Differential privacy is commonly used in the computer science literature as a mathematical definition of privacy for the purpose of quantifying and bounding privacy loss. It induces a preference order over the set of privacy-jeopardizing mechanisms which, in turn, adhere to some properties of this order. We show that a set of five such properties uniquely captures the ordinal implications of prioritizing

A fan is a set of edges with a single common endpoint. A drawing of a graph in the plane is fan-crossing if each edge can only be crossed by edges of a fan. It is fan-planar if, in addition, the common endpoint is on the same side of the crossed edge. A drawing is adjacency-crossing if any two edges are adjacent if they cross the same edge. Then multiple independent crossings are excluded, in which

We study the problem of fairly allocating indivisible goods between groups of agents using the recently introduced relaxations of envy-freeness. We consider the existence of fair allocations under different assumptions on the valuations of the agents. In particular, our results cover cases of arbitrary monotonic, responsive, and additive valuations, while for the case of binary valuations we fully

A set of mobile robots (represented as points) is distributed in the Cartesian plane. The collection contains an unknown subset of byzantine robots which are indistinguishable from the reliable ones. The reliable robots need to gather, i.e., arrive to a configuration in which at the same time, all of them occupy the same point on the plane. The robots are equipped with GPS devices and at the beginning

Basing on the two-player Voronoi game introduced by Ahn et al. [1] and the multi-player diffusion game introduced by Alon et al. [2], we investigate the following one-round multi-player discrete Voronoi game on grids and trees. There are n players playing this game on a graph G=(V,E). Each player chooses an initial vertex from the vertex set of the graph and tries to maximize the size of the nearest

Evolutionary algorithms (EAs) have found many successful real-world applications, where the optimization problems are often subject to a wide range of uncertainties. To understand the practical behaviors of EAs theoretically, there are a series of efforts devoted to analyzing the running time of EAs for optimization under uncertainties. Existing studies mainly focus on noisy and dynamic optimization

We study the mixed approach to fault tolerance in the general context of server assignment in networks. The approach is based on mixing two different existing strategies, namely, reinforcement and backup. The former strategy protects clients by reinforcing the servers assigned to them and making them fault-resistant, possibly at a high cost, while the latter protects clients by assigning to them alternate

It is known that the class of all graphs not containing a graph H as an induced subgraph is cop-bounded if and only if H is a forest whose every component is a path [4]. In this paper, we characterize all sets H of graphs with bounded diameter, such that H-free graphs are cop-bounded. This, in particular, gives a characterization of cop-bounded classes of graphs defined by a finite set of connected

In this paper, we study the minimum (connected) k-bounded-degree node deletion problem (Min(C)kBDND). For a connected graph G, a constant k and a weight function w:V→R+, a vertex set C⊆V(G) is a kBDND-set if the maximum degree of graph G−C is at most k. If furthermore, the subgraph of G induced by C is connected, then C is a CkBDND-set. The goal of MinWkBDND (resp. MinWCkBDND) is to find a kBDND-set

We derive a local criterion for a plane near-triangulated graph to be perfect. It is shown that a plane near-triangulated graph is perfect if and only if it does not contain either a vertex, an edge or a triangle, the neighbourhood of which has an odd hole as its boundary. The characterization leads to an O(n2) algorithm for checking perfectness of plane near-triangulations.

The concept of rainbow connection number of a graph was introduced by Chartrand et al. in 2008. Inspired by this concept, other concepts on colored version of connectivity in graphs were introduced, such as the monochromatic connection number by Caro and Yuster in 2011, the proper connection number by Borozan et al. in 2012, and the conflict-free connection number by Czap et al. in 2018, as well as

In the spherical k-means problem (SKMP), which is a well-studied clustering problem in text mining, we are given an n-point set D in d-dimensional unit sphere Sd, and an integer k≤n. The goal is to find a center subset S⊂Sd with |S|≤k that minimizes the sum of cosine dissimilarity measure for each point in D to the nearest center. We prove that any γ-approximation algorithm for the k-means problem

