We introduce and prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binaryquadratic problems subject to assignment constraints that has been proposed by...
详细信息
We introduce and prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binaryquadratic problems subject to assignment constraints that has been proposed by Liberti (4OR 5(3):231-245, 2007, The new conditions resolve inconsistencies that can occur when the original method is used. We also present a mixed-integer linear program to compute a minimally sized linearization. When all the assignment constraints have non-overlapping variable support, this program is shown to have a totally unimodular constraint matrix. Finally, we give a polynomial-time combinatorial algorithm that is exact in this case and can be used as a heuristic otherwise.
Mixed fruit-vegetable cropping systems are a promising way of ensuring environmentally sustainable agricultural production systems in response to the challenge of being able to fulfill local market requirements. Indee...
详细信息
ISBN:
(纸本)9783319600451;9783319600444
Mixed fruit-vegetable cropping systems are a promising way of ensuring environmentally sustainable agricultural production systems in response to the challenge of being able to fulfill local market requirements. Indeed, they combine productions and they make a better use of biodiversity. These agroforestry systems are based on a complex set of interactions modifying the utilization of light, water and nutrients. Thus, designing such a system must optimize the use of these resources: by maximizing positive interactions (facilitation) and minimizing negative ones (competition). To attain these objectives, the system's design has to include the spatial and temporal dimensions, taking into account the evolution of above-and belowground interactions over a time horizon. For that, we define the Mixed Fruit-Vegetable Crop Allocation Problem (MFVCAP) using a discrete representation of the land and the interactions between vegetable crops and fruit trees. First, we give a direct formulation as a binaryquadratic program (BQP). Then we reformulate the problem using a Benders decomposition approach. The master problem has 0/1 binary variables and deals with tree positioning. The subproblem deals with crop quantities. The BQP objective function becomes linear in the continuous subproblem by exploiting the fact that it depends only on the quantity of crops assigned to land units having shade, root, or nothing. This problem decomposition allows us to reformulate the MFVCAP into a Mixed Integer linear Program (MIP). The detailed spatial-temporal crop allocation plan is easy to obtain after solving the MIP. Experimental results show the efficiency of our approach compared to a direct solving of the original BQP formulation.
The efficiency of top-k recommendation is vital to large-scale recommender systems. Hashing is not only an efficient alternative but also complementary to distributed computing, and also a practical and effective opti...
详细信息
ISBN:
(纸本)9781450355520
The efficiency of top-k recommendation is vital to large-scale recommender systems. Hashing is not only an efficient alternative but also complementary to distributed computing, and also a practical and effective option in a computing environment with limited resources. Hashing techniques improve the efficiency of online recommendation by representing users and items by binary codes. However, objective functions of existing methods are not consistent with ultimate goals of recommender systems, and are often optimized via discrete coordinate descent, easily getting stuck in a local optimum. To this end, we propose a Discrete Ranking-based Matrix Factorization (DRMF) algorithm based on each user's pairwise preferences, and formulate it into binary quadratic programming problems to learn binary codes. Due to non-convexity and binary constraints, we further propose self-paced learning for improving the optimization, to include pairwise preferences gradually from easy to complex. We finally evaluate the proposed algorithm on three public real-world datasets, and show that the proposed algorithm outperforms the state-of-the-art hashing-based recommendation algorithms, and even achieves comparable performance to matrix factorization methods.
作者：
Mallach, SvenUniv Bonn
High Performance Comp & Analyt Lab Friedrich Hirzebruch Allee 8 D-53115 Bonn Germany
We present a family of integer programming formulations for the maximum cut problem. These formulations encode the incidence vectors of the cuts of a connected graph by employing a subset of the odd-cycle inequalities...
详细信息
ISBN:
(纸本)9783031609237;9783031609244
We present a family of integer programming formulations for the maximum cut problem. These formulations encode the incidence vectors of the cuts of a connected graph by employing a subset of the odd-cycle inequalities that relate to a spanning tree, and they require only the corresponding edge variables to be integral explicitly. They so describe sufficient restrictions of the classic integer linear program by Barahona and Mahjoub. In addition, we characterize according formulations comprising facet-defining inequalities only. Trade-offs and comparisons to prevalent formulations concerning size and relaxation strength are subject to an experimental study.
3D (or stereo) video has been a visually appealing and costly affordable technology. More sophisticated multi-view videos have also been demonstrated. Yet their remarkably increased data volume poses greater challenge...
详细信息
ISBN:
(纸本)9781457701498
3D (or stereo) video has been a visually appealing and costly affordable technology. More sophisticated multi-view videos have also been demonstrated. Yet their remarkably increased data volume poses greater challenges to the conventional client/server streaming systems, which has already suffered from supporting 2D videos. The stringent multi-stream synchronization further complicate the system design. In this paper, we present an initial attempt toward efficient streaming of stereo/multi-view videos over a peer-to-peer network. We show that the inherent multi-stream nature of stereo video makes segment scheduling more difficult, which is particularly acute with the existence of multiple senders in a peer-to-peer overlay. We formulate the stereo segment scheduling problem as a binary quadratic programming problem and optimally solve it using an MIQP solver. However, given the high peer dynamics and the stringent playback deadline in real-time streaming, the optimal solution is too costly to be obtained. Thus, we develop two efficient algorithms to allow peers frequently compute the scheduling. We show that one of the proposed algorithms can achieve an analytical guarantee in the worst case performance, in particular, the approximation factor is at most 3 comparing with the optimal solution. We implement the proposed algorithms and the optimal in a peer-to-peer simulating system, and show that the proposed algorithms can achieve near-optimal performance efficiently. We further implement two other scheduling algorithms that are used in popular peer-to-peer streaming systems for comparison, and extend our design to support multi-view video with view diversity and dynamics. Under different end-system and network configurations with both stereo and multi-view streaming, the simulation results demonstrate that our algorithms outperform others in terms of streaming quality, stream synchronization/smoothness and scalability.
