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

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

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

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

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

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.

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.

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

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 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)

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

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 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

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

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 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.

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

The VC-dimension, which has wide uses in learning theory, has been used in the analysis and design of graph algorithms recently. In this paper, we study the problem of bounding the VC-dimension of unique round-trip shortest path set systems (URTSP), which are set systems induced by sets of vertices in unique round-trip shortest paths in directed graphs. We first show that different from the VC-dimensions

Minimizing the Boolean circuit implementation of a given cryptographic function is an important issue. A number of papers [1], [2], [3], [4] only consider cancellation-free straight-line programs for producing small circuits over GF(2). Cancellation is allowed by the Boyar-Peralta (BP ) heuristic [5, 6]. This yields a valuable tool for practical applications such as building fast software and low-power

We consider the problem of pattern matching with k mismatches, where there can be don't care or wild card characters in the pattern. Specifically, given a pattern P of length m and a text T of length n, we want to find all occurrences of P in T that have no more than k mismatches. The pattern can have don't care characters, which match any character. Without don't cares, the best known algorithm for

We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in [Formula: see text] time and [Formula: see text] space, where n denotes the number of vertices of the polygon.

In this paper, we study several interesting intensity map splitting (IMSp) problems that arise in Intensity-Modulated Radiation Therapy (IMRT), a state-of-the-art radiation therapy technique for cancer treatments. In current clinical practice, a multi-leaf collimator (MLC) with a maximum leaf spread is used to deliver the prescribed intensity maps (IMs). However, the maximum leaf spread of an MLC may