Time Optimal Algorithm Research Articles

Strong minimum energy $$2$$ 2 -hop rooted topology for hierarchical wireless sensor networks

Given a set of sensors, the strong minimum energy topology (SMET) problem is to assign transmit power to each sensor such that the sum of the transmit powers of all the sensors is minimum subject to the constraint that the resulting topology containing only bidirectional links is strongly connected. This problem is known to be NP-hard. However, most of the wireless sensor networks are hierarchical in nature, where shorter path lengths are preferred for communication between any two nodes. Given a set of sensors and a specified sensor, say $$r$$r, the strong minimum energy $$2$$2-hop rooted topology problem ($$2$$2h-SMERT) is to assign transmit power to each sensor such that the sum of the transmit powers of all the sensors is minimum subject to the constraints that the resulting topology containing only bidirectional links is strongly connected and the length of the path from $$r$$r to any other node is at most $$2$$2. We prove that the $$2$$2h-SMERT problem is NP-hard. We also prove that $$2$$2h-SMERT problem is APX-hard. We then show that $$2$$2h-SMERT problem is not approximable within a factor of $$\frac{1}{2}(1-\epsilon ) \ln n$$12(1-∈)lnn unless NP $$\subseteq DTIME(n^{\log \log n})$$⊆DTIME(nloglogn). On the positive side, we propose a $$2(1+ \ln n)$$2(1+lnn)-approximation algorithm for the $$2$$2h-SMERT problem. We also study two special cases of the $$2$$2h-SMERT problem, namely, the $$d$$d-rest-$$2$$2h-SMERT problem and the $$k$$k-int-$$2$$2h-SMERT problem. We propose a $$2(1+ \ln d)$$2(1+lnd)-approximation algorithm for the $$d$$d-rest-$$2$$2h-SMERT problem. The $$k$$k-int-$$2$$2h-SMERT problem is NP-hard for arbitrary $$k$$k. However, for fixed constant $$k$$k, we propose a $$\frac{k+1}{2}$$k+12-approximation algorithm for the $$k$$k-int-$$2$$2h-SMERT problem and obtain a polynomial time optimal algorithm for the $$k$$k-int-$$2$$2h-SMERT problem for $$k=2$$k=2.

Interval incidence coloring of bipartite graphs

In this paper11The extended abstract of this paper appeared on PPAM 2009, LNCS 6067 (2010) 11–20. we study the problem of interval incidence coloring of bipartite graphs. We show the upper bound for interval incidence coloring number (χii) for bipartite graphs χii≤2Δ, and we prove that χii=2Δ holds for regular bipartite graphs. We solve this problem for subcubic bipartite graphs, i.e. we fully characterize the subcubic graphs that admit 4, 5 or 6 coloring, and we construct a linear time exact algorithm for subcubic bipartite graphs. We also study the problem for bipartite graphs with Δ=4 and we show that 5-coloring is easy and 6-coloring is hard (NP-complete). Moreover, we construct an O(nΔ3.5logΔ) time optimal algorithm for trees.

The time-dependent pollution-routing problem

The Time-Dependent Pollution-Routing Problem (TDPRP) consists of routing a fleet of vehicles in order to serve a set of customers and determining the speeds on each leg of the routes. The cost function includes emissions and driver costs, taking into account traffic congestion which, at peak periods, significantly restricts vehicle speeds and increases emissions. We describe an integer linear programming formulation of the TDPRP and provide illustrative examples to motivate the problem and give insights about the tradeoffs it involves. We also provide an analytical characterization of the optimal solutions for a single-arc version of the problem, identifying conditions under which it is optimal to wait idly at certain locations in order to avoid congestion and to reduce the cost of emissions. Building on these analytical results we describe a novel departure time and speed optimization algorithm for the cases when the route is fixed. Finally, using benchmark instances, we present results on the computational performance of the proposed formulation and on the speed optimization procedure.