We present efficient fully persistent B-trees in the I/O model with block size B that support range searches on t reported elements at any accessed version of size n in O(logB⁡n+t/B) I/Os and updates at any accessed version in O(logB⁡n+log2⁡B) amortized I/Os, using O(m/B) disk blocks after m updates. This improves both the query and update I/O-efficiency of the previous fully persistent B-trees of

The t-admissibility problem aims to decide whether a graph G has a spanning tree T in which the distance between any two adjacent vertices of G is at most t. Regarding its optimization version, the smallest t for which G is t-admissible is the stretch index of G, denoted by σT(G). The problem of deciding whether σT(G)≤t, t≥4 is NP-complete and polynomial-time solvable for t=2. However, deciding if

In this note we present a counterexample for a result in [2], where the concept of continuous interval posets (CI-posets for short) was introduced. A CI-poset is a poset in which every nonempty interval [x,y] is a continuous poset (in the restricted order) and the above mentioned result is about continuous functions spaces [X⟶P], where X is a core compact topological space and P is a CI-poset (with

We analyze the computational complexity of the many types of pencil-and-paper-style puzzles featured in the 2016 puzzle video game The Witness. In all puzzles, the goal is to draw a simple path in a rectangular grid graph from a start vertex to a destination vertex. The different puzzle types place different constraints on the path: preventing some edges from being visited (broken edges); forcing some

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

We consider the dynamic graph coloring problem restricted to the class of interval graphs in the incremental and fully dynamic setting. The input consists of a sequence of intervals that are to be either colored, or deleted, if previously colored. For the incremental setting, we consider the well studied optimal online algorithm (KT-algorithm) for interval coloring due to Kierstead and Trotter [1]

We propose a randomized approximation scheme for the Euclidean Steiner Multi Cycle problem which runs in quasilinear time. In this problem, we are given a set of n pairs of points (terminals) T={{ti,ti′}}i=1n in the Euclidean plane, and the objective is to find a collection of cycles of minimum cost such that ti and ti′ belong to a same cycle, for each i∈{1,…,n}. This problem extends the Steiner Cycle

We consider the problem of scheduling jobs with sizes, release times and delivery times on identical parallel batch machines. All machines have the same capacity. Each machine can simultaneously process several jobs as a batch as long as the total size of these jobs does not exceed the capacity. The release time, processing time and delivery time of a batch are defined to be the latest release time

We study the dynamical behavior of additive D-dimensional (D≥1) cellular automata where the alphabet is any finite abelian group. This class of discrete time dynamical systems is a generalization of the systems extensively studied by many authors among which one may list [38], [44], [41]. Among our major contributions, there is the proof that topologically transitive additive D-dimensional cellular

Decreasing sandpiles model the dynamics of configurations where each position i∈N contains a finite number of stacked grains hi, such that hi≥hi+1 (decrease property). Grains move according to a decreasing local rule R=(r1,r2,…,rp) such that rj≥rj+1, meaning that rj grains move from columns i to i+j for all 1≤j≤p, if it does not contradict the decrease property. We are interested in the fixed point

The encryption schemes based on coding theory are one of the most accredited choices in post-quantum scenario, where QC-LDPC codes are usually employed to construct concrete schemes due to the well security and good efficiency. In this work, we introduce a new IND-CCA secure multi-instance framework for code-based hybrid encryption primitive in the random oracle model, which is derived from our new

An Automata Network is a map f:Qn→Qn where Q is a finite alphabet. It can be viewed as a network of n entities, each holding a state from Q, and evolving according to a deterministic synchronous update rule in such a way that each entity only depends on its neighbors in the network's graph, called interaction graph. In this work we introduce the following property called expansivity: the observation

In the Minimum Installation Path problem, we are given a graph G with edge weights w(⋅) and two vertices s,t of G. We want to assign a non-negative power p:V→R≥0 to the vertices of G, so that the activated edges {uv∈E(G)|p(u)+p(v)≥w(uv)} contain some s-t-path, and minimize the sum of assigned powers. In the Minimum Barrier Shrinkage problem, we are given, in the plane, a family of disks and two points

Component (edge) connectivity is a generalization of traditional (edge) connectivity. Let F be a vertex set (resp., an edge set), if G−F has at least g components, F is a g-component (edge) cut. The g-component (edge) connectivity of graph G is the minimum size of the g-component (edge) cut. In this paper, we study the g-component (edge) connectivity of shuffle-cubes for small g.

