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  1. Oblivious routing has a long history in both the theory and practice of networking. In this work we initiate the formal study of oblivious routing in the context of reconfigurable networks, a new architecture that has recently come to the fore in datacenter networking. These networks allow a rapidly changing bounded-degree pattern of interconnections between nodes, but the network topology and the selection of routing paths must both be oblivious to the traffic demand matrix. Our focus is on the trade-off between maximizing throughput and minimizing latency in these networks. For every constant throughput rate, we characterize (up to a constant factor) the minimum latency achievable by an oblivious reconfigurable network design that satisfies the given throughput guarantee. The trade-off between these two objectives turns out to be surprisingly subtle: the curve depicting it has an unexpected scalloped shape reflecting the fact that load-balancing becomes more difficult when the average length of routing paths is not an integer because equalizing all the path lengths is not possible. The proof of our lower bound uses LP duality to verify that Valiant load balancing is the most efficient oblivious routing scheme when used in combination with an optimally-designed reconfigurable network topology. The proof of our upper bound uses an algebraic construction in which the network nodes are identified with vectors over a finite field, the network topology is described by either the elementary basis or a sequence of Vandermonde matrices, and routing paths are constructed by selecting columns of these matrices to yield the appropriate mixture of path lengths within the shortest possible time interval. 
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  2. In many networking scenarios, long-lived flows can be rerouted to free up resources and accommodate new flows, but doing so comes at a cost in terms of disruption. An archetypical example is the transmission of live streams in a content delivery network: audio and video encoders (clients) generate live streams and connect to a server which rebroadcasts their stream to the rest of the network. Reconnecting a client to a different server mid-stream is very disruptive. We abstract these scenarios in the setting of a capacitated network where clients arrive one by one and request to send a unit of flow to a designated set of servers subject to edge/vertex capacity constraints. An online algorithm maintains a sequence of flows that route the clients present so far to the set of servers. The cost of a sequence of flows is defined as the net switching cost, i.e. total length of all augmenting paths used to transform each flow into its successor. We prove that for unit-vertex-capacitated networks, the algorithm that successively updates the flow using the shortest augmenting path from the new client to a free server incurs a total switching cost of O(n log2 n), where n is the number of vertices in the network. This result is obtained by reducing to the online bipartite matching problem studied in prior work and applying their result. Finally, we identify a slightly more general class of networks for which essentially the same reduction idea can be applied to get the same bound. 
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  3. There are many settings in which a principal performs a task by delegating it to an agent, who searches over possible solutions and proposes one to the principal. This describes many aspects of the workflow within organizations, as well as many of the activities undertaken by regulatory bodies, who often obtain relevant information from the parties being regulated through a process of delegation. A fundamental tension underlying delegation is the fact that the agent's interests will typically differ -- potentially significantly -- from the interests of the principal, and as a result the agent may propose solutions based on their own incentives that are inefficient for the principal. A basic problem, therefore, is to design mechanisms by which the principal can constrain the set of proposals they are willing to accept from the agent, to ensure a certain level of quality for the principal from the proposed solution. In this work, we investigate how much the principal loses -- quantitatively, in terms of the objective they are trying to optimize -- when they delegate to an agent. We develop a methodology for bounding this loss of efficiency, and show that in a very general model of delegation, there is a family of mechanisms achieving a universal bound on the ratio between the quality of the solution obtained through delegation and the quality the principal could obtain in an idealized benchmark where they searched for a solution themself. Moreover, it is possible to achieve such bounds through mechanisms with a natural threshold structure, which are thus structurally simpler than the optimal mechanisms typically considered in the literature on delegation. At the heart of our framework is an unexpected connection between delegation and the analysis of prophet inequalities, which we leverage to provide bounds on the behavior of our delegation mechanisms. 
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