A Polynomial Time Optimal Algorithm for Linear Bin Packing Problem

일반적으로 상자포장 문제는 다항시간으로 근사 해를 찾는 알고리즘만이 존재하여 NP-완전 문제로 알려져 있다. 본 논문은 선형 상자문제의 정확한 해를 다항시간으로 찾을 수 있는 알고리즘을 제안한다. n개 물품의 물품 크기 a<SUB>i</SUB>, (i=1, 2, …)를 내림차순으로 정렬시켜 용량이 C인 필요한 상자 수 k의 약 75% 상자들에 ?0.5C≤a<SUB>i</SUB>?개의 물품을 순서대로 1개씩 넣고, 나머지 물품을 찾아 넣는 방법으로 문제를 25%로 단축시켰다. 나머지 필요한 상자 25%에 대해서도 유사한 방법으로 물품을 채우는 방법을 적용하였다. 제안된 알고리즘을 OR-LIB의 120, 250과 500개의 데이터에 적용한 결과 100% 정확한 해를 얻는데 성공하였다. 제안된 알고리즘은 상자 포장 문제가 P-문제임을 증명하였으며, NP-완전으로 알려진 멀티프로세서 스케쥴링 문제에도 적용할 수 있을 것이다.

ALATO: An efficient intelligent algorithm for time optimization in an economic grid based on adaptive stochastic Petri net

Cost and execution time are important issues in economic grids, which are widely used for parallel computing. This paper proposes ALATO, an intelligent algorithm based on learning automata and adaptive stochastic Petri nets (ASPNs) that optimizes the execution time for tasks in economic grids. ASPNs are based on learning automata that predict their next state based on current information and the previous state and use feedback from the environment to update their state. The environmental reactions are extremely helpful for teaching Petri nets in dynamic environments. We use SPNP software to model ASPNs and evaluate execution time and costs for 200 tasks with different parameters based on World Wide Grid standard resources. ALATO performs better than all other heuristic methods in reducing execution time for these tasks.

Finding a minimum-regret many-to-many Stable Matching

The many-to-many Stable Matching (MM) problem is defined on a set of workers and a set of firms and asks for an allocation of workers to firms that satisfies the firms' quotas and the preferences of workers for firms and vice-versa. This article proposes a time-optimal algorithm for solving the minimum-regret problem for the MM, i.e. the problem of finding the MM solution in which the agent that is least well off is matched with the best possible set of agents of the opposite set. The proposed algorithm utilizes the notion of rotations and extends an analogous result for the Stable Marriage problem.

A Computationally Efficient Approach to Trajectory Management for Coordinated Aerial Surveillance

Time optimal path planning and trajectory management algorithms for air vehicles with limited on-board computing resources require an efficient approach to satisfy flight dynamic constraints needed to guarantee paths are feasible. B-spline curves enable compact definition of feasible airplane trajectories that are suited for on-board real-time computation. The design of a trajectory definition and management algorithm suited for a multi-agent persistent surveillance application is described. The proposed solution post-processes the output of a point-by-point path planner and converts it into a minimal representation. Key design requirements include minimization of mission execution time, ability to seamlessly redirect agents based on information acquired by sensor feedback, and robust adherence to mission and vehicle motion constraints. A simple coordinated aerial surveillance scenario is described and demonstrated using the algorithms presented.

