Algorithms and Optimization Gabriel Robins CS Corporate Partners
Algorithms and Optimization Gabriel Robins CS Corporate Partners Annual Meeting Department of Computer Science University of Virginia www. cs. virginia. edu
“Perfection in design is achieved not when there’s nothing to left to add, but when there’s nothing left to remove. ” 2
“Make everything as simple as possible, but not simpler. ” - Albert Einstein (1879 -1955)
Algorithms Solution fast approximate Short & sweet Quick & dirty slow Speed exact Slowly but surely Too little, too late
Complexity
VLSI Design Requirements e. g. , “secure communication” Design Specification Data encryption Fabrication Functional Design p C(M) = M mod N Physical Layout Logic Design Z=x+yw Structural Design x y w z
Trends in Interconnect time
Placement & Routing
Steiner Trees 2 3
Steiner Trees Theorem: Optimal for £ 4 points Theorem: Solutions cost < 3/2 · OPT Theorem: Solutions cost £ 4/3 · OPT for “difficult” pointsets In practice: Solution cost is within 0. 5% of OPT on average
Bounded Radius Trees Algorithm: Input: • points / graph • any e > 0 Output: tree T with • radius(T) £ (1+e) OPT • cost(T) £ (1+2/e) OPT · ·
“You want proof? I’ll give you proof!”
Circuit Testing B A Theorem: # leaves / 2 probes are necessary Theorem: # leaves / 2 probes are sufficient Algorithm: linear time
Improving Manufacturability
Moving-Target TSP Origin
Moving-Target TSP 2 3 Origin 1 4 Theorem: “waiting” can never help Algorithms: · efficient exact solution for 1 -dimension · efficient heuristics for other variants
Robust Paths
Minimum Surfaces
Evolutionary Trees time 19
Evolutionary Trees herpes. EC crnv. HH 2 hum. RSC cmv. HH 3 humf. MLF hum. IL 8 rat. G 10 d rat. ANG bov. LOR 1 chk. GPCR RBS 11 hum. SSR 1 gp. PAF dog. RDC 1 musdelto mus. P 2 u hum. C 5 a chk. P 2 y rat. BK 2 rat. ODOR rat. LH rat. RTA hum. MRG hum. MAS bov. OP hum. EDG 1 rat. CGPCR rat. POT hum. ACTH hum. MSH mus. EP 3 hum. TXA 2 hum. THR rat. NPYY