In this paper we study a recently proposed variant of the r-gathering problem. An r-gathering of customers C to facilities F is an assignment A of C to open facilities F' ⊂ F such that r or more customers are assigned to each open facility. (Each facility needs enough number of customers to open.) Given an opening cost op(f) for each f∈F, and a connecting cost co(c,f) for each pair of c∈C and f∈F, the cost of an r-gathering A is max{maxc∈C{co(c, A(c))}, maxf∈F'{op(f)}}. The r-gathering problem consists of finding an r-gathering having the minimum cost. Assume that F is a set of locations for emergency shelters, op(f) is the time needed to prepare a shelter f∈F, and co(c,f) is the time needed for a person c∈C to reach assigned shelter f=A(c)∈F. Then an r-gathering corresponds to an evacuation plan such that each open shelter serves r or more people, and the r-gathering problem consists of finding an evacuation plan minimizing the evacuation time span. However in a solution above some person may be assigned to a farther open shelter although it has a closer open shelter. It may be difficult for the person to accept such an assignment for an emergency situation. Therefore, Armon considered the problem with one more additional constraint, that is, each customer should be assigned to a closest open facility, and gave a 9-approximation polynomial-time algorithm for the problem. We have designed a simple 3-approximation algorithm for the problem. The running time is O(r|C||F|).

An interconnection network is an inevitable component for constructing parallel computers. It connects computation nodes so that the nodes can communicate with each other. As a parallel computation essentially requires inter-node communication according to a parallel algorithm, the interconnection network plays an important role in terms of communication performance. This paper focuses on the collective communication that is frequently performed in parallel computation and this paper addresses the Cup-Stacking method that is proposed in our preceding work. The key issues of the method are splitting a large packet into slices, re-shaping the slice, and stacking the slices, in a genetic algorithm (GA) manner. This paper discusses extending the Cup-Stacking method by introducing additional items (genes) and proposes the extended Cup-Stacking method. Furthermore, this paper places comprehensive discussions on the drawbacks and further optimization of the method. Evaluation results reveal the effectiveness of the extended method, where the proposed method achieves at most seven percent improvement in duration time over the former Cup-Stacking method.

For any m strings of total length n, we propose an O(mn log n)-time, O(n)-space algorithm that finds a maximal common subsequence of all the strings, in the sense that inserting any character in it no longer yields a common subsequence of them. Such a common subsequence could be treated as indicating a nontrivial common structure we could find in the strings since it is NP-hard to find any longest common subsequence of the strings.

Many optimisation algorithms improve the algorithm from the perspective of population structure. However, most improvement methods simply add hierarchical structure to the original population structure, which fails to fundamentally change its structure. In this paper, we propose an umbrellalike hierarchical artificial bee colony algorithm (UHABC). For the first time, a historical information layer is added to the artificial bee colony algorithm (ABC), and this information layer is allowed to interact with other layers to generate information. To verify the effectiveness of the proposed algorithm, we compare it with the original artificial bee colony algorithm and five representative meta-heuristic algorithms on the IEEE CEC2017. The experimental results and statistical analysis show that the umbrellalike mechanism effectively improves the performance of ABC.

Given a set of n disjoint intervals on a line and an integer k, we want to find k points in the intervals so that the minimum pairwise distance of the k points is maximized. Intuitively, given a set of n disjoint time intervals on a timeline, each of which is a time span we are allowed to check something, and an integer k, which is the number of times we will check something, we plan k checking times so that the checks occur at equal time intervals as much as possible, that is, we want to maximize the minimum time interval between the k checking times. We call the problem the k-dispersion problem on intervals. If we need to choose exactly one point in each interval, so k=n, and the disjoint intervals are given in the sorted order on the line, then two O(n) time algorithms to solve the problem are known. In this paper we give the first O(n) time algorithm to solve the problem for any constant k. Our algorithm works even if the disjoint intervals are given in any (not sorted) order. If the disjoint intervals are given in the sorted order on the line, then, by slightly modifying the algorithm, one can solve the problem in O(log n) time. This is the first sublinear time algorithm to solve the problem. Also we show some results on the k-dispersion problem on disks, including an FPTAS.

A vertex subset I of a graph G is called a k-path vertex cover if every path on k vertices in G contains at least one vertex from I. The K-PATH VERTEX COVER RECONFIGURATION (K-PVCR) problem asks if one can transform one k-path vertex cover into another via a sequence of k-path vertex covers where each intermediate member is obtained from its predecessor by applying a given reconfiguration rule exactly once. We investigate the computational complexity of K-PVCR from the viewpoint of graph classes under the well-known reconfiguration rules: TS, TJ, and TAR. The problem for k=2, known as the VERTEX COVER RECONFIGURATION (VCR) problem, has been well-studied in the literature. We show that certain known hardness results for VCR on different graph classes can be extended for K-PVCR. In particular, we prove a complexity dichotomy for K-PVCR on general graphs: on those whose maximum degree is three (and even planar), the problem is PSPACE-complete, while on those whose maximum degree is two (i.e., paths and cycles), the problem can be solved in polynomial time. Additionally, we also design polynomial-time algorithms for K-PVCR on trees under each of TJ and TAR. Moreover, on paths, cycles, and trees, we describe how one can construct a reconfiguration sequence between two given k-path vertex covers in a yes-instance. In particular, on paths, our constructed reconfiguration sequence is shortest.

