Auction algorithms for generalized nonlinear network flow problems

Thesis (Ph.D.)--Boston UniversityNetwork flow is an area of optimization theory concerned with optimization over networks with a range of applicability in fields such as computer networks, manufacturing, finance, scheduling and routing, telecommunications, and transportation. In both linear and nonlinear networks, a family of primal-dual algorithms based on "approximate" Complementary Slackness (ε-CS) is among the fastest in centralized and distributed environments. These include the auction algorithm for the linear assignment/transportation problems, ε-relaxation and Auction/Sequential Shortest Path (ASSP) for the min-cost flow and max-flow problems. Within this family, the auction algorithm is particularly fast, as it uses "second best" information, as compared to using the more generic ε-relaxation for linear assignment/transportation. Inspired by the success of auction algorithms, we extend them to two important classes of nonlinear network flow problems. We start with the nonlinear Resource Allocation Problem (RAP). This problem consists of optimally assigning N divisible resources to M competing missions/tasks each with its own utility function. This simple yet powerful framework has found applications in diverse fields such as finance, economics, logistics, sensor and wireless networks. RAP is an instance of generalized network (networks with arc gains) flow problem but it has significant special structure analogous to the assignment/transportation problem. We develop a class of auction algorithms for RAP: a finite-time auction algorithm for both synchronous and asynchronous environments followed by a combination of forward and reverse auction with ε-scaling to achieve pseudo polynomial complexity for any non-increasing generalized convex utilities including non-continuous and/ or non-differentiable functions. These techniques are then generalized to handle shipping costs on allocations. Lastly, we demonstrate how these techniques can be used for solving a dynamic RAP where nodes may appear or disappear over time. In later part of the thesis, we consider the convex nonlinear min-cost flow problem. Although E-relaxation and ASSP are among the fastest available techniques here, we illustrate how nonlinear costs, as opposed to linear, introduce a significant bottleneck on the progress that these algorithms make per iteration. We then extend the core idea of the auction algorithm, use of second best to make aggressive steps, to overcome this bottleneck and hence develop a faster version of ε-relaxation. This new algorithm shares the same theoretical complexity as the original but outperforms it in our numerical experiments based on random test problem suites

Learning to Prune: Speeding up Repeated Computations

It is common to encounter situations where one must solve a sequence of similar computational problems. Running a standard algorithm with worst-case runtime guarantees on each instance will fail to take advantage of valuable structure shared across the problem instances. For example, when a commuter drives from work to home, there are typically only a handful of routes that will ever be the shortest path. A naive algorithm that does not exploit this common structure may spend most of its time checking roads that will never be in the shortest path. More generally, we can often ignore large swaths of the search space that will likely never contain an optimal solution. We present an algorithm that learns to maximally prune the search space on repeated computations, thereby reducing runtime while provably outputting the correct solution each period with high probability. Our algorithm employs a simple explore-exploit technique resembling those used in online algorithms, though our setting is quite different. We prove that, with respect to our model of pruning search spaces, our approach is optimal up to constant factors. Finally, we illustrate the applicability of our model and algorithm to three classic problems: shortest-path routing, string search, and linear programming. We present experiments confirming that our simple algorithm is effective at significantly reducing the runtime of solving repeated computations

On distributed virtual network embedding with guarantees

To provide wide-area network services, resources from different infrastructure providers are needed. Leveraging the consensus-based resource allocation literature, we propose a general distributed auction mechanism for the (NP-hard) virtual network (VNET) embedding problem. Under reasonable assumptions on the bidding scheme, the proposed mechanism is proven to converge, and it is shown that the solutions guarantee a worst case efficiency of (?????) relative to the optimal solution, and that this bound is optimal, that is, no better approximation exists. Using extensive simulations, we confirm superior convergence properties and resource utilization when compared with existing distributed VNET embedding solutions, and we show how byappropriate policy design, our mechanism can be instantiated to accommodate the embedding goals of different service and infrastructure providers, resulting in an attractive and flexible resource allocation solution.This work is supported in part by the National Science Foundation under grant CNS-0963974

