Micah Adler

Optimal proxy cache allocation for efficient streaming media distribution

We address the problem of efficiently streaming a set of heterogeneous videos from a remote server through a proxy to multiple asynchronous clients so that they can experience playback with low startup delays. We determine the optimal proxy prefix cache allocation to the videos that minimizes the aggregate network bandwidth cost. We integrate proxy caching with traditional server-based reactive transmission schemes such as hatching, patching and stream merging to develop a set of proxy-assisted delivery schemes. We quantitatively explore the impact of the choice of transmission scheme, cache allocation policy, proxy cache size, and availability of unicast versus multicast capability, on the resulting transmission cost. Our evaluations show that even a relatively small prefix cache (10%-20% of the video repository) is sufficient to realize substantial savings in transmission cost. We find that carefully designed proxy-assisted reactive transmission schemes can produce significant cost savings even in a predominantly unicast environment such as the Internet.

The predecessor attack: An analysis of a threat to anonymous communications systems

There have been a number of protocols proposed for anonymous network communication. In this paper, we investigate attacks by corrupt group members that degrade the anonymity of each protocol over time. We prove that when a particular initiator continues communication with a particular responder across path reformations, existing protocols are subject to the attack. We use this result to place an upper bound on how long existing protocols, including Crowds, Onion Routing, Hordes, Web Mixes, and DC-Net, can maintain anonymity in the face of the attacks described. This provides a basis for comparing these protocols against each other. Our results show that fully connected DC-Net is the most resilient to these attacks, but it suffers from scalability issues that keep anonymity group sizes small. We also show through simulation that the underlying topography of the DC-Net affects the resilience of the protocol: as the number of neighbors a node has increases the strength of the protocol increases, at the cost of higher communication overhead.

Towards compressing Web graphs

We consider the problem of compressing graphs of the link structure of the World Wide Web. We provide efficient algorithms for such compression that are motivated by random graph models for describing the Web. The algorithms are based on reducing the compression problem to the problem of finding a minimum spanning free in a directed graph related to the original link graph. The performance of the algorithms on graphs generated by the random graph models suggests that by taking advantage of the link structure of the Web, one may achieve significantly better compression than natural Huffman-based schemes. We also provide hardness results demonstrating limitations on natural extensions of our approach.

Trade-offs in probabilistic packet marking for IP traceback

There has been considerable recent interest in probabilistic packet marking schemes for the problem of tracing a sequence of network packets back to an anonymous source. An important consideration for such schemes is the number of packet header bits that need to be allocated to the marking protocol. Let b denote this value. All previous schemes belong to a class of protocols for which b must be at least log n, where n is the number of bits used to represent the path of the packets. In this article, we introduce a new marking technique for tracing a sequence of packets sent along the same path. This new technique is effective even when b = 1. In other words, the sequence of packets can be traced back to their source using only a single bit in the packet header. With this scheme, the number of packets required to reconstruct the path is O(22n), but we also show that Ω(2n) packets are required for any protocol where b = 1. We also study the trade-off between b and the number of packets required. We provide a protocol and a lower bound that together demonstrate that for the optimal protocol, the number of packets required (roughly) increases exponentially with n, but decreases doubly exponentially with b. The protocol we introduce is simple enough to be useful in practice. We also study the case where the packets are sent along k different paths. For this case, we demonstrate that any protocol must use at least log(2k − 1) header bits. We also provide a protocol that requires ⌈log(2k + 1)⌉ header bits in some restricted scenarios. This protocol introduces a new coding technique that may be of independent interest.

Minimum energy reliable paths using unreliable wireless links

We address the problem of energy-efficient reliable wireless communication in the presence of unreliable or lossy wireless link layers in multi-hop wireless networks. Prior work [1] has provided an optimal energy efficient solution to this problem for the case where link layers implement perfect reliability. However, a more common scenario --- a link layer that is not perfectly reliable, was left as an open problem. In this paper we first present two centralized algorithms, BAMER and GAMER, that optimally solve the minimum energy reliable communication problem in presence of unreliable links. Subsequently we present a distributed algorithm, DAMER, that approximates the performance of the centralized algorithm and leads to significant performance improvement over existing single-path or multi-path based techniques.

