Zvi Lotker

Buffer Overflow Management in QoS Switches

We consider two types of buffering policies that are used in network switches supporting Quality of Service (QoS). In the FIFO type, packets must be transmitted in the order in which they arrive; the constraint in this case is the limited buffer space. In the bounded-delay type, each packet has a maximum delay time by which it must be transmitted, or otherwise it is lost. We study the case of overloads resulting in packet loss. In our model, each packet has an intrinsic value, and the goal is to maximize the total value of transmitted packets. Our main contribution is a thorough investigation of some natural greedy algorithms in various models. For the FIFO model we prove tight bounds on the competitive ratio of the greedy algorithm that discards packets with the lowest value when an overflow occurs. We also prove that the greedy algorithm that drops the earliest packets among all low-value packets is the best greedy algorithm. This algorithm can be as much as 1.5 times better than the tail-drop greedy policy, which drops the latest lowest-value packets. In the bounded-delay model we show that the competitive ratio of any on-line algorithm for a uniform bounded-delay buffer is bounded away from 1, independent of the delay size. We analyze the greedy algorithm in the general case and in three special cases: delay bound 2, link bandwidth 1, and only two possible packet values. Finally, we consider the off-line scenario. We give efficient optimal algorithms and study the relation between the bounded-delay and FIFO models in this case.

Conflict-Free Colorings of Simple Geometric Regions with Applications to Frequency Assignment in Cellular Networks

Motivated by a frequency assignment problem in cellular networks, we introduce and study a new coloring problem that we call minimum conflict-free coloring (min-CF-coloring). In its general form, the input of the min-CF-coloring problem is a set system

How to Explore a Fast-Changing World (Cover Time of a Simple Random Walk on Evolving Graphs)

(X,{\cal S})

Many random walks are faster than one

, where each

Buffer overflow management in QoS switches

S \in {\cal S}

Improved approximation algorithms for connected sensor cover

is a subset of X. The output is a coloring

Collaborative search on the plane without communication

\chi

Tight bounds for algebraic gossip on graphs

of the sets in

Rent, Lease, or Buy: Randomized Algorithms for Multislope Ski Rental

{\cal S}

SINR diagrams: towards algorithmically usable SINR models of wireless networks

that satisfies the following constraint: for every