Algorithms as Mechanisms: The Price of Anarchy of Relax-and-Round

Many algorithms that are originally designed without explicitly considering incentive properties are later combined with simple pricing rules and used as mechanisms. The resulting mechanisms are often natural and simple to understand. But how good are these algorithms as mechanisms? Truthful reporting of valuations is typically not a dominant strategy (certainly not with a pay-your-bid, first-price rule, but it is likely not a good strategy even with a critical value, or second-price style rule either). Our goal is to show that a wide class of approximation algorithms yields this way mechanisms with low Price of Anarchy. The seminal result of Lucier and Borodin [SODA 2010] shows that combining a greedy algorithm that is an $\alpha$-approximation algorithm with a pay-your-bid payment rule yields a mechanism whose Price of Anarchy is $O(\alpha)$. In this paper we significantly extend the class of algorithms for which such a result is available by showing that this close connection between approximation ratio on the one hand and Price of Anarchy on the other also holds for the design principle of relaxation and rounding provided that the relaxation is smooth and the rounding is oblivious. We demonstrate the far-reaching consequences of our result by showing its implications for sparse packing integer programs, such as multi-unit auctions and generalized matching, for the maximum traveling salesman problem, for combinatorial auctions, and for single source unsplittable flow problems. In all these problems our approach leads to novel simple, near-optimal mechanisms whose Price of Anarchy either matches or beats the performance guarantees of known mechanisms.Comment: Extended abstract appeared in Proc. of 16th ACM Conference on Economics and Computation (EC'15

Merlin: A Language for Provisioning Network Resources

This paper presents Merlin, a new framework for managing resources in software-defined networks. With Merlin, administrators express high-level policies using programs in a declarative language. The language includes logical predicates to identify sets of packets, regular expressions to encode forwarding paths, and arithmetic formulas to specify bandwidth constraints. The Merlin compiler uses a combination of advanced techniques to translate these policies into code that can be executed on network elements including a constraint solver that allocates bandwidth using parameterizable heuristics. To facilitate dynamic adaptation, Merlin provides mechanisms for delegating control of sub-policies and for verifying that modifications made to sub-policies do not violate global constraints. Experiments demonstrate the expressiveness and scalability of Merlin on real-world topologies and applications. Overall, Merlin simplifies network administration by providing high-level abstractions for specifying network policies and scalable infrastructure for enforcing them

Flow Maximization Problem as Linear Programming Problem with Capacity Constraints

Flow maximization is a fundamental problem in mathematics; there are several algorithms available to solve this problem, but these algorithms have some limitations. This paper presents the flow maximization problem as a Linear Programming Problem (L.P.P.). The solution given by L.P.P. formulation of the problem and provided by Ford Fulkerson algorithm is same. This paper also compares the single path flow and k-splitting of the flow and suggests that k-splitting of flow is better than single path flow

Approximating the single source unsplittable min-cost flow problem

In the single source unsplittable min-cost flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given graph with edge capacities and costs; the demand of each commodity must be routed along a single path and the total cost must not exceed a given budget. This problem has been introduced by Kleinberg and generalizes several NP-complete problems from various areas in combinatorial optimization such as packing, partitioning, scheduling, load balancing and virtual-circuit routing

Fault Tolerant Placement of Stateful VNFs and Dynamic Fault Recovery in Cloud Networks

Traditional network functions such as firewalls are implemented in costly dedicated hardware. By decoupling network functions from physical devices, network function virtualization enables virtual network functions (VNF) to run in virtual machines (VMs). However, VNFs are vulnerable to various faults such as software and hardware failures. To enhance VNF fault tolerance, the deployment of backup VNFs in stand-by VM instances is necessary. In case of stateful VNFs, stand-by instances require constant state updates from active instances during its operation. This will guarantee a correct and seamless handover from failed instances to stand-by instances after failures. Nevertheless, such state updates to stand-by instances could consume significant network bandwidth resources and lead to potential admission failures for VNF requests. In this paper, we study the fault-tolerant VNF placement problem with the optimization objective of admitting as many requests as possible. In particular, the VNF placement of active/stand-by instances, the request routing paths to active instances, and state transfer paths to stand-by instances are jointly considered. We devise an efficient heuristic algorithm to solve this problem. For the fault tolerance problem without computing or bandwidth constraints, we also propose two bicriteria approximation algorithms with performance guarantees for a special case of the problem. Given the placement locations of VNFs, some of them may go faulty. We thus consider the dynamic fault recovery problem, for which we propose an approximation algorithm that dynamically switches traffic processing from faulty VNFs to normal ones. Simulations with realistic settings show that our algorithms can significantly improve the request admission rate compared to conventional approaches