The divide-and-swap cube network is a new hypercube variant network proposed recently. Compared to hypercube, it keeps the same number of vertices and the same asymptotic performances for fundamental algorithms while reducing the network cost. Connectivity and super connectivity are important indices to measure the reliability of networks. In this work, we get the connectivity and super connectivity

Two vertex-labelled polygons are compatible if they have the same clockwise cyclic ordering of vertices. The definition extends to polygonal regions (polygons with holes) and to triangulations—for every face, the clockwise cyclic order of vertices on the boundary must be the same. It is known that every pair of compatible n-vertex polygonal regions can be extended to compatible triangulations by adding

System families (Software Product Lines) are becoming omnipresent in application areas ranging from embedded system domains to system-level software and communication protocols. Software Product Line methods and architectures allow effective building many custom variants of a software system in these domains. In many of the applications, their rigorous verification and quality assurance are of paramount

We study the problem of online graph exploration on undirected graphs, where a searcher has to visit every vertex and return to the origin. Once a new vertex is visited, the searcher learns of all neighboring vertices and the connecting edge weights. The goal of such an exploration is to minimize its total cost, where each edge traversal incurs a cost of the corresponding edge weight. We investigate

This article introduces a general framework for fault ascription, which consists in identifying, within a multi-component system, the components whose faulty behavior has caused the failure of said system. Our framework uses configuration structures as a general semantical model to handle truly concurrent executions, partial and distributed observations in a uniform way. As a first contribution, and

As a part of the smart urban construction, automated driving is introduced to improve the utilization efficiency of cars and roads, which not only reduces the incidence of traffic accidents, but also improves the environment quality. With the development of the smart urban, it is predictable that, in the city of the future, the service of package pickup and delivery or takeout will be supported mainly

Given two vertices u and v in a connected undirected graph G, a w⁎-container C(u,v) is a set of w internally vertex disjoint paths between u and v spanning all the vertices in G. A bipartite graph G is w⁎-laceable if there exists a w⁎-container between any two vertices belonging to different partitions of G. In [8], [33] a class Bn′ of bipartite graphs called hypercube-like bipartite netwroks was defined

We study the problem of visualizing phylogenetic networks, which are extensions of the Tree of Life in biology. We use a space filling visualization method, called DAGmaps, in order to obtain clear visualizations using limited space. In this paper, we first show that the general problem of drawing galled networks as DAGmaps is NP-complete. Next, we restrict our attention to galled trees and planar

The vertex arboricity va(G) of G is the smallest integer k which the acyclic partition of V(G) make the vertex set V(G) be partitioned into k subsets which each subset induces an acyclic graph. In this paper, we mainly study vertex arboricity of planar graphs, and we prove that if there is without 4-cycles intersecting with 6-cycles, then va(G)⩽2.

