We study the isomorphism problem for random hypergraphs. We show that it is solvable in polynomial time for the binomial random k-uniform hypergraph Hn,p;k, for a wide range of p. We also show that it is solvable w.h.p. for random r-regular, k-uniform hypergraphs Hn,r;k,r=O(1).

A k-container of a graph G is a set of k internally disjoint paths between two distinct vertices. A k-container of G is a k⁎-container if it contains all vertices of G. Graph G is k⁎-connected if there exists a k⁎-container between any two distinct vertices. A k-connected graph G is super spanning connected if G is k⁎-connected for every r with 1≤r≤k. This study demonstrates that the split-star network

In this paper, we introduce two new notions of S-continuous information systems and S-abstract bases which provide concrete representations of stably continuous semi-lattices. We shed light on how the states of an S-continuous information system and the round ideal completion of an S-abstract basis form a stably continuous semi-lattice, respectively. Then we obtain two representation theorems for stably

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. The class of data center networks has been proposed as a good class of models in the design of computer networks. Such a data center network can be viewed as a server-centric interconnection network structure

The non-uniform dispersion process on the infinite integer line is a synchronous process where n particles are placed at the origin initially, and any particle not exclusively occupying an integer site will move at the next time step to the right adjacent integer with probability pn and to the left with probability 1−pn independently. We characterize the longest distance from the origin when the dispersion

We consider a single machine lot scheduling problem. A number of customer orders of different sizes may be processed in the same lot. We consider first the setting that splitting orders between consecutive lots is allowed. We focus on minimizing the number of tardy orders. A polynomial time solution algorithm is introduced for this problem. We then study the extension to minimizing the weighted number

A secret sharing scheme is a cryptographic technique to protect a secret from loss and leakage by dividing it into shares. A ramp secret sharing scheme can improve efficiency in terms of the information ratio by allowing partial information about the secret which is composed of several sub-secrets to leak out. The notion of strong security has been introduced to control the amount of information on

This paper extends the problem of 2-dimensional palindrome search into the area of approximate matching. Using the Hamming distance as the measure, we search for 2D palindromes that allow up to k mismatches. We consider two different definitions of 2D palindromes and describe efficient algorithms for both of them. The first definition implies a square, while the second definition (also known as a centrosymmetric

The length a(n) of the longest common subsequence of the nth Thue-Morse word and its bitwise complement is studied. An open problem suggested by Jean Berstel in 2006 is to find a formula for a(n). In this paper we prove new lower bounds on a(n) by explicitly constructing a common subsequence between the Thue-Morse words and their bitwise complement. We obtain the lower bound a(n)=2n(1−o(1)), saying

In the restricted Santa Claus problem we are given resources R and players P. Every resource j∈R has a value vj and every player i∈P desires a set of resources R(i). We are interested in distributing the resources to players that desire them. The quality of a solution is measured by the least happy player, i.e., the lowest sum of resource values. This value should be maximized. The local search algorithm

Fici et al. defined a word to be a k-power if it is the concatenation of k consecutive identical blocks, and an r-antipower if it is the concatenation of r pairwise distinct blocks of the same size. They defined N(k,r) as the smallest ℓ such that every binary word of length ℓ contains either a k-power or an r-antipower. In this note we obtain some new upper and lower bounds on N(k,r). We also consider

A geometric graph is a graph whose vertices are points in general position in the plane and its edges are straight line segments joining these points. In this paper we give an O(n2log⁡n) time algorithm to compute the number of pairs of edges that cross in a geometric graph on n vertices. For layered graphs and convex geometric graphs the algorithm takes O(n2) time.

We show that the number of length-n words over a k-letter alphabet having no even palindromic prefix is the same as the number of length-n unbordered words, by constructing an explicit bijection between the two sets. A slightly different but analogous result holds for those words having no odd palindromic prefix. Using known results on borders, we get an asymptotic enumeration for the number of words

The complexity of computing the Fourier transform is a longstanding open problem. Very recently, Ailon (2013, 2014, 2015) showed in a collection of papers that, roughly speaking, a speedup of the Fourier transform computation implies numerical ill-condition. The papers also quantify this tradeoff. The main method for proving these results is via a potential function called quasi-entropy, reminiscent

In parameterized string matching, a string comprises static and parameterized symbols. Two strings are said to be matched if there exists a one-to-one mapping of parameterized symbols onto itself such that it transforms one string into the other. Traditionally, to construct a full-text index for this problem, suffixes are transformed in a manner referred to as previous occurrence encoding. Although

