Algorithms and Optimization Aravind Srinivasan University of Maryland

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, …)

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

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)

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)

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, …