With the rapid increase in the number of CPU cores, software that can utilize these many cores is required. A lock-free algorithm based on compare-and-swap (CAS) operations is one of the concurrency control methods to implement such multi-threading software. A multi-word CAS (MwCAS) operation is an extension of a CAS operation to swap multiple words atomically. However, we noticed that the performance of the existing MwCAS implementation is limited because of garbage collection even if in a low-contention environment. To achieve high performance in low-contention workloads, we propose a new MwCAS algorithm without garbage collection. Experimental results show that our approach is three to five times faster than implementation with garbage collection in low-contention workloads. Moreover, the performance of the proposed method is also superior in a high-contention environment.

The challenges posed by big data in the 21st Century are complex: Under the previous common sense, we considered that polynomial-time algorithms are practical; however, when we handle big data, even a linear-time algorithm may be too slow. Thus, sublinear- and constant-time algorithms are required. The academic research project, “Foundations of Innovative Algorithms for Big Data,” which was started in 2014 and will finish in September 2021, aimed at developing various techniques and frameworks to design algorithms for big data. In this project, we introduce a “Sublinear Computation Paradigm.” Toward this purpose, we first provide a survey of constant-time algorithms, which are the most investigated framework of this area, and then present our recent results on sublinear progressive algorithms. A sublinear progressive algorithm first outputs a temporary approximate solution in constant time, and then suggests better solutions gradually in sublinear-time, finally finds the exact solution. We present Sublinear Progressive Algorithm Theory (SPA Theory, for short), which enables to make a sublinear progressive algorithm for any property if it has a constant-time algorithm and an exact algorithm (an exponential-time one is allowed) without losing any computation time in the big-O sense.

In 2019, a new selection method, named fitness-distance balance (FDB), was proposed. FDB has been proved to have a significant effect on improving the search capability for evolutionary algorithms. But it still suffers from poor flexibility when encountering various optimization problems. To address this issue, we propose a functional weights-enhanced FDB (FW). These functional weights change the original weights in FDB from fixed values to randomly generated ones by a distribution function, thereby enabling the algorithm to select more suitable individuals during the search. As a case study, FW is incorporated into the spherical search algorithm. Experimental results based on various IEEE CEC2017 benchmark functions demonstrate the effectiveness of FW.

Given a set P of n points on which facilities can be placed and an integer k, we want to place k facilities on some points so that the minimum distance between facilities is maximized. The problem is called the k-dispersion problem. In this paper, we consider the 3-dispersion problem when P is a set of points on a plane (2-dimensional space). Note that the 2-dispersion problem corresponds to the diameter problem. We give an O(n) time algorithm to solve the 3-dispersion problem in the L∞ metric, and an O(n) time algorithm to solve the 3-dispersion problem in the L1 metric. Also, we give an O(n2 log n) time algorithm to solve the 3-dispersion problem in the L2 metric.

Due to most of the existing graph repartitioning methods are known for poor efficiency in distributed environments. In this paper, we introduce a new graph repartitioning method with two phases in distributed environments. In the first phase, a local method is designed to identify all the potential candidate vertices that should be moved to the other partitions at once in each partition locally. In the second phase, a streaming graph processing model is adopted to reassign the candidate vertices to achieve lightweight graph repartitioning. During the reassignment of the vertex, we propose an objective function to balance both the load balance and the number of crossing edges among the distributed partitions. The experimental results with a large set of real word and synthetic graph datasets show that the communication cost can be reduced by nearly 1 to 2 orders of magnitude compared with the existing methods.

In this article, we propose a method to identify the link layer home network topology, motivated by applications to cost reduction of support centers. If the topology of home networks can be identified automatically and efficiently, it is easier for operators of support centers to identify fault points. We use MAC address forwarding tables (AFTs) which can be collected from network devices. There are a couple of existing methods for identifying a network topology using AFTs, but they are insufficient for our purpose; they are not applicable to some specific network topologies that are typical in home networks. The advantage of our method is that it can handle such topologies. We also implemented these three methods and compared their running times. The result showed that, despite its wide applicability, our method is the fastest among the three.

Skip Graph is a promising distributed data structure for large scale systems and known for its capability of range queries. Although several methods of routing range queries in Skip Graph have been proposed, they have inefficiencies such as a long path length or a large number of messages. In this paper, we propose a novel routing method for range queries named Split-Forward Broadcasting (SFB). SFB introduces a divide-and-conquer approach, enabling nodes to make full use of their routing tables to forward a range query. It brings about a shorter average path length than existing methods, as well as a smaller number of messages by avoiding duplicate transmission. We clarify the characteristics and effectiveness of SFB through both analytical and experimental comparisons. The results show that SFB can reduce the average path length roughly 30% or more compared with a state-of-the-art method.