We obtain a polynomial-time deterministic (2ee−1+ϵ)-approximation algorithm for maximizing symmetric submodular functions under a budget constraint. Although there exist randomized algorithms with better expected performance, our algorithm achieves the best known factor achieved by a deterministic algorithm, improving on the previously known factor of 6. Furthermore, it is simple, combining two elegant

Given an unpredictable Boolean function f:{0,1}n→{0,1}, the standard Yao's XOR lemma is a statement about the unpredictability of computing ⊕i∈[k]f(xi) given x1,...,xk∈{0,1}n, whereas the Selective XOR lemma is a statement about the unpredictability of computing ⊕i∈Sf(xi) given x1,...,xk∈{0,1}n and S⊆{1,...,k}. We give a reduction from the Selective XOR lemma to the standard XOR lemma. Our reduction

We explore global verifiability; discovering that voting systems vulnerable to attack can be proven to satisfy that security notion, whereas many secure systems cannot. We conclude that current definitions are unsuitable for the analysis of voting systems, fuelling the exploration for a suitable definition.

A dealer-free and non-interactive dynamic threshold secret sharing scheme has been proposed by Harn and Hsu in Information Processing Letters in 2015. In this scheme, a (t,n) secret sharing scheme in secret sharing phase can turn into a (m,n) scheme in secret reconstruction phase, where m is the number of participating shareholders. It has been claimed that the secrecy of shares and the secrecy of

In turn-based games played on graphs, the constrained existence problem of equilibria is a well studied problem. This problem is already known to be decidable in P for weak subgame perfect equilibria in Boolean games with Büchi objectives. In this paper, we prove that this problem is P-complete.

The known linear-time kernelizations for d-Hitting Set guarantee linear worst-case running times using a quadratic-size data structure (that is not fully initialized). Getting rid of this data structure, we show that problem kernels of asymptotically optimal size O(kd) for d-Hitting Set are computable in linear time and space. Additionally, we experimentally compare the linear-time kernelizations for

A vertex v is a Grundy vertex with respect to a proper k-coloring c of a graph G=(V,E) if v has a neighbor of color j for every j (1≤j

We consider two natural problems about nondeterministic finite automata (NFA). First, given an NFA M of n states, and a length ℓ, does M accept a word of length ℓ? We show that the classic problem of triangle-free graph recognition reduces to this problem, and give an O(nω(log⁡n)1+ϵlog⁡ℓ)-time algorithm to solve it, where ω is the optimal exponent for matrix multiplication. Second, provided L(M) is

We study the puzzle game Buttons and Scissors in which the goal is to remove all buttons from an n×m grid by a series of horizontal and vertical cuts. We show that the corresponding decision problem has an algorithm with time complexity 2O(k2log⁡k)+(n+m)O(1), where k is an upper bound on the number of cuts.

QUIXO is a two-player strategic board game played on a 5×5 game board. Players alternately move cubes on the game board, and the player who first made a line of five cubes with the player's symbol wins the game. In this paper, we prove EXPTIME-completeness of deciding the winner on generalized QUIXO played on an n×n game board.

We present a simple reduction of the problem of nondecreasing paths (with minimal last edge weight) in a directed edge-weighted graph to a reachability problem in a directed unweighted graph. The reduction yields an alternative simple method of solving the single-source nondecreasing paths problem in almost linear time. If the edge weights are integers then our algorithm can be implemented in O((n+m)log⁡log⁡n)

The skyline of a set P of points consists of the “best” points with respect to minimization or maximization of the attribute values. A point p dominates another point q if p is as good as q in all dimensions and it is strictly better than q in at least one dimension. In this work, we focus on the 2-d space and provide expected performance guarantees for dynamic (insertions and deletions) 3-sided range

We prove that the constructive weighted coalitional manipulation problem for the Schulze voting rule can be solved in polynomial time for an unbounded number of candidates and an unbounded number of manipulators.

In this paper, we consider a scheduling problem on multiple speed-scalable processors, where the objective is to minimize a weighted sum of total completion times of jobs and total energy consumption on processors. We propose a simple algorithm for the scheduling problem that runs faster than the existing algorithm.

We consider two sub-classes of fully dynamic algorithms for maintaining a maximal matching, which we define as lazy algorithms and eager algorithms. We prove a conditional lower bound which is sub-linear in the number of edges for the update time of lazy algorithms and eager algorithms. Our result is conditioned on the well known conjecture about the hardness of triangle detection in a graph.

