Liran Katzir

An efficient approximation for the generalized assignment problem

We present a simple family of algorithms for solving the Generalized Assignment Problem (GAP). Our technique is based on a novel combinatorial translation of any algorithm for the knapsack problem into an approximation algorithm for GAP. If the approximation ratio of the knapsack algorithm is α and its running time is O(f(N)), our algorithm guarantees a (1 + α)-approximation ratio, and it runs in O(M ċ f(N) + M ċ N), where N is the number of items and M is the number of bins. Not only does our technique comprise a general interesting framework for the GAP problem; it also matches the best combinatorial approximation for this problem, with a much simpler algorithm and a better running time.

Computational analysis and efficient algorithms for micro and macro OFDMA downlink scheduling

Orthogonal frequency-division multiple access (OFDMA) is one of the most important modulation and access methods for the future mobile networks. Before transmitting a frame on the downlink, an OFDMA base station has to invoke an algorithm that determines which of the pending packets will be transmitted, what modulation should be used for each of them, and how to construct the complex OFDMA frame matrix as a collection of rectangles that fit into a single matrix with fixed dimensions. We propose efficient algorithms, with performance guarantee, that solve this intricate OFDMA scheduling problem by breaking it down into two subproblems, referred to as macro and micro scheduling. We analyze the computational complexity of these subproblems and develop efficient algorithms for solving them.

Speeding up the Xbox recommender system using a euclidean transformation for inner-product spaces

A prominent approach in collaborative filtering based recommender systems is using dimensionality reduction (matrix factorization) techniques to map users and items into low-dimensional vectors. In such systems, a higher inner product between a user vector and an item vector indicates that the item better suits the users preference. Traditionally, retrieving the most suitable items is done by scoring and sorting all items. Real world online recommender systems must adhere to strict response-time constraints, so when the number of items is large, scoring all items is intractable. We propose a novel order preserving transformation, mapping the maximum inner product search problem to Euclidean space nearest neighbor search problem. Utilizing this transformation, we study the efficiency of several (approximate) nearest neighbor data structures. Our final solution is based on a novel use of the PCA-Tree data structure in which results are augmented using paths one hamming distance away from the query (neighborhood boosting). The end result is a system which allows approximate matches (items with relatively high inner product, but not necessarily the highest one). We evaluate our techniques on two large-scale recommendation datasets, Xbox Movies and Yahoo~Music, and show that this technique allows trading off a slight degradation in the recommendation quality for a significant improvement in the retrieval time.

Cross-layer hybrid FEC/ARQ reliable multicast with adaptive modulation and coding in broadband wireless networks

In this paper, we define and address a new problem that arises when a base station in a broadband wireless network wishes to multicast information to a large group of nodes and to guarantee some level of reliability using Application-layer forward error correction (FEC) codes. Every data block to be multicast is translated into a sequence of packets, from which every receiver must receive at least in order to correctly decode the block. The new problem is to determine which PHY-layer modulation and coding scheme (MCS) the base station should use for each packet. We present several variants of this problem, which differ in the number of automatic repeat request (ARQ) rounds during which the delivery of a data block must be completed. Most of these variants are shown to be NP-hard. However, we present optimal solutions for practical instances, where the number of MCSs is small, and efficient approximations and heuristics for the general case of each variant.

Computational Analysis and Efficient Algorithms for Micro and Macro OFDMA Scheduling

OFDMA is one of the most important modulation and access methods for the future mobile networks. Before transmitting a frame on the downlink, an OFDMA base station has to invoke an algorithm that determines which of the pending packets will be transmitted, what modulation should be used for each of them, and how to construct the complex OFDMA frame matrix as a collection of rectangles that fit into a single matrix with fixed dimensions. We propose efficient, and theoretically best possible, algorithms that solves this intricate OFDMA scheduling problem by breaking it down into two sub-problems, referred to as macro and micro scheduling. We analyze the computational complexity of these sub-problems and develop efficient algorithms for solving them.

On the Trade-Off between Energy and Multicast Efficiency in 802.16e-Like Mobile Networks

In this paper, we define a new problem that has not been addressed in the past: the trade-off between energy efficiency and throughput for multicast services in 802.16e or similar mobile networks. In such networks, the mobile host can reduce its energy consumption by entering the sleep mode when it is not supposed to receive or transmit information. For unicast applications, the tradeoff between delay and energy efficiency has been extensively researched. However, for mobile hosts running multicast (usually push- based) applications, it is much more difficult to determine when data should be transmitted by the base station and when each host should enter the sleep mode. In order to maximize the channel throughput while limiting the energy consumption, a group of hosts needing similar data items should be active during the same time intervals. We define this as an optimization problem and present several algorithms for it. We show that the most efficient solution is the one that employs cross-layer optimization by dividing the hosts into groups according to the quality of their downlink physical (PHY) channels.

Cross-Layer Hybrid FEC/ARQ Reliable Multicast with Adaptive Modulation and Coding in Broadband Wireless Networks

In this paper we define and address a new problem that arises when a base station in a broadband wireless network wishes to multicast information to a large group of nodes and to guarantee some level of reliability using Application layer FEC codes. Every data block to be multicast is translated into a sequence of K + n packets, from which every receiver must receive at least K in order to correctly decode the block. The new problem is to determine which PHY layer MCS (Modulation and Coding Scheme) the base station should use for each packet. We present several variants of this problem, which differ in the number of ARQ (Automatic Repeat reQuest) rounds during which the delivery of a data block must be completed. Most of these variants are shown to be NP-hard. However, we present optimal solutions for practical instances, where the number of MCSs is small, and efficient approximations and heuristics for the general case of each variant.

A generic quantitative approach to the scheduling of synchronous packets in a shared uplink wireless channel

The scheduling logic at the base station of a shared wireless medium supports time-dependent (synchronous) applications by allocating timely transmission grants. To this end, it must take into account not only the deadlines of the pending packets, but also the channel conditions for each potential sender, the requirements of nonsynchronous applications, and the packet retransmission strategy. With respect to these factors, we identify three scheduling scenarios and show that the scheduler logic faces a different challenge in addressing each of them. We then present a generic scheduling algorithm that translates all the factors relevant to each scenario into a common profit parameter, and selects the most profitable transmission instances.

Optimizing data plane resources for multipath flows

In many modern networks, such as datacenters, optical networks, and multiprotocol label switching (MPLS), the delivery of a traffic flow with a certain bandwidth demand over a single network path is either not possible or not cost-effective. In these cases, it is very often possible to improve the networks bandwidth utilization by splitting the traffic flow over multiple efficient paths. While using multiple paths for the same traffic flow increases the efficiency of the network, it consumes expensive forwarding resources from the network nodes, such as TCAM entries of Ethernet/MPLS switches and wavelengths/lightpaths of optical switches. In this paper, we define several problems related to splitting a traffic flow over multiple paths while minimizing the consumption of forwarding resources, and present efficient algorithms for solving these problems.

A unified scheme for generalizing cardinality estimators to sum aggregation

Cardinality estimation algorithms receive a stream of elements that may appear in arbitrary order, with possible repetitions, and return the number of distinct elements. Such algorithms usually seek to minimize the required storage at the price of inaccuracy in their output. This paper shows how to generalize every cardinality estimation algorithm that relies on extreme order statistics (min/max sketches) to a weighted version, where each item is associated with a weight and the goal is to estimate the total sum of weights. The proposed unified scheme uses the unweighted estimator as a black-box, and manipulates the input using properties of the beta distribution. We discuss cardinality estimation algorithms.We show how to generalize every such an algorithm to a weighted version.To this end, we use properties of the beta distribution.