Tight Bounds for Distributed Minimum-Weight Spanning Tree Verification

This paper introduces the notion of distributed verification without preprocessing. It focuses on the Minimum-weight Spanning Tree (MST) verification problem and establishes tight upper and lower bounds for the time and message complexities of this problem. Specifically, we provide an MST verification algorithm that achieves simultaneously O(m) messages and O($\sqrt$ n+D) time, where m is the number of edges in the given graph G, n is the number of nodes, and D is G's diameter. On the other hand, we show that any MST verification algorithm must send {\Omega}(m) messages and incur {\Omega}($\sqrt$ n + D) time in worst case. Our upper bound result appears to indicate that the verification of an MST may be easier than its construction, since for MST construction, both lower bounds of {\Omega}(m) messages and {\Omega}($\sqrt$ n+D time hold, but at the moment there is no known distributed algorithm that constructs an MST and achieves simultaneously O(m) messages and O($\sqrt$ n + D) time. Specifically, the best known time-optimal algorithm (using O($\sqrt$ n + D) time) requires O(m + n 3/2) messages, and the best known message-optimal algorithm (using O(m) messages) requires O(n) time. On the other hand, our lower bound results indicate that the verification of an MST is not significantly easier than its construction.

An optimal time algorithm for minimum linear arrangement of chord graphs

A linear arrangement ϕ of an undirected graph G=(V,E) with ∣V∣=n nodes is a bijective function ϕ:V→{0,…,n−1}. The cost function is cost(G,ϕ)=∑uv∈E|(ϕ(u)-ϕ(v))| and opt(G)=min∀ϕcost(G,ϕ). The problem of finding opt(G) is called minimum linear arrangement (MINLA). The Minimum Linear Arrangement is an NP-hard problem in general. But there are some classes of graphs optimally solvable in polynomial time. In this paper, we show that the label of each node equals to the reverse of binary representation of its id in the optimal arrangement. Then, we design an O(n) algorithm to solve the minimum linear arrangement problem of Chord graphs.

Linear time and space gathering of anonymous mobile agents in asynchronous trees

We investigate the relation between the (ideal) time and space complexities for the gathering problem with k anonymous agents in asynchronous anonymous tree networks. The gathering problem requires that all the agents in the network have to meet at a single node within a finite time. Although an asymptotically space-optimal algorithm is known, its time complexity is quite large. In this paper, we consider asymptotically (ideal-)time-optimal algorithms and investigate the minimum memory requirement per agent for asymptotically time-optimal algorithms. First, we show that there exists a tree with n nodes in which Ω(n) bits of memory per agent is required to solve the gathering problem in O(n) time (asymptotically time-optimal). Then, we present an asymptotically time-optimal gathering algorithm. This algorithm can be executed if each agent has O(n) bits of memory. From this lower/upper bound, this algorithm is asymptotically space-optimal on the condition that the time complexity is asymptotically optimal.

Time-Optimal Gathering Algorithm of Mobile Robots with Local Weak Multiplicity Detection in Rings

Time-Optimal Gathering Algorithm of Mobile Robots with Local Weak Multiplicity Detection in Rings

Spectrum Sensing Time Optimization Algorithm for Spectrum Efficiency Maximization in the Low-power Cognitive Radio Ultra Wideband System

For energy detection in a cognitive radio (CR) system, the spectrum sensing time required to successfully detect a primary user (PU) is inversely proportional to the PU's signal strength. When the PU operates in low-SNR regime, the effective transmission time of the CR system with a fixed transmission window can be extremely short for the CR system to fully utilize the spectrum. This paper presents a sensing time optimization algorithm aiming at maximizing the spectral efficiency of the Ultra Wideband (UWB) based CR system by finding the optimal tradeoff between the length of the sensing window and the detection probability in low-SNR regime. Compared with the time fixed sensing methods, the optimization algorithm can produce a significantly longer transmission time for the UWB based CR system to effectively utilize the detected spectrum band while guaranteeing protection to the PUs.

Timing-Driven Variation-Aware Partitioning and Optimization of Mixed Static-Dynamic CMOS Circuits

The advancement in CMOS technology has surpassed the progress in computer aided design tools, creating an avenue for new design optimization flows. This paper presents a design level transistor sizing based timing optimization algorithms for mixed-static-dynamic CMOS logic designs. This optimization algorithm performs timing optimization through partitioning a design into static and dynamic circuits based on timing critical paths, and is further extended through a process variation aware circuit level timing optimization algorithm for dynamic CMOS circuits. Implemented on a 64-b adder and ISCAS benchmark circuits for mixed-static-dynamic CMOS, the design level optimization algorithm demonstrated a critical path delay improvement of over 52% in comparison with static CMOS implementation by state-of-the-art commercial optimization tools.