Optimizing Emergency Transportation through Multicommodity Quickest Paths

In transportation networks with limited capacities and travel times on the arcs, a class of problems attracting a growing scientific interest is represented by the optimal routing and scheduling of given amounts of flow to be transshipped from the origin points to the specific destinations in minimum time. Such problems are of particular concern to emergency transportation where evacuation plans seek to minimize the time evacuees need to clear the affected area and reach the safe zones. Flows over time approaches are among the most suitable mathematical tools to provide a modelling representation of these problems from a macroscopic point of view. Among them, the Quickest Path Problem (QPP), requires an origin-destination flow to be routed on a single path while taking into account inflow limits on the arcs and minimizing the makespan, namely, the time instant when the last unit of flow reaches its destination. In the context of emergency transport, the QPP represents a relevant modelling tool, since its solutions are based on unsplittable dynamic flows that can support the development of evacuation plans which are very easy to be correctly implemented, assigning one single evacuation path to a whole population. This way it is possible to prevent interferences, turbulence, and congestions that may affect the transportation process, worsening the overall clearing time. Nevertheless, the current state-of-the-art presents a lack of studies on multicommodity generalizations of the QPP, where network flows refer to various populations, possibly with different origins and destinations. In this paper we provide a contribution to fill this gap, by considering the Multicommodity Quickest Path Problem (MCQPP), where multiple commodities, each with its own origin, destination and demand, must be routed on a capacitated network with travel times on the arcs, while minimizing the overall makespan and allowing the flow associated to each commodity to be routed on a single path. For this optimization problem, we provide the first mathematical formulation in the scientific literature, based on mixed integer programming and encompassing specific features aimed at empowering the suitability of the arising solutions in real emergency transportation plans. A computational experience performed on a set of benchmark instances is then presented to provide a proof-of-concept for our original model and to evaluate the quality and suitability of the provided solutions together with the required computational effort. Most of the instances are solved at the optimum by a commercial MIP solver, fed with a lower bound deriving from the optimal makespan of a splittable-flow relaxation of the MCQPP

Single-source k-splittable min-cost flows

Motivated by a famous open question on the single-source unsplittable minimum cost flow problem, we present a new approximation result for the relaxation of the problem where, for a given number k, each commodity must be routed along at most k paths

Algorithms for Fault-Tolerant Placement of Stateful Virtualized Network Functions

Traditional network functions (NFs) such as firewalls are implemented in costly dedicated hardware. By decoupling NFs from physical devices, network function virtualization enables virtual network functions (VNF) to run in virtual machines (VMs). However, VNFs are vulnerable to various faults such as software and hardware failures. To enhance VNF fault tolerance, the deployment of backup VNFs in stand-by VM instances is necessary. In case of stateful VNFs, stand-by instances require constant state updates from active instances during its operation. This will guarantee a correct and seamless handover from failed instances to stand-by instances after failures. Nevertheless, such state updates to stand-by instances could consume significant network bandwidth resources and lead to potential admission failures for VNF requests. In this paper, we study the fault-tolerant VNF placement problem with the optimization objective of admitting as many requests as possible. In particular, the VNF placement of active/stand-by instances, the request routing paths to active instances, and state transfer paths to stand-by instances are jointly considered. We devise an efficient heuristic algorithm to solve this problem, and propose a bi-criteria approximation algorithm with performance guarantees for a special case of the problem. Simulations with realistic settings show that our algorithms can significantly improve the request admission rate compared to conventional approaches