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Solving Billion-Scale Knapsack Problems [article]

Xingwen Zhang, Feng Qi, Zhigang Hua, Shuang Yang
2020 arXiv   pre-print
Knapsack problems (KPs) are common in industry, but solving KPs is known to be NP-hard and has been tractable only at a relatively small scale.  ...  As an example, our implementation leads to one of the most efficient KP solvers known to date -- capable to solve KPs at an unprecedented scale (e.g., KPs with 1 billion decision variables and 1 billion  ...  CONCLUSIONS We introduce distributed algorithms for solving billion-scale knapsack problems.  ... 
arXiv:2002.00352v1 fatcat:nvdevbjmp5enfcyuugvytuchqi

The Second-Price Knapsack Problem: Near-Optimal Real Time Bidding in Internet Advertisement [article]

Jonathan Amar, Nicholas Renegar
2020 arXiv   pre-print
The main results of this paper establish general methods for adapting these primal and dual online knapsack selection algorithms to the second-price knapsack problem, where the prices are revealed only  ...  This is in contrast to the traditional online knapsack problem, where posted prices are revealed when ads arrive, and for which there exists a rich literature of primal and dual algorithms.  ...  For every ad arrival t, we solve a fractional scaled ad selection for the knapsack problem, where in particular the scaling factor is t T .  ... 
arXiv:1810.10661v4 fatcat:yf34tngz6najvklmfa44qaff2u

The Mathematics of Public-Key Cryptography

Martin E. Hellman
1979 Scientific American  
of solving a problem.  ...  The receiver simply applies his secret vector a' to solve the knapsack problem for C' and recover x.  ... 
doi:10.1038/scientificamerican0879-146 fatcat:7t6pp7s2gveq5cj7vjug6xrdmy

Genetic Algorithms as Multi-Coordinators in Large-Scale Optimization [chapter]

Ioannis T. Christou, Wayne Martin, Robert R. Meyer
1999 IMA Volumes in Mathematics and its Applications  
We present high-level, decomposition-based algorithms for large-scale block-angular optimization problems containing integer variables, and demonstrate their e ectiveness in the solution of large-scale  ...  Even for graph partitioning problems requiring billions of variables in a standard 0-1 formulation, this approach produces high-quality solutions (as measured by deviations from an easily computed lower  ...  (In contrast, the knapsack approach solved to optimality problems with N as large as 1000 in less than 1 second.)  ... 
doi:10.1007/978-1-4612-1542-4_1 fatcat:2lv64dxto5arvfkzaibpz4l7bi

Truthful Strategy and Resource Integration for Multi-tenant Data Center Demand Response [chapter]

Youshi Wang, Fa Zhang, Zhiyong Liu
2015 Lecture Notes in Computer Science  
the actual resource migration and integration problem.  ...  achieving the overall coordination, we integrate tenants' resources to increase the colocation's resource utilization and optimize the whole colocation's energy efficiency, then devise two algorithms to solve  ...  This is a 0-1 multi-knapsack problem. According to the assumption, the resource integration problem can be solved within polynomial time, the subproblem should also be solved within polynomial time.  ... 
doi:10.1007/978-3-319-19647-3_24 fatcat:uo7p5oikofbjvji2iwt7iqqywu

An overview of public key cryptography

M.E. Hellman
2002 IEEE Communications Magazine  
(The scale is calibrated to deduct the weight of the empty knapsack.)  ...  The problem is to solve for the subset, or equivalently, for the binary vector x which is the solution to the equation S = a * x . (11) While the knapsack problem is very difficult to solve in general,  ...  A major problem that confronts cryptography is the certification of these systems. How can we decide which proposed systems really are secure, and which only appear to be secure?  ... 
doi:10.1109/mcom.2002.1006971 fatcat:4q4ia4zsqjekdnq56j7aca7rfm

Three scalable approaches to improving many-core throughput for a given peak power budget

John Sartori, Rakesh Kumar
2009 2009 International Conference on High Performance Computing (HiPC)  
The proposed techniques (mapping the power management problem to a knapsack problem, mapping it to a genetic search problem, and mapping it to a simple learning problem with confidence counters) prevent  ...  by the DCKP [30] , solving the DCKP is an O(n) problem in this case (though in a general, it is not).  ...  The objective of the knapsack problem is to fill a knapsack of limited capacity in such a way that the profit of the carried items is maximized.  ... 
doi:10.1109/hipc.2009.5433221 dblp:conf/hipc/SartoriK09 fatcat:6z2axrme6rgy3j7naaquua3fku

An overview of public key cryptography

M. Hellman
1978 Communications Society  
There is no apparent, easy way to solve knapsack problems involving a unless one knows the trap-door'information.  ...  Given the weight of the filled knapsack, 1156 grams, can you determine which of the items are contained in the knapsack? (The scale is calibrated to deduct the weight of the empty knapsack.)  ... 
doi:10.1109/mcom.1978.1089772 fatcat:hgzmjajgi5gnzpub6ghy23wai4


