OPTIMIZING DATA THROUGHPUT IN CLIENT/SERVER SYSTEMS BY KEEPING QUEUE SIZES BALANCED

2012 ◽  
Vol 04 (02) ◽  
pp. 1250040
Author(s):  
E. KRANAKIS ◽  
D. KRIZANC ◽  
I. LAMBADARIS ◽  
L. NARAYANAN ◽  
J. OPATRNY
Keyword(s):  
Data Gathering ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Base Stations ◽  
Single Server ◽  
Wireless Devices ◽  
Time Step ◽  
Data Throughput ◽  
Server Systems ◽  
Overall Performance

Consider a synchronous system of clients and servers whereby client requests may be satisfied by any one of the servers the clients are assigned to and where the association between clients and servers is determined by an arbitrary but predefined apportionment of the set of servers to clients and of clients to servers. A client can get the required service from any of the servers it is assigned to and at each time step all clients make a request to the servers which then provide the service according to requests. Since clients can make requests simultaneously, if there is no coordination in the "client-to-server" assignment process some clients may have to wait longer if they are assigned simultaneously to a single server when overall performance could improve had they been assigned to separate available servers. Therefore a principal approach to optimizing throughput when assigning client requests to supporting servers, is to keep the client queue sizes well balanced so as to prevent servers from having to remain idle while other servers are being overused. There are several potential examples of such systems involving data gathering and forwarding among sensors in a sensor network or when the servers are base-stations and the clients may be either rotating satellites or other wireless devices, for example. In this paper we consider the problem of finding an assignment of clients to servers that results in all clients receiving a packet while optimally balancing the sizes of remaining queues at the clients. We give a polynomial time algorithm for solving this problem which requires O((m + n)3n) arithmetic operations, where m is the number of client queues and n is the number of servers.

scholarly journals Optimizing Reachability Sets in Temporal Graphs by Delaying

2020 ◽  
Vol 34 (06) ◽  
pp. 9810-9817
Author(s):  
Argyrios Deligkas ◽  
Igor Potapov
Keyword(s):  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Control Mechanisms ◽  
Scheduling Problems ◽  
Dynamic Graph ◽  
Time Step ◽  
Supply Networks ◽  
Reachability Sets ◽  
Network Epidemiology ◽  
Temporal Graphs

A temporal graph is a dynamic graph where every edge is assigned a set of integer time labels that indicate at which discrete time step the edge is available. In this paper, we study how changes of the time labels, corresponding to delays on the availability of the edges, affect the reachability sets from given sources. The questions about reachability sets are motivated by numerous applications of temporal graphs in network epidemiology and scheduling problems in supply networks in manufacturing. We introduce control mechanisms for reachability sets that are based on two natural operations of delaying time events. The first operation, termed merging, is global and batches together consecutive time labels in the whole network simultaneously. This corresponds to postponing all events until a particular time. The second, imposes independent delays on the time labels of every edge of the graph. We provide a thorough investigation of the computational complexity of different objectives related to reachability sets when these operations are used. For the merging operation, we prove NP-hardness results for several minimization and maximization reachability objectives, even for very simple graph structures. For the second operation, we prove that the minimization problems are NP-hard when the number of allowed delays is bounded. We complement this with a polynomial-time algorithm for the case of unbounded delays.

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

scholarly journals Metric Dimension Parameterized By Treewidth

Algorithmica ◽  
2021 ◽  
Author(s):  
Édouard Bonnet ◽  
Nidhi Purohit
Keyword(s):  
Computable Function ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Minimum Size ◽  
Metric Dimension ◽  
Resolving Set ◽  
Input Graph ◽  
Outerplanar Graphs ◽  
Bounded Treewidth ◽  
Fpt Algorithm

AbstractA resolving set S of a graph G is a subset of its vertices such that no two vertices of G have the same distance vector to S. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a resolving set of size at most some specified integer. This problem is NP-complete, and remains so in very restricted classes of graphs. It is also W[2]-complete with respect to the size of the solution. Metric Dimension has proven elusive on graphs of bounded treewidth. On the algorithmic side, a polynomial time algorithm is known for trees, and even for outerplanar graphs, but the general case of treewidth at most two is open. On the complexity side, no parameterized hardness is known. This has led several papers on the topic to ask for the parameterized complexity of Metric Dimension with respect to treewidth. We provide a first answer to the question. We show that Metric Dimension parameterized by the treewidth of the input graph is W[1]-hard. More refinedly we prove that, unless the Exponential Time Hypothesis fails, there is no algorithm solving Metric Dimension in time $$f(\text {pw})n^{o(\text {pw})}$$ f ( pw ) n o ( pw ) on n-vertex graphs of constant degree, with $$\text {pw}$$ pw the pathwidth of the input graph, and f any computable function. This is in stark contrast with an FPT algorithm of Belmonte et al. (SIAM J Discrete Math 31(2):1217–1243, 2017) with respect to the combined parameter $$\text {tl}+\Delta$$ tl + Δ , where $$\text {tl}$$ tl is the tree-length and $$\Delta$$ Δ the maximum-degree of the input graph.

scholarly journals A Fast and Exact Greedy Algorithm for the Core–Periphery Problem

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 94 ◽  
Author(s):  
Dario Fasino ◽  
Franca Rinaldi
Keyword(s):  
Structural Analysis ◽  
Optimization Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Combinatorial Optimization Problem ◽  
Connected Subgraph ◽  
Optimal Solutions ◽  
The Core ◽  
Core Set ◽  
Key Concepts

The core–periphery structure is one of the key concepts in the structural analysis of complex networks. It consists of a partitioning of the node set of a given graph or network into two groups, called core and periphery, where the core nodes induce a well-connected subgraph and share connections with peripheral nodes, while the peripheral nodes are loosely connected to the core nodes and other peripheral nodes. We propose a polynomial-time algorithm to detect core–periphery structures in networks having a symmetric adjacency matrix. The core set is defined as the solution of a combinatorial optimization problem, which has a pleasant symmetry with respect to graph complementation. We provide a complete description of the optimal solutions to that problem and an exact and efficient algorithm to compute them. The proposed approach is extended to networks with loops and oriented edges. Numerical simulations are carried out on both synthetic and real-world networks to demonstrate the effectiveness and practicability of the proposed algorithm.

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