1. Algorithms and Optimization Aravind Srinivasan University of Maryland

2. State-of-the-art, recent advances • Protocol Design • individual layers: e.g., random-access protocols with good efficiency ratio • cross-layer optimization; e.g., MAC+routing • Capacity-estimation • well-developed for “random” instances • beginnings of algorithmic (worst-case) approaches • Selfishness (initial stages) and locality • The role of random walks (opt., resource discovery, epid. protocols, diffusion, …)

3. Open Problems • Distributed Linear Programming for wireless, more general optimization • Capacity vs. latency • Traffic models (for all of the above): periodic, gradually-varying? Adversarial queuing theory? • New measures: e.g., interaction between lifetime maximization and Markov-Chain conductance • Group-Steiner models for relays • Rigorous analysis of random access for emerging standards

4. Desired advances at PHY layer • Realistic models that are amenable to analysis (e.g., latency-minimization for SINR model) • Overheads of new technologies: e.g., in opportunistic freq. assignment (lessons from WDM)

5. Challenges for future networks • Need for distributed alg.s; even a standard definition is lacking (theory suggests polylogarithmic convergence-time) • Understanding of emerging technologies, e.g., cognitive/MCMR networks. Sample questions: • incorporate delays due to channel-hopping into latency-minimization alg.s • channel assignment in heterogeneous MCMR networks • Robustness:fault/attack models, robustness against node inactivity (e.g., directed diffusion)

6. Gaps, Discussion • Models: for new technologies (e.g., MCMR, cognitive), mobility, fault-tolerance • How much re-optimization is feasible? Continually-improving algorithms, stochastic opt. • Potentially very rich collaboration between “CS theory” and “networking”: graph theory, geometry, distributed and randomized alg.s, security, adversarial models, self-stabilization, …