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We show that the perfect matching problem in general graphs is in Quasi-NC. That is, we give a deterministic parallel algorithm which runs in O(\log^3 n) time on n^{O(\log^2 n)} processors. The result is obtained by a derandomization of the Isolation Lemma for perfect matchings, which was introduced in the classic paper by Mulmuley, Vazirani and Vazirani [1987] to obtain a Randomized NC algorithm...
In a non-uniform Constraint Satisfaction problem CSP(Γ), where G is a set of relations on a finite set A, the goal is to find an assignment of values to variables subject to constraints imposed on specified sets of variables using the relations from Γ. The Dichotomy Conjecture for the non-uniform CSP states that for every constraint language \Gm the problem CSP(Γ)...
Clustering is a classic topic in optimization with k-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for k-means with a provable guarantee is a simple local search heuristic yielding an approximation guarantee of 9+≥ilon, a ratio that is known to be tight with respect to such methods.We overcome this barrier...
A tight criterion under which the abstract version Lovász Local Lemma (abstract-LLL) holds was given by Shearer [41] decades ago. However, little is known about that of the variable version LLL (variable-LLL) where events are generated by independent random variables, though variable- LLL naturally models and is enough for almost all applications of LLL. We introduce a necessary and sufficient...
We study the two-dimensional geometric knapsack problem (2DK) in which we are given a set of n axis-aligned rectangular items, each one with an associated profit, and an axis-aligned square knapsack. The goal is to find a (non-overlapping) packing of a maximum profit subset of items inside the knapsack (without rotating items). The best-known polynomial-time approximation factor for this problem (even...
The deletion channel takes as input a bit string x ∊ {0,1}^n, and deletes each bit independently with probability q, yielding a shorter string. The trace reconstruction problem is to recover an unknown string x ∊ from many independent outputs (called traces) of the deletion channel applied to x.We show that if x is drawn uniformly at random and q
In this paper, we formulate an anchored alignment distance between rooted labeled unordered trees as the minimum cost of the anchored alignment whose anchoring is constructed from the minimum cost isolated-subtree mapping by adding the pairs of non-mapped leaves, and design the algorithm to compute it. Since this algorithm runs in exponential time with respect to the number of leaves in theoretical,...
The struggle of technology to understand natural language has been one of the greatest hurdles of humankind. Various techniques and algorithms have contributed to significant advancements in the field of NLP. One of the most primary challenges that NLP faces is being able to determine the meaning and essence of a sentence which may have multiple variations of syntax and semantics. Crossword solving...
Finding shortest distances and paths have always been a crucial area of study. In this article, we have proposed a linear time pre-processing method for optimization of shortest path and distance algorithms, for an undirected weighted graph with non-negative edges. In this approach, certain parts of a graph are grouped together as subgraphs termed as optimized deterministic routing areas (ODRAs)....
The performance of Differential Evolution (DE) algorithms is highly dependent on the trial population diversity and on the way the control parameter space is sampled. Therefore, identifying critical regions containing control parameters (e.g. scale factor, crossover rate) which can induce undesired behaviour (e.g. premature convergence) is useful. In this context, the aim of the paper is twofold....
There is very little practicable significance to prove the equivalency between a pseudo-inverse linear discriminant (PILD) with the desired outputs in reverse proportion to the number of within-class samples and a Fisher linear discriminant (FLD) with the totally projected mean thresholds which are disadvantageous to improve the overall classification accuracy. Even if so, several examples have borne...
Random walks play an important role in computer science, spreading a wide range of topics in theory and practice, including networking, distributed systems, and optimization. Levy flight is a family of random walks whose the distance of a walk is chosen from the power law distribution. There are lots of works of Levy flight in the context of target detection in swarm robotics, analyzing human walk...
Voting (or election) algorithms are used widely in many safety-critical systems to mask errors. Most systems only tolerate malicious (or Byzantine) voters – these systems assume the existence of a correct and centralized mechanism to collect the votes and propagate the voting output to each voter. However, in many realistic scenarios, such a centralized voting mechanism is not feasible. Thus, we study...
A group of directional sensors coordinate to form directional sensor network. Directional sensors have a limited angle of sensing and hence coverage is an important issue in directional sensor network. The sensors need to be deployed optimally to ensure maximum object coverage in the given area. In this paper, we propose a directional sensor deployment scheme. The sensors are placed based on the location...
Modularity is widely-used objective function to detect communities and there are lots of algorithms based on modularity maximization. The leading eigenvector method is one of them where modularity is maximized by choosing the first eigenvector as partition result. To analyze in depth the information provided by other eigenvectors, modularity maximization could be transformed to vector partitioning...
In this paper, we study the influence of using variable grouping inside mutation operators for large-scale multi-objective optimization. We introduce three new mutation operators based on the well-known Polynomial Mutation. The variable grouping in these operators is performed using two different grouping mechanisms, including Differential Grouping from the literature. In our experiments, two popular...
We present an algorithm for value based redundancy detection in Static Single Assignment(SSA) code. For this, we adopted the idea of Global Value Numbering from the Simple Algorithm for GVN (Saleena and Paleri, 2014). The novel approach is to make use of the φ-functions present at the join points to compute the meet operation. The algorithm is implemented using the LLVM compiler infrastructure. Experimental...
In this paper, a self-adaptive two phase approach for large scaleoptimization is proposed. In the first phase, we design a uniformdiscrete search method which can quickly and roughly scan the searchspace and find good initial points. Thenwe continuously narrow the search space and make moreprecise search in a dynamically self-adaptive way. Inthe second phase, we design a dynamically self-adaptivegrouping...
We study the problem of minimizing total completion time in 2-stage flowshop with availability constraint. This problem is NP-hard in the strong sense even if both machines are always available. With availability constraint, although a bulk of research papers have studied the makespan minimization problem, there is no research done on the total completion time minimization. This paper is the first...
In combinatorial optimization, the goal is to find the optimal object from a finite set. Since such problems are hard to be solved, usually some metaheuristics is applied. One of the most successful techniques for a number of classes of problems is Ant Colony Optimization (ACO). Some start strategies can be applied, to the ACO algorithms, to improve their performance. Here, the InterCriteria Analysis...
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