Optimal peer selection for P2P downloading and streaming

In a P2P system, a client peer may select one or more server peers to download a specific file. In a P2P resource economy, the server peers charge the client for the downloading. A server peers price would naturally depend on the specific object being downloaded, the duration of the download, and the rate at which the download is to occur. The optimal peer selection problem is to select, from the set of peers that have the desired object, the subset of peers and download rates that minimizes cost. In this paper we examine a number of natural peer selection problems for both P2P downloading and P2P streaming. For downloading, we obtain the optimal solution for minimizing the download delay subject to a budget constraint, as well as the corresponding Nash equilibrium. For the streaming problem, we obtain a solution that minimizes cost subject to continuous playback while allowing for one or more server peers to fail during the streaming process. The methodologies developed in this paper are applicable to a variety of P2P resource economy problems.

A stochastic process on the hypercube with applications to peer-to-peer networks

Consider the following stochastic process executed on a graph G=(V,E) whose nodes are initially uncovered. In each step, pick a node at random and if it is uncovered, cover it. Otherwise, if it has an uncovered neighbor, cover a random uncovered neighbor. Else, do nothing. This can be viewed as a structured coupon collector process. We show that for a large family of graphs, O(n) steps suffice to cover all nodes of the graph with high probability, where n is the number of vertices. Among these graphs are d-regular graphs with d =Ω(log n log log n), random d-regular graphs with d =Ω(log n) and the k-dimensional hypercube where n=2k.This process arises naturally in answering a question on load balancing in peer-to-peer networks. We consider a distributed hash table in which keys are partitioned across a set of processors, and we assume that the number of processors grows dynamically, starting with a single processor. If at some stage there are n processors, the number of queries required to find a key is log2 n+O(1), the number of pointers maintained by each processor is log2 n+O(1), and moreover the worst ratio between the loads of processors is O(1), with high probability. To the best of our knowledge, this is the first analysis of a distributed hash table that achieves asymptotically optimal load balance, while still requiring only O(log n) pointers per processor and O(log n) queries for locating a key; previous methods required Ω(log2 n) pointers per processor and Ω(log n) queries for locating a key.

Tradeoffs in probabilistic packet marking for IP traceback

There has been considerable recent interest in probabilistic packet marking schemes for the problem of tracing a sequence of network packets back to an anonymous source. An important consideration for such schemes is the number of packet header bits that need to be allocated to the marking protocol. Let b denote this value. All previous schemes belong to a class of protocols for which b must be at least log n, where n is the number of bits used to represent the path of the packets. In this paper, we introduce a new marking technique for tracing a sequence of packets sent along the same path. This new technique is effective even when b=1. In other words, the sequence of packets can be traced back to their source using only a single bit in the packet header. With this scheme, the number of packets required to reconstruct the path is O(22n), but we also show that ω(2n) packets are required for any protocol where b=1. We also study the tradeoff between b and the number of packets required. We provide a protocol and a lower bound that together demonstrate that for the optimal protocol, the number of packets required (roughly) increases exponentially with n, but decreases doubly exponentially with b. The protocol we introduce is simple enough to be useful in practice. We also study the case where the packets are sent along k different paths. For this case, we demonstrate that any protocol must use at least log(2k—1) header bits. We also provide a protocol that requires ⌈log(2k+1)⌉ header bits in some restricted scenarios. This protocol introduces a new coding technique that may be of independent interest.

Parallel randomized load balancing

It is well known that after placing n balls independently and uniformly at Ž . random into n bins, the fullest bin holds Q log nrlog log n balls with high probability. More recently, Azar et al. analyzed the following process: randomly choose d bins for each ball, and then place the balls, one by one, into the least full bin from its d choices. Azar et al. They show that after all n balls have been placed, the fullest bin contains only Ž . log log nrlog dqQ 1 balls with high probability. We explore extensions of this result to parallel and distributed settings. Our results focus on the tradeoff between the amount of Correspondence to: M. Mitzenmacher * A preliminary version of this work appeared in the Proceedings of the Twenty-Se enth Annual ACM Symposium on the Theory of Computing, May 1995, pp. 238]247. † This work was primarily done while attending U.C. Berkeley, and was supported by a Schlumberger Foundation graduate fellowship. ‡ This work was primarily done while attending U.C. Berkeley, and was supported in part by ARPA Ž . under contract DABT63-92-C-0026, by NSF numbers CCR-9210260 and CDA-8722788 , and by Lawrence Livermore National Laboratory. § This work was primarily done while attending U.C. Berkeley, and was supported by the Office of Naval Research and by NSF grant CCR-9505448. ¶ Supported by a fellowship from U.C. Berkeley. Q 1998 John Wiley & Sons, Inc. CCC 1042-9832r98r020159-30

Randomized Pursuit-Evasion in Graphs

We analyse a randomized pursuit-evasion game played by two players on a graph, a hunter and a rabbit. Let