A generalized lexicographic order on words is a lexicographic order where the total order of the (possibly infinite) alphabet depends on the position of the comparison. A generalized Lyndon word is a finite word which is strictly smallest among its class of rotations with respect to a generalized lexicographic order. This notion can be extended to infinite words: an infinite generalized Lyndon word

Influence Maximization (IM) over the online social networks have been widely explored in recent years, which selects a seed set from nodes in the network using a limited budget such that the expected number of nodes influenced by the seed set is maximized. However, how to activate a considered set of targeting users T, e.g., selling a product to a specific target group, is a more practical problem

We present the first solution to finding τ-majorities on tree paths. Given a tree of n nodes, each with a label from [1..σ], and a fixed threshold 0<τ<1, such a query gives two nodes u and v and asks for all the labels that appear more than τ⋅|Puv| times in the path Puv from u to v, where |Puv| denotes the number of nodes in Puv. Note that the answer to any query is of size up to 1/τ. On a w-bit RAM

For the game of Cops and Robbers, it is known that in 1-cop-win graphs, the cop can capture the robber in O(n) time, and that there exist graphs in which this capture time is tight. When k≥2, a simple counting argument shows that in k-cop-win graphs, the capture time is at most O(nk+1), however, no non-trivial lower bounds were previously known; indeed, in their 2011 book, Bonato and Nowakowski ask

Generic submodularity ratio γ is a general measurement to characterize how close a nonnegative monotone set function is to be submodular. In this paper, we make a systematic analysis of greedy algorithms for maximizing a monotone and normalized set function with a generic submodularity ratio γ under Cardinality constraints, Knapsack constraints, Matroid constraints and K-intersection constraints.

In this paper, we study the Maximum Happy Vertices and the Maximum Happy Edges problems (MHV and MHE for short). Very recently, the problems attracted a lot of attention and were studied in Agrawal '18, Aravind et al. '16, Choudhari and Reddy '18, Misra and Reddy '18. Main focus of our work is lower bounds on the computational complexity of these problems. Established lower bounds can be divided into

The Markoff equation is the Diophantine equation x2+y2+z2=3xyz. A solution is called a Markoff triple. We give a bijection between the free monoid on two letters and the set of Markoff triples, using the palindromization map of Aldo de Luca. In our construction, special Christoffel words appear, whose lengths are Markoff numbers; we study their standard and palindromic factorizations, and show that

An efficient algorithm for determining the equivalence of two deterministic multitape finite automata is suggested. It is based on an already published proof of solvibility for this problem. It is shown that the suggested algorithm has polynomial complexity. The asymptotic running time of the algorithm is bounded by k⁎sn+1, where k is some constant, n is the number of tapes and s is the sum of the

We consider a cops and robber game where the cops are blocking edges of a graph, while the robber occupies its vertices. At each round of the game, the cops choose some set of edges to block and right after the robber is obliged to move to another vertex traversing at most s unblocked edges (s can be seen as the speed of the robber). Both parts have complete knowledge of the opponent's moves and the

It is a challenging open problem to construct an explicit 1-factorization of the bipartite Kneser graph H(v,t), which contains as vertices all t-element and (v−t)-element subsets of [v]:={1,…,v} (where v>2t) and an edge between any two vertices when one is a subset of the other. In this paper, for the special case where t=2 and v is an odd prime power, we construct such 1-factorizations using perpendicular

In this paper, we study the problem of computing a minimum-width double-strip or parallelogram annulus that encloses a given set of n points in the plane. A double-strip is a closed region in the plane whose boundary consists of four parallel lines and a parallelogram annulus is a closed region between two edge-parallel parallelograms. We present several first algorithms for these problems. Among them

A graph is called a split graph if its vertex set can be partitioned into a clique and an independent set. Split graphs have rich mathematical structure and interesting algorithmic properties making it one of the most well-studied special graph classes. In the Split Vertex Deletion problem, given a graph and a positive integer k, the objective is to test whether there exists a subset of at most k vertices

In this paper, we study the Boolean function parameters sensitivity (s), block sensitivity (bs), and alternation (alt) under specially designed affine transforms and show several applications. For a function f:F2n→{−1,1}, and A=Mx+b for M∈F2n×n and b∈F2n, the result of the transformation g is defined as ∀x∈F2n,g(x)=f(Mx+b). As a warm up, we study alternation under linear shifts (when M is restricted