Disassembly leveling and lot sizing for multiple product types: a basic model and its extension

We consider two interrelated problems that occurred in disassembly systems: disassembly leveling and lot sizing. Disassembly leveling, one of disassembly process planning decisions, is to determine disassembly structures that specify parts and/or subassemblies to be obtained from disassembling used/end-of-life products, and disassembly lot sizing is the problem of determining the amounts of disassembly operations required to satisfy the demands of their parts and/or subassemblies. Unlike the existing studies, this study considers the two problems at the same time for the objective of minimizing the sum of disassembly setup and operation costs. In particular, we consider a generalized version in which disassembly levels may be different even for products of the same type. Two types of the problem are considered in this study. The first one is the basic problem without parts commonality, i.e., products do not share their parts or subassemblies, for which a polynomial time optimal algorithm is suggested after developing a mathematical programming model. The second one is an extended problem with parts commonality. After developing another mathematical programming model for the extension, we prove that it is NP hard. Then, a heuristic algorithm is suggested together with its computational results.

Bi-criteria and tri-criteria analysis to minimize maximum lateness makespan and resource consumption for scheduling a single machine

We analyze two single machine scheduling problems for the case where job processing times are controllable, by allocating continuous and non-renewable resources to the processing operations. The first problem to analyze is constructing the trade-off curve between maximum lateness and total resource consumption; an O(n 2) computational time optimization algorithm was constructed to solve this problem. This algorithm was extended to solve the second problem, which is to construct the trade-off surface between maximum lateness, makespan, and total resource consumption. As part of this algorithm we identify a plane in the 3D field that is formed by the three criteria, which is parallel only to the maximum lateness, and calculate the optimal makespan and total resource consumption as functions of points on this plane. The extended algorithm keeps the same complexity of O(n 2) time. Both algorithms are very robust as they solve the problem for a very large set of resource consumption functions which has to follow only some mild (and commonly acceptable) conditions. Moreover, as far as we know, this is the first research of its kind in the field of multi-objective scheduling to present an algorithm that constructs a 3D trade-off surface.

Using a Guiding Network to Determine Efficient Evacuation Routes in a Public Building

AbstractPrevious studies of models for evacuation routing usually divide the space into multiple interlinked zones. However, for public buildings that are characterized by a more complicated spatial composition, it may be harder to clearly and objectively define the margins for each zone. This paper proposes an approach that determines the most appropriate guidance locations and assembles them into an efficient guiding network. This allows evacuation routes to be constructed based on the links between starting points, guiding nodes, and terminal points. This approach avoids the difficulty of dividing a space into multiple zones and conforms more to real-life evacuation behavior. This paper also proposes an integrated model that applies simulation to estimate the evacuation time and ant colony optimization algorithms to search for an evacuation routing plan and a near-optimal guiding solution. The feasibility of the model is evaluated through a case of one floor in a hospital building. The results indicate...

Explicit Allocation Strategy with Deadline and Budget Constraint Algorithm in Bag of Tasks Grid