On distributed virtual network embedding with guarantees

To provide wide-area network services, resources from different infrastructure providers are needed. Leveraging the consensus-based resource allocation literature, we propose a general distributed auction mechanism for the (NP-hard) virtual network (VNET) embedding problem. Under reasonable assumptions on the bidding scheme, the proposed mechanism is proven to converge, and it is shown that the solutions guarantee a worst case efficiency of (?????) relative to the optimal solution, and that this bound is optimal, that is, no better approximation exists. Using extensive simulations, we confirm superior convergence properties and resource utilization when compared with existing distributed VNET embedding solutions, and we show how byappropriate policy design, our mechanism can be instantiated to accommodate the embedding goals of different service and infrastructure providers, resulting in an attractive and flexible resource allocation solution.This work is supported in part by the National Science Foundation under grant CNS-0963974

On distributed virtual network embedding with guarantees

To provide wide-area network services, resources from different infrastructure providers are needed. Leveraging the consensus-based resource allocation literature, we propose a general distributed auction mechanism for the (NP-hard) virtual network (VNET) embedding problem. Under reasonable assumptions on the bidding scheme, the proposed mechanism is proven to converge, and it is shown that the solutions guarantee a worst-case efficiency of (1-(1/e)) relative to the optimal node embedding, or VNET embedding if virtual links are mapped to exactly one physical link. This bound is optimal, that is, no better polynomial-time approximation algorithm exists, unless P=NP. Using extensive simulations, we confirm superior convergence properties and resource utilization when compared to existing distributed VNET embedding solutions, and we show how by appropriate policy design, our mechanism can be instantiated to accommodate the embedding goals of different service and infrastructure providers, resulting in an attractive and flexible resource allocation solution.CNS-0963974 - National Science Foundationhttp://www.cs.bu.edu/fac/matta/Papers/ToN-CAD.pdfAccepted manuscrip

Exact algorithms for the matrix bid auction.

In a combinatorial auction, multiple items are for sale simultaneously to a set of buyers. These buyers are allowed to place bids on subsets of the available items. A special kind of combinatorial auction is the so-called matrix bid auction, which was developed by Day (2004). The matrix bid auction imposes restrictions on what a bidder can bid for a subsets of the items. This paper focusses on the winner determination problem, i.e. deciding which bidders should get what items. The winner determination problem of a general combinatorial auction is NP-hard and inapproximable. We discuss the computational complexity of the winner determination problem for a special case of the matrix bid auction. We present two mathematical programming formulations for the general matrix bid auction winner determination problem. Based on one of these formulations, we develop two branch-and-price algorithms to solve the winner determination problem. Finally, we present computational results for these algorithms and compare them with results from a branch-and-cut approach based on Day & Raghavan (2006).Algorithms; Bids; Branch-and-price; Combinatorial auction; Complexity; Computational complexity; Exact algorithm; Mathematical programming; Matrix; Matrix bids; Research; Winner determination;

Rational coordination of crowdsourced resources for geo-temporal request satisfaction

Existing mobile devices roaming around the mobility field should be considered as useful resources in geo-temporal request satisfaction. We refer to the capability of an application to access a physical device at particular geographical locations and times as GeoPresence, and we pre- sume that mobile agents participating in GeoPresence-capable applica- tions should be rational, competitive, and willing to deviate from their routes if given the right incentive. In this paper, we define the Hitch- hiking problem, which is that of finding the optimal assignment of re- quests with specific spatio-temporal characteristics to competitive mobile agents subject to spatio-temporal constraints. We design a mechanism that takes into consideration the rationality of the agents for request sat- isfaction, with an objective to maximize the total profit of the system. We analytically prove the mechanism to be convergent with a profit com- parable to that of a 1/2-approximation greedy algorithm, and evaluate its consideration of rationality experimentally.Supported in part by NSF Grants; #1430145, #1414119, #1347522, #1239021, and #1012798

An auction/sequential shortest path algorithm for the minimum cost network flow problem

Caption title.Includes bibliographical references (p. 9-10).Supported by the NSF. CCR-9103804by Dimitri P. Bertsekas

An auction algorithm for the max-flow problem

Caption title.Includes bibliographical references.Supported by the NSF. CCR-9103804by Dimitri P. Bertsekas