrary dimension, rotations about a fixed point and rigid motions in two dimensions. As opposed to previous

In this paper, we revisit the r-gathering problem. Given sets C and F of points on the plane and distance d(c,f) for each c∈C and f∈F, an r-gathering of C to F is an assignment A of C to open facilities F′⊆F such that r or more members of C are assigned to each open facility. The cost of an r-gathering is maxc∈C⁡d(c,A(c)). The r-gathering problem computes the r-gathering minimizing the cost. In this

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, “beyond worst-case analysis” of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many optimization problems are essentially a discrete metric space. Probabilistic

In this paper we study the approximability of the Maximum Happy Set problem (MaxHS) and the computational complexity of MaxHS on graph classes: For an undirected graph G=(V,E) and a subset S⊆V of vertices, a vertex v is happy if v and all its neighbors are in S; otherwise unhappy. Given an undirected graph G=(V,E) and an integer k, the goal of MaxHS is to find a subset S⊆V of k vertices such that the

We study the k-center problem in a kinetic setting: given a set of continuously moving points P in the plane, determine a set of k (moving) disks that cover P at every time step, such that the disks are as small as possible at any point in time. Whereas the optimal solution over time may exhibit discontinuous changes, many practical applications require the solution to be stable: the disks must move

Energy efficiency is a crucial desideratum in the design of computer systems, from small-sized mobile devices with limited battery to large scale data centers. In such computing systems, processors and memory are considered as two major power consumers among all the system components. One recent trend to reduce power consumption is using shared memory in multi-core systems, such architecture has become

The exploration of one-factorizations of complete graphs is the foundation of some classical sports scheduling problems. One has to traverse the landscape of such one-factorizations by moving from one of those to a so-called neighbor one-factorization. This approach amounts to modifying locally the coloring associated with a one-factorization. We consider some particular types of modifications and

We study the problem of finding a minimal edge dominating set of maximum size in a given graph G=(V,E), called Upper EDS. We show that this problem is not approximable within a ratio of nε−12, for any ε∈(0,12), assuming P≠NP, where n=|V|. On the other hand, for graphs of minimum degree at least 2, we give an approximation algorithm with ratio 1n, matching this lower bound. We further show that Upper

Consider a discrete-time process on a graph G where a set B of initial vertices are chosen to be colored blue (the remainder being white) and then a time step consists of every currently blue vertex forcing all of its neighbors to become blue; this process stops when every vertex of the graph is blue, and the process is called full forcing. The full throttling number of G is then defined to be the

In a cardinality constrained inverse center location problem on networks, the goal is to modify the edge lengths at the minimum total cost subject to the given modification bounds so that a prespecified vertex becomes an absolute center location of the underlying network under the perturbed edge lengths and further the cardinality of the modified edge lengths obeys an upper bound. Using a set of self-constructed

For any integer k>2, the infinite k-bonacci word W(k), on the infinite alphabet is defined as the fixed point of the morphism φk:N⁎→N⁎, starting with 0, whereφk(ki+j)={(ki)(ki+j+1)if j=0,…,k−2,(ki+j+1)if j=k−1. We obtain the structure of all square factors occurring in W(k). Moreover, we prove that the critical exponent of W(k) is 3−32k−1. Finally, we provide all critical factors of W(k).

A subset S⊆V(G) is a disjunctive total dominating set if each vertex has a neighbor in S or has at least two vertices in S at distance two from it. The disjunctive total domination number γtd(G) is the minimum cardinality of a disjunctive total dominating set in G. Disjunctive total bondage number, btd(G), of a graph G with no isolated vertex is defined as the minimum cardinality of edge set B⊆E(G)

Attribute-based proxy re-encryption (ABPRE), which combines the notions of proxy re-encryption (PRE) and attribute-based encryption (ABE), allows a semi-trusted proxy to transform a ciphertext under a particular access-policy into a ciphertext under another access policy, without revealing any information about the underlying plaintext. This primitive is very useful in some applications, where encrypted