Problem statement: This study is for effective scheduling of grid job s based on economy for space shared resources in Bag of tasks grid. Gr id Computing aims in combining the power of heterogeneous, geographically distributed, multi-do main computational resources to provide high performance or high throughput. Approach: Space shared resources are parallel supercomputers and clusters of workstations that provides a great amou nt of computational power. These resources require jobs to be specified formally in terms of the amoun t of time (tr) and number of processors (p) needed for execution. Bag-of-Tasks (BoT) is an application consists of several uniprocessor and independent tasks that have no inter-task communications or tas k-dependencies. BoT is highly suitable for executio n in grids. It is capable of tolerating network delay s or faults and does not require formal job submiss ion. The Explicit allocation strategy assigns the formal job parameters (p, tr) to the job requests, minimi zing the overhead on the grid users to provide a formal job specification. This strategy uses adaptive heur istics to determine the parameters based on certain heuris tics, in order to improve throughput. In the propos ed system, explicit allocation strategy combined with Deadline and Budget Constraint (DBC) Cost Time optimization algorithm performs effective schedulin g of the jobs based on the user's quality of servic e (QoS) requirements such as deadline, budget and optimization strategy. Results: The cost-time optimization scheduling allocates the cheapest reso urces to ensure that the deadline can be met and computation is minimized. In case if there are two resources with the same cost, scheduling is done in any affordable resource so that the job gets execut ed as early as possible. Conclusion: The performance of this scheme against the existing system is evalu ated using cost factor (C factor ) and speed up ratio (T speedup ) and this scheme is more effective than the existi ng system.

Finding All Stable Pairs and Solutions to the Many-to-Many Stable Matching Problem

The many-to-many stable matching problem (MM), defined in the context of a job market, asks for an assignment of workers to firms satisfying the quota of each agent and being stable, pairwise or setwise, with respect to given preference lists or relations. In this paper, we propose a time-optimal algorithm that identifies all stable worker–firm pairs and all stable assignments under pairwise stability, individual preferences, and the max-min criterion. We revisit the poset graph of rotations to obtain an optimal algorithm for enumerating all solutions to the MM and an improved algorithm finding the minimum-weight one. Furthermore, we establish the applicability of all aforementioned algorithms under more complex preference and stability criteria. In a constraint programming context, we introduce a constraint that models the MM and an encoding of the MM as a constraint satisfaction problem. Finally, we provide a series of computational results, including the case where side constraints are imposed.

VART Model–Based Method for Estimation of Instream Dissolved Oxygen and Reaeration Coefficient

AbstractDissolved oxygen (DO) is essential to maintaining flora and fauna in aquatic ecosystems. The DO replenishment through the surface reaeration mechanism is commonly described using the reaeration coefficient (K2). This paper presents a new approach to modeling instream DO and estimating K2. The new approach includes an extension of the Variable Residence Time (VART) model and optimization algorithms for inverse modeling. The VART model is modified in this paper to incorporate the DO reaeration mechanism across the air-water interface, forming the VART-DO model. A major advantage of the VART-DO model is that it is capable of simulating DO exchange across the water-sediment interface through the hyporheic exchange mechanism in addition to the air-water exchange. A sensitivity analysis is conducted to investigate the relative importance of key model parameters to DO modeling. It is found that the K2 value increases markedly with the dispersion coefficient. The simplex-simulated annealing and the geneti...

Modelagem e otimização da operação de veículos na mineração de cobre subterrânea

Na mineração subterrânea, diariamente, uma frota de veículo LHD (load-haul-dump) deve ser alocada à rede de galerias para extrair o minério segundo um plano estratégico de trabalho. Esse plano é definido pela alta gerência e contém o número de cargas a serem extraídas desde os pontos de remoção de uma dada galeria para cada turno de trabalho. Nesse trabalho, formula-se um modelo de programação inteira (PI), para minimizar o makespan de uma galeria de trabalho, e propõe-se um algoritmo ótimo em tempo polinomial, para a sua resolução. Em seguida, obtém-se um conjunto de regras de decisão, a partir do algoritmo proposto, o qual é integrado a um processo de tomada de decisão (PTD). Esse PTD é de simples execução para os operadores de LHDs, determina o makespan ótimo e, se existe a possibilidade de conclusão dentro do turno de trabalho. Finalmente, realiza-se uma análise comparativa entre o PTD proposto e àquele utilizado na mina chilena subterrânea de cobre El Teniente. Os resultados mostram que a experiência acumulada dos operadores converge para soluções próximas ao makespan ótimo.