Yossi Richter

All-norm approximation algorithms

A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different lp norms. We address this problem by introducing the concept of an all-norm p-approximation algorithm, which supplies one solution that guarantees p-approximation to all lp norms simultaneously. Specifically, we consider the problem of scheduling in the restricted assignment model, where there are m machines and n jobs, each job is associated with a subset of the machines and should be assigned to one of them. Previous work considered approximation algorithms for each norm separately. Lenstra et al. [Math. Program. 46 (1990) 259-271] showed a 2-approximation algorithm for the problem with respect to the l∞ norm. For any fixed lp norm the previously known approximation algorithm has a performance of θ(p). We provide an all-norm 2-approximation polynomial algorithm for the restricted assignment problem. On the other hand, we show that for any given lp norm (p > 1) there is no PTAS unless P=NP by showing an APX-hardness result. We also show for any given lp norm a FPTAS for any fixed number of machines.

The zero-one principle for switching networks

Recently, approximation analysis has been extensively used to study algorithms for routing weighted packets in various network settings. Although different techniques were applied in the analysis of diverse models, one common property was evident: the analysis of input sequences composed solely of two different values is always substantially easier, and many results are known only for restricted value sequences. Motivated by this, we introduce our zero-one principle for switching networks which characterizes a wide range of algorithms for which achieving c-approximation (as well as c-competitiveness) with respect to sequences composed of 0s and 1s implies achieving c-approximation. The zero-one principle proves to be very efficient in the design of switching algorithms, and substantially facilitates their analysis. We present three applications. First, we consider the Multi-Queue QoS Switching model and design a 3-competitive algorithm, improving the result from [6]. Second, we study the Weighted Dynamic Routing problem on a line topology of length k and present a (k+1)-competitive algorithm, which improves and generalizes the results from [1,12]. As a third application, we consider the work of [11], that compares the performance of local algorithms to the global optimum in various network topologies, and generalize their results from 2-value sequences to arbitrary value sequences.

Management of multi-queue switches in QoS networks

The concept of Quality of Service (QoS) networks has gained growing attention recently, as the traffic volume in the Internet constantly increases, and QoS guarantees are essential to ensure proper operation of most communication based applications. A QoS switch serves m incoming queues by transmitting packets arriving at these queues through one output port, one packet per time unit. Each packet is marked with a value indicating its guaranteed quality of service. Since the queues have bounded capacity and the rate of arriving packets can be much higher than the transmission rate, packets can be lost due to insufficient queue space. The goal is to maximize the total value of transmitted packets. This problem encapsulates two dependent questions: admission control, namely which packets to discard in case of queue overflow, and scheduling, i.e. which queue to use for transmission in each time unit. We use competitive analysis to study online switch performance in QoS based networks. Specifically, we provide a novel generic technique that decouples the admission control and scheduling problems. Our technique transforms any single queue admission control strategy (preemptive or nonpreemptive) to a scheduling and admission control algorithm for our general m queues model, whose competitive ratio is at most twice the competitive ratio of the given admission control strategy. We use our technique to derive concrete algorithms for the general preemptive and nonpreemptive cases, as well as for the interesting special cases of the 2-value model and the unit value model. To the best of our knowledge this is the first result combining both scheduling and admission control decisions for arbitrary packets sequences in multi-queue switches. We also provide a 1.58-competitive randomized algorithm for the unit value case. This case is interesting by itself since most current networks (e.g. IP networks) only support a best-effort service in which all packets streams are treated equally.