Wook-Shin Han, Sangyeon Lee, Kyungyeol Park, Jeong-Hoon Lee, Min-Soo Kim, Jinha Kim, Hwanjo Yu
2013 Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '13  
In this paper, we propose a general, disk-based graph engine called Tur-boGraph to process billion-scale graphs very efficiently by using modern hardware on a single PC.  ...  Although distributed graph engines such as GBase and Pregel handle billion-scale graphs, the user needs to be skilled at managing and tuning a distributed system in a cluster, which is a nontrivial job  ...  Therefore, we need a systematic approach to solve this problem.  ... 
doi:10.1145/2487575.2487581 dblp:conf/kdd/HanLPL0KY13 fatcat:wm3oy6qgdfh4hgo5ma2ygcrtc4

Memory access aware on-line voltage control for performance and energy optimization

Xi Chen, Chi Xu, Robert P. Dick
2010 2010 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)  
The P-DVFS problem is formulated as a multiplechoice knapsack problem, which can be efficiently and optimally solved online.  ...  We first propose a two-stage DVFS algorithm based on formulating the throughput-constrained energy minimization problem as a multiple-choice knapsack problem (MCKP).  ...  Thus, the formulation can be treated as an multiple-choice knapsack problem (MCKP) [12] . We solve this problem optimally using "lp solve" [13].  ... 
doi:10.1109/iccad.2010.5653631 dblp:conf/iccad/ChenXD10 fatcat:nnma7eirazekplsothuzrly2rm

Energy-aware routing in data center network

Yunfei Shang, Dan Li, Mingwei Xu
2010 Proceedings of the first ACM SIGCOMM workshop on Green networking - Green Networking '10  
To overcome the problem of tree architecture in current practice, many new network architectures are proposed, represented by Fat-Tree, BCube, and etc.  ...  Our idea is to reduce the classical 0-1 Knapsack problem into the ERP-2 problem. 0-1 Knapsack problem belongs to the well known Karp's 21 NP-complete problems [9] .  ...  Then, we proposed a heuristic algorithm to solve the energy-aware routing problem.  ... 
doi:10.1145/1851290.1851292 dblp:conf/sigcomm/ShangLX10 fatcat:bgx5vbya5ng3foj4z7ddsxay3m

Content Replication in Large Distributed Caches [article]

Sharayu Moharir, Nikhil Karamchandani
2016 arXiv   pre-print
We use a novel mapping between our content replication problem and the Knapsack problem to prove a lower bound on the transmission rate for any content replication policy.  ...  Using insights obtained from the mapping, we propose a content replication policy - Knapsack Storage - which achieves this lower bound.  ...  Knapsack Storage: Part 1 -The first part of the Knapsack Storage policy determines how many caches each content is stored on by solving a fractional Knapsack problem.  ... 
arXiv:1603.09153v1 fatcat:gwx24seqcnak3d3477wfw2hrrq

Discriminating Instance Generation for Automated Constraint Model Selection [chapter]

Ian P. Gent, Bilal Syed Hussain, Christopher Jefferson, Lars Kotthoff, Ian Miguel, Glenna F. Nightingale, Peter Nightingale
2014 Lecture Notes in Computer Science  
If all models solve a given instance in a trivial amount of time, or if no models solve it in the time available, then the instance is not useful for model selection.  ...  The instance space is determined by the parameters of the associated problem class.  ...  Reconsider the Knapsack Problem from Figure 1 .  ... 
doi:10.1007/978-3-319-10428-7_27 fatcat:hbbdkrlidjcvbdc6lmkv2weruy

Learning Data-Driven Drug-Target-Disease Interaction via Neural Tensor Network

Huiyuan Chen, Jing Li
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
Moreover, this very specific formulation is known as cardinality constrained knapsack or Exact K-item Knapsack Problem(E-KKP). This problem is proved to be NP-Complete [Kellerer et al., 2004] .  ...  We are interested in solving the problem with the discussed constraints.  ... 
doi:10.24963/ijcai.2020/473 dblp:conf/ijcai/MirzadehG20 fatcat:3c4ibgs7zjgdff5hk2aky4b3bu

Prioritization of K-12 School Maintenance Construction Projects Using Genetic Algorithm and Dynamic Programming Models

Tariq Shehab, Reza Haghighat, Kiran K Sajjan, Vahid Balali
2021 Journal of Information Technology in Construction  
These models help to find the optimum solutions among the given data through mutations and crossover in deriving a possible solution to a multi-layered problem.  ...  The complicated Knapsack problems could be solved through DP.  ...  Rong and Figueira (2012) proved that the best approach to solve a tedious Knapsack problem is by utilizing DP.  ... 
doi:10.36680/j.itcon.2021.007 fatcat:eyn7dd6ri5avhnvfencvj6nhoy
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