Inter-node communication is essential in parallel computation. The performance of parallel processing depends on the efficiencies in both computation and communication, thus, the communication cost is not negligible. A parallel application program involves a logical communication structure that is determined by the interchange of data between computation nodes. Sometimes the logical communication structure mismatches to that in a real parallel machine. This mismatch results in large communication costs. This paper addresses the node-mapping problem that rearranges logical position of node so that the degree of mismatch is decreased. This paper assumes that parallel programs execute one or more collective communications that follow specific traffic patterns. An appropriate node-mapping achieves high communication performance. This paper proposes a strong heuristic method for solving the node-mapping problem and adapts the method to a genetic algorithm. Evaluation results reveal that the proposed method achieves considerably high performance; it achieves 8.9 (4.9) times speed-up on average in single-(two-)traffic-pattern cases in 32×32 torus networks. Specifically, for some traffic patterns in small-scale networks, the proposed method finds theoretically optimized solutions. Furthermore, this paper discusses in deep about various issues in the proposed method that employs genetic algorithm, such as population of genes, number of generations, and traffic patterns. This paper also discusses applicability to large-scale systems for future practical use.

The bulk execution of a sequential algorithm is to execute it for many different inputs in turn or at the same time. It is known that the bulk execution of an oblivious sequential algorithm can be implemented to run efficiently on a GPU. The bulk execution supports fine grained bitwise parallelism, allowing it to achieve high acceleration over a straightforward sequential computation. The main contribution of this work is to present a Bitwise Parallel Bulk Computation (BPBC) to accelerate the Smith-Waterman Algorithm (SWA) using the affine gap penalty. Thus, our idea is to convert this computation into a circuit simulation using the BPBC technique to compute multiple instances simultaneously. The proposed BPBC technique for the SWA has been implemented on the GPU and CPU. Experimental results show that the proposed BPBC for the SWA accelerates the computation by over 646 times as compared to a single CPU implementation and by 6.9 times as compared to a multi-core CPU implementation with 160 threads.

Unitary operator discrimination is a fundamental problem in quantum information theory. The basic version of this problem can be described as follows: Given a black box implementing a unitary operator U∈S:={U1, U2} under some probability distribution over S, the goal is to decide whether U=U1 or U=U2. In this paper, we consider the query complexity of this problem. We show that there exists a quantum algorithm that solves this problem with bounded error probability using $lceil{sqrt{6} heta_{ m cover}^{-1}} ceil$ queries to the black box in the worst case, i.e., under any probability distribution over S, where the parameter θcover, which is determined by the eigenvalues of $U_1^dagger {U_2}$, represents the “closeness” between U1 and U2. We also show that this upper bound is essentially tight: we prove that for every θcover > 0 there exist operators U1 and U2 such that any quantum algorithm solving this problem with bounded error probability requires at least $lceil{rac{2}{3 heta_{ m cover}}} ceil$ queries under uniform distribution over S.

The k-edge-connectivity augmentation problem for a specified set of vertices (kECA-SV for short) is defined by “Given a graph G=(V, E) and a subset Γ ⊆ V, find a minimum set E' of edges such that G'=(V, E ∪ E') has at least k edge-disjoint paths between any pair of vertices in Γ.” Let σ be the edge-connectivity of Γ (that is, G has at least σ edge-disjoint paths between any pair of vertices in Γ). We propose an algorithm for (σ+1)ECA-SV which is done in O(|Γ|) maximum flow operations. Then the time complexity is O(σ2|Γ||V|+|E|) if a given graph is sparse, or O(|Γ||V||BG|log(|V|2/|BG|)+|E|) if dense, where |BG| is the number of pairs of adjacent vertices in G. Also mentioned is an O(|V||E|+|V|2 log |V|) time algorithm for a special case where σ is equal to the edge-connectivity of G and an O(|V|+|E|) time one for σ ≤ 2.

A parallel phrase matching (PM) engine for dictionary compression is presented. Hardware based parallel chaining hash can eliminate erroneous PM results raised by hash collision; while newly-designed storage architecture holding PM results solved the data dependency issue; Thus, the average compression speed is increased by 53%.

In this letter, we consider several optimization problems associated with the configuration of grouping-based framed slotted ALOHA protocols. Closed-form formulas for determining the optimal values of system parameters such as the process termination time and confidence levels for partitioned groups are presented. Further, we address the maximum group size required for meaningful grouping gain and the effectiveness of the grouping technique in light of signaling overhead.

A linear-time constructible data structure for a real number sequence supporting O(1)-time queries of the maximal local maximum-sum segment of any contiguous subsequence containing any specific position is proposed, where a local maximum-sum segment is a segment whose maximum-sum segment is itself.