Management of Multi-Queue Switches in QoS Networks

AbstractThe concept of Quality of Service (QoS) networks has gained growing attention recently, as the traffic volume in the Internet constantly increases, and QoS guarantees are essential to ensure proper operation of most communication-based applications. A QoS switch serves m incoming queues by transmitting packets arriving to these queues through one output port, one packet per time step. Each packet is marked with a value indicating its priority in the network. Since the queues have bounded capacities and the rate of arriving packets can be much higher than the transmission rate, packets can be lost due to insufficient queue space. The goal is to maximize the total value of transmitted packets. This problem encapsulates two dependent questions: buffer management, namely which packets to admit into the queues, and scheduling, i.e. which queue to use for transmission in each time step. We use competitive analysis to study online switch performance in QoS-based networks. Specifically, we provide a novel generic technique that decouples the buffer management and scheduling problems. Our technique transforms any single-queue buffer management policy (preemptive or non-preemptive) to a scheduling and buffer management algorithm for our general m queues model, whose competitive ratio is at most twice the competitive ratio of the given buffer management policy. We use our technique to derive concrete algorithms for the general preemptive and non-preemptive cases, as well as for the interesting special cases of the 2-value model and the unit-value model. We also provide a 1.58-competitive randomized algorithm for the unit-value case. This case is interesting by itself since most current networks (e.g. IP networks) do not yet incorporate full QoS capabilities, and treat all packets equally.

Tradeoffs in Worst-Case Equilibria

We investigate the problem of routing traffic through a congested network in an environment of non-cooperative users. We use the worst-case coordination ratio suggested by Koutsoupias and Papadimitriou to measure the performance degradation due to the lack of a centralized traffic regulating authority. We provide a full characterization of the worst-case coordination ratio in the restricted assignment and unrelated parallel links models. In particular, we quantify the tradeoff between the ”negligibility” of the traffic controlled by each user and the coordination ratio. We analyze both pure and mixed strategies systems and identify the range where their performance is similar.

An Improved Algorithm for CIOQ Switches

The problem of maximizing the weighted throughput in various switching settings has been intensively studied recently through competitive analysis. To date, the most general model that has been investigated is the standard CIOQ (Combined Input and Output Queued) switch architecture with internal fabric speedup S ≥ 1. CIOQ switches, that comprise the backbone of packet routing networks, are N × N switches controlled by a switching policy that incorporates two components: admission control and scheduling. An admission control strategy is essential to determine the packets stored in the FIFO queues in input and output ports, while the scheduling policy conducts the transfer of packets through the internal fabric, from input ports to output ports. The online problem of maximizing the total weighted throughput of CIOQ switches was recently investigated by Kesselman and Rosen in [12]. They presented two different online algorithms for the general problem that achieve non-constant competitive ratios (linear in either the speedup or the number of distinct values or logarithmic in the value range). We introduce the first constant-competitive algorithm for the general case of the problem, with arbitrary speedup and packet values. Specifically, our algorithm is 9.47-competitive, and is also simple and easy to implement.

All-Norm Approximation Algorithms

A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different lp norms. We address this problem by introducing the concept of an All-norm ?approximation algorithm, which supplies one solution that guarantees ?approximation to all lp norms simultaneously. Specifically, we consider the problem of scheduling in the restricted assignment model, where there are m machines and n jobs, each is associated with a subset of the machines and shouldb e assignedto one of them. Previous work considered approximation algorithms for each norm separately. Lenstra et al. [12] showeda 2-approximation algorithm for the problem with respect to the l? norm. For any fixed lp norm the previously known approximation algorithm has a performance of ?(p). We provide an all-norm 2-approximation polynomial algorithm for the restricted assignment problem. On the other hand, we show that for any given lp norm (p > 1) there is no PTAS unless P=NP by showing an APX-hardness result. We also show for any given lp norm a FPTAS for any fixedn umber of machines.

Optimatch: applying constraint programming to workforce management of highly skilled employees

Today many companies face the challenge of matching highly skilled professionals to high-end positions in large organisations and human deployment agencies. Unlike traditional workforce management problems, such as shift scheduling, highly skilled employees are professionally distinguishable from each other and hence non-interchangeable. Our work specifically focuses on the services industry, where much of the revenue comes from the assignment of highly professional workers. Here, non-accurate matches may result in significant monetary losses and other negative effects. We deal with very large pools of both positions and employees, where optimal decisions should be made rapidly in a dynamic environment. Since traditional operations research methods fail to answer this problem, we employ Constraint Programming (CP), a subfield of Artificial Intelligence with strong algorithmic foundations. Our CP model builds on new constraint propagators designed for this problem (but applicable elsewhere), as well as on ...