An RNA secondary structure is designable if there is an RNA sequence which can attain its maximum number of base pairs only by adopting that structure. The combinatorial RNA design problem, introduced by Haleš et al. in 2016, is to determine whether or not a given RNA secondary structure is designable. Haleš et al. identified certain classes of designable and non-designable secondary structures by

For a given graph G, the minimum weight connected-k-subgraph cover problem (MinWCkSC) is to find a minimum weight vertex subset C of G such that each connected subgraph of G on k vertices contains at least one vertex of C. Previously, Zhang et al. [39] presented a (k−1)-approximation algorithm for MinWCkSC under the assumption that the girth of G, which is the length of a shortest cycle of G, is at

We show the undecidability of whether a team has a forced win in a number of well known video games including: Team Fortress 2, Super Smash Brothers: Brawl, and Mario Kart. To do so, we give a simplification of the Team Computation Game from Hearn and Demaine's “Games, Puzzles, and Computation” [7], and use that to give an undecidable abstract game on graphs. This graph game framework better captures

We propose and study the MpUFLP (universal facility location problem in the p-th power of metric space) in this paper, where the universal facility location problem (UFLP) extends several classical facility location problems like the uncapacitated facility location, hard-capacitated facility location, soft-capacitated facility location, incremental-cost facility location, concave-cost facility location

Given a k-coloring of a graph G, a Kempe-change for two colors a and b produces another k-coloring of G, as follows: first choose a connected component in the subgraph of G induced by the two color classes of a and b, and then swap the colors a and b in the component. Two k-colorings are called Kempe-equivalent if one can be transformed into the other by a sequence of Kempe-changes. We consider two

We propose a new method to construct code-based signature scheme following the Lyubashevsky's lattice-based framework. Our technique ensures that the Hamming weight of each row of the private key matrix is below the GV bound instead of fixed weight. Our scheme can generate signatures whose maximum Hamming weight is below the GV bound of random linear codes with the public key matrix as parity-check

Let G be a graph with diameter d. A radio labelling of G is a function f that assigns to each vertex with a non-negative integer such that the following holds for all vertices u,v: |f(u)−f(v)|⩾d+1−d(u,v), where d(u,v) is the distance between u and v. The span of f is the absolute difference of the largest and smallest values in f(V). The radio number of G is the minimum span of a radio labelling admitted

Spanners are fundamental graph structures that sparsify graphs at the cost of small stretch. In particular, in recent years, many sequential algorithms constructing additive all-pairs spanners were designed, providing very sparse small-stretch subgraphs. Remarkably, it was then shown that the known (+6)-spanner constructions are essentially the sparsest possible, that is, larger additive stretch cannot

Connected dominating set (CDS) is a subset of vertices in a graph which dominates all vertices and induces a connected subgraph. This paper proposes a game theoretic approach to find a CDS, and proves that starting from a non-trivial initial state, every non-trivial Nash equilibrium is a minimal CDS and reaching a non-trivial Nash equilibrium needs O(n) rounds in the worst case.

We show that the problem of deciding whether a collection of polyominoes, each fitting in a 2×O(log⁡n) rectangle, can be packed into a 3×n box does not admit a 2o(n/log⁡n)-time algorithm, unless the Exponential Time Hypothesis fails. We also give an algorithm that attains this lower bound, solving any instance of polyomino packing with total area n in 2O(n/log⁡n) time. This establishes a tight bound

The expressiveness of communication primitives has been explored in a common framework based on the π-calculus by considering four features: synchronism (asynchronous vs synchronous), arity (monadic vs polyadic data), communication medium (shared dataspaces vs channel-based), and pattern-matching (binding to a name vs testing name equality). Here pattern-matching is generalised to account for terms

In 2009, Gradwohl, Naor, Pinkas, and Rothblum proposed physical zero-knowledge proof protocols for Sudoku. That is, for a puzzle instance of Sudoku, their excellent protocols allow a prover to convince a verifier that there is a solution to the Sudoku puzzle and the prover knows it, without revealing any information about the solution. The possible drawback is that the existing protocols have an extractability