There are two options for the leasing problem, buying at a high price or leasing at a low price. Once you choose to purchase the resources, you lose the opportunity to invest in other financial assets for additional benefits, such as a risk-free return of the interest rate. Thus, opportunity cost is an important factor to consider in the leasing problem. Accounting for opportunity cost, this paper

Detecting and eliminating logic hazards in Boolean circuits is a fundamental problem in logic circuit design. We show that there is no O(3(1−ϵ)npoly(s)) time algorithm, for any ϵ>0, that detects logic hazards in Boolean circuits of size s on n variables under the assumption that the strong exponential time hypothesis is true. This lower bound holds even when the input circuits are restricted to be

In 2015, Chou and Orlandi presented an oblivious transfer protocol that already drew a lot of attention both from theorists and practitioners due to its extreme simplicity and high efficiency. Chou and Orlandi claimed that their protocol is universally composable secure (UC-secure) in the random oracle model under dynamic corruptions. UC-security is a very strong security guarantee that assures that

In this paper, we consider the all best swap edges problem in a distributed environment. We are given a 2-edge connected positively weighted network X, where all communication is routed through a rooted spanning tree T of X. If a tree edge e={x,y} fails, the communication network will be disconnected. However, since X is 2-edge connected, communication can be restored by replacing e by non-tree edge

Given a constant number d of n×n matrices with total m non-infinity entries, we show how to construct in (essentially optimal) O˜(mn+n2) time a data structure that can compute in (essentially optimal) O˜(n2) time the distance product of these matrices after incrementing the value (possibly to infinity) of a constant number k of entries. Our result is obtained by designing an oracle for single source

A blockchain is designed to be a self-sufficient decentralised ledger: a peer verifying the validity of past transactions only needs to download the blockchain (the ledger) and nothing else. However, it might be of interest to make two different blockchains interoperable, i.e., to allow one to transmit information from one blockchain to another blockchain. In this paper, we give a formalisation of

In 2014, Mesnager proposed two open problems in [4] on the construction of bent functions. One problem has been settled by Tang et al. in 2017. However, the other is still outstanding, which is solved in this letter by considering a class of PS− vectorial bent functions.

We revisit the notions of cryptographic anonymity and share unpredictability in secret sharing, introducing more systematic and fine grained definitions. We derive tight negative and positive results characterizing access structures with respect to the generalized definitions.

In the sequential setting, a decades-old fundamental result in online algorithms states that if there is a c-competitive randomized online algorithm against an adaptive, offline adversary, then there is a c-competitive deterministic algorithm. The adaptive, offline adversary is the strongest adversary among the ones usually considered, so the result states that if one has to be competitive against

It is well known that in a bipartite (and more generally in a König-Egerváry) graph, the size of the minimum vertex cover is equal to the size of the maximum matching. We first address the question whether (and if not, when) this property still holds in a König-Egerváry graph if we consider vertex covers containing a given subset of vertices. We characterize such graphs using the classic notions of

We revisit the following problem: Given a convex polygon P, find the largest-area inscribed triangle. We prove by counterexample that the linear-time algorithm presented in 1979 by Dobkin and Snyder [5] for solving this problem fails, as well as a renewed analysis of the problem. We also provide a counterexample proving that their algorithm fails finding the largest-area inscribed quadrilateral. Combined

We show that any ternary Euclidean (resp. quaternary Hermitian) linear complementary dual [n,k] code contains a Euclidean (resp. Hermitian) linear complementary dual [n,k−1] subcode for 2≤k≤n. As a consequence, we derive a bound on the largest minimum weights among ternary Euclidean linear complementary dual codes and quaternary Hermitian linear complementary dual codes.

Many discrete minimization problems, including various versions of the shortest path problem, can be efficiently solved by dynamic programming (DP) algorithms that are “pure” in that they only perform basic operations, as min, max, +, but no conditional branchings via if-then-else in their recursion equations. It is known that any pure (min⁡,+) DP algorithm solving the minimum weight spanning tree

We analyze the authenticated encryption algorithm of ORANGE, a submission to the NIST lightweight cryptography standardization process. We show that it is practically possible to craft forgeries out of two observed transmitted messages that encrypt the same plaintext. The authors of ORANGE have confirmed the attack, and they discuss a fix for this attack in their second-round submission of ORANGE to

In this paper we introduce an a priori variant of the capacitated vehicle routing problem and provide a constant factor approximation algorithm, when the demands of customers are independent and identically distributed Bernoulli experiments. In the capacitated vehicle routing problem (CVRP) a vehicle, starting at a depot, must visit a set of customers to deliver the requested quantity of some item