Semidefinite programming has been used successfully to build hierarchies of convex relaxations to approximate polynomial programs. This approach rapidly becomes computationally expensive and is often tractable only fo...
详细信息
ISBN:
(纸本)9783642208072
Semidefinite programming has been used successfully to build hierarchies of convex relaxations to approximate polynomial programs. This approach rapidly becomes computationally expensive and is often tractable only for problems of small sizes. We propose an iterative scheme that improves the semidefinite relaxations without incurring exponential growth in their size. The key ingredient is a dynamic scheme for generating valid polynomial inequalities for general polynomial programs. These valid inequalities are then used to construct better approximations of the original problem. As a result, the proposed scheme is in principle scalable to large general combinatorial optimization problems. For binary polynomial programs, we prove that the proposed scheme converges to the global optimal solution for interesting cases of the initial approximation of the problem. We also present examples illustrating the computational behaviour of the scheme and compare it to other methods in the literature.
Routing and Wavelength Assignment (RWA) is the most concern in wavelength routed optical networks. This paper proposes a novel binary quadratic programming (BQP) formulation for the static RWA problem. Subsequently, a...
详细信息
ISBN:
(纸本)9781479933433
Routing and Wavelength Assignment (RWA) is the most concern in wavelength routed optical networks. This paper proposes a novel binary quadratic programming (BQP) formulation for the static RWA problem. Subsequently, a heuristic algorithm namely variable-weight routing and wavelength assignment (VW-RWA) is proposed to solve the BQP problem. In this method, the weight of a link is proportional to the link congestion. Performance evaluation results show that our proposed algorithm not only can decrease the number of required wavelengths in the network but also can reduce the blocking rate.
Merkle tree is a fundamental part of blockchain technology, especially in Ethereum cryptocurrency system. The balance of the accounts involved in each transaction is stored on the leaf nodes and must be updated in the...
详细信息
ISBN:
(纸本)9783031414558;9783031414565
Merkle tree is a fundamental part of blockchain technology, especially in Ethereum cryptocurrency system. The balance of the accounts involved in each transaction is stored on the leaf nodes and must be updated in the State Merkle tree. In this paper, we take advantage of typical transaction characteristics for better constructing the Merkle tree to improve blockchain network performance. It consists of identifying a tree structure with the minimum number of hash values required to update the account data associated with each transaction based on the distribution of all transactions. The proposed optimization model is a combinatorial problem with quadratic functions and binary variables. By using the binary character of variables and penalty techniques, we provide a conventional DC (Difference of Convex functions) program that is efficiently solvable by the DCA (DC Algorithm). Additionally, we suggest an effective recursive DCA-based method for building a Merkle tree for a great amount of blockchain accounts. Numerical experiments on several datasets illustrate the efficiency of our approaches.
A way of minimizing the opportunity of cheating in exams is to assign different tests to students. The likelihood of cheating then depends on the proximity of the students' desks, and the similarity of the tests. ...
详细信息
ISBN:
(纸本)9781509060177
A way of minimizing the opportunity of cheating in exams is to assign different tests to students. The likelihood of cheating then depends on the proximity of the students' desks, and the similarity of the tests. The test-assignment problem is to find an assignment of tests to desks that minimizes that total likelihood of cheating. The problem is a variant of a graph coloring problem and is NP-hard. We propose a new heuristic solution for this problem. Our approach differs from the usual way of designing heuristics in two ways. First, we reduce test-assignment to the more general unconstrained binary quadratic programming. Second, we search for a good heuristic using an automatic algorithm configuration tool that evolves heuristics in a space of algorithms built from known components for binary quadratic programming. The best hybrid heuristics found repeatedly recombine elements of a population of elite solutions and improve them by a tabu search. Computational tests suggest that the resulting algorithms are competitive with existing heuristics that have been designed manually.
Based on the special kind of spreading sequence and semidefinite programming relaxation, A new multiuser detector for asynchronous code division multiple access system is presented. At each transmitter, the special sp...
详细信息
ISBN:
(纸本)9781424437092
Based on the special kind of spreading sequence and semidefinite programming relaxation, A new multiuser detector for asynchronous code division multiple access system is presented. At each transmitter, the special spreading sequence whose second half is the replica of the first is employed. Maximum-likelihood(ML) multiuser detection only need detect 2K once. Then ML detection can be efficiently and accurately approximated using the semidefinite relaxation. Its time complexity decrease to the order of O(2K(3.5)), while the Viterbi Algorithm (optimum detector) requires a exponentially computational complexity. We compare the performances of the new SDP method and a joint method of block coordinate ascent and semidefinite programming relaxation(BCA-SDR) method for the asynchronous multiuser detection problem in various situations, and simulations demonstrate that the new semidefinite programming method often yields better bit error rate (BER) performances than the BCA-SDR method, but the average CPU time of this method is significantly reduced.
暂无评论