Traditionally, automatic design rule correction (DRC) problem is modeled as a Linear Program (LP) with design rules as difference constraints under minimum perturbation objective. This yields Totally Uni-Modular (TUM) constraint matrices thereby guaranteeing integral grid-compliant solutions with LP solvers. However, advanced technology nodes introduce per-layer grids or discrete tracks that result into non-TUM constraint matrices for the DRC problem. Consequently, LP solvers do not guarantee integral solutions. In this work, we propose a novel formulation using an 'un-rolling' technique. Our formulation guarantees TUM constraint matrices and hence integral multiple grid/track compliant solutions. We demonstrate its efficacy on layouts at advanced nodes.

In this paper, we consider the problem of energy-efficient uplink scheduling with delay constraint for a multiuser wireless system. We address this problem within the framework of constrained Markov decision processes (CMDPs) wherein one seeks to minimize one cost (average power) subject to a hard constraint on another (average delay). We do not assume the arrival and channel statistics to be known. To handle state-space explosion and informational constraints, we split the problem into individual CMDPs for the users, coupled through their Lagrange multipliers; and a user selection problem at the base station. To address the issue of unknown channel and arrival statistics, we propose a reinforcement learning algorithm. The users use this learning algorithm to determine the rate at which they wish to transmit in a slot and communicate this to the base station. The base station then schedules the user with the highest rate in a slot. We analyze convergence, stability, and optimality properties of the algorithm. We also demonstrate the efficacy of the algorithm through simulations within IEEE 802.16 system.

We consider the problem of scheduling users on the downlink of a Time Division Multiplexed(TDM) system with constraints on the average packet delays over a fading wireless channel. Our objective is to maximize the sum throughput with constraints on the user delays. Due to the difficulty in computing optimal policy, we propose a suboptimal scheduling algorithm which is based on computing appropriate indices and scheduling the user with the highest index. Our simulations for the IEEE 802.16 system indicate that our algorithm satisfies the delay constraints of the users and is highly throughput efficient.

In this paper, we consider the problem of energy efficient scheduling under average delay constraint for a single user fading channel. We propose a new approach for on-line implementation of the optimal packet scheduling algorithm. This approach is based on reformulating the value iteration equation by introducing a virtual state called post-decision state. The resultant value iteration equation becomes amenable to online implementation based on stochastic approximation. This approach has an advantage that an explicit knowledge of the probability distribution of the channel state as well as the arrivals is not required for the implementation. We prove that the on-line algorithm indeed converges to the optimal policy.