Let n1 and n2 be two integers with n1,n2≥3 and G a graph of order n=n1+n2. As a variation of Ore's degree condition for the existence of Hamilton cycle in G, El-Zahar proved that if δ(G)≥⌈n12⌉+⌈n22⌉, then G contains two disjoint cycles of length n1 and n2. Recently, Yan et al. considered the problem by extending the degree condition to degree sum condition and proved that if d(u)+d(v)≥n+4 for any pair

Regular expressions are extended by splitting the terminals into left brackets, right brackets, and neutral terminals and by adding terminal annotations. These extended expressions define the set of well-nested input-driven languages. They are parsed in linear time in the size of the input. The parse trees are based on brackets and operator priorities.

Coffman and Sethi proposed a heuristic algorithm, called LD (Longest Decreasing), for multi-processor scheduling, to minimize makespan over flowtime-optimal schedules. The LD algorithm is an extension of a very well-known list scheduling algorithm, Longest Processing Time (LPT) list scheduling, to this bicriteria scheduling problem. Coffman and Sethi conjectured (in 1976) that the LD algorithm has

Probabilistic branching bisimilarity allows us to compare process behaviour with respect to their branching structure and probabilistic features, while abstracting away from those computation steps that can be marked as irrelevant to the analysis at hand. To the best of our knowledge, in the context of nondeterministic probabilistic processes, no proof of probabilistic branching bisimilarity being

In this paper, we study tradeoffs between curve complexity and area of Right Angle Crossing drawings (RAC drawings), which is a challenging theoretical problem in graph drawing. Given a graph with n vertices and m edges, we provide a RAC drawing algorithm with curve complexity 6 and area O(n2.75), which takes time O(n+m). Our algorithm improves the previous upper bound O(n3), by Di Giacomo et al.,

In the Cograph Deletion (resp., Cograph Editing) problem the input is a graph G and an integer k, and the goal is to decide whether there is a set of edges of size at most k whose removal from G (resp., removal and addition to G) results in a graph that does not contain an induced path with four vertices. In this paper we give algorithms for Cograph Deletion and Cograph Editing whose running times

We present some complexity results concerning the problems of covering a graph with p convex sets and of partitioning a graph into p convex sets. The following convexities are considered: digital convexity, monophonic convexity, P3-convexity, and P3⁎-convexity.

We show the reverse greedy algorithm is between a (2k−2)- and a 2k-approximation for k-center.

Almost 10 years ago, Impagliazzo and Kabanets [5] gave a new combinatorial proof of Chernoff's bound for sums of bounded independent random variables. Unlike previous methods, their proof is constructive. This means that it provides an efficient randomized algorithm for the following task: given a set of Boolean random variables whose sum is not concentrated around its expectation, find a subset of

This paper addresses the connected maximum coverage problem, motivated by the detection of mutated driver pathways in cancer. The connected maximum coverage problem is NP-hard and therefore approximation algorithms are of interest. We provide here an approximation algorithm for the problem with an approximation bound that strictly improves on previous results. A second approximation algorithm with

The Additive Coloring Problem is a variation of the Coloring Problem where labels of {1,…,k} are assigned to the vertices of a graph G so that the sum of labels over the neighborhood of each vertex is a proper coloring of G. The least value k for which G admits such labeling is called additive chromatic number of G. This problem was first presented by Czerwiński, Grytczuk and Żelazny who also proposed

We analyze in detail the probability that sequences of equal length generated by a pseudorandom number generator starting from random points of the state space overlap, providing for the first time an exact result and manageable bounds. While the computation of the probability is almost elementary, the value has been reported erroneously several times in the literature.

Process anonymity has been studied for a long time. Memory anonymity is more recent. In an anonymous memory system, there is no a priori agreement among the processes on the names of the shared registers. As an example, a shared register named A by a process p and a shared register named B by another process q may correspond to the very same register X, while the same name C may correspond to different

(t,n) threshold secret sharing (SS) is an important cryptographic primitive in which a secret is divided into n shares, and then any t or more shareholders can exchange shares to reconstruct the secret without help of any trusted third party. However, if an illegal participant, without any valid share, impersonates a shareholder to recover the secret with m (m≥t) legal shareholders in a traditional

In this work we consider modified versions of quadratic double circulant and quadratic bordered double circulant constructions over the binary field and the rings F2+uF2 and F4+uF4 for different prime values of p. Using these constructions with extensions and neighbors we are able to construct a number of extremal binary self-dual codes of different lengths with new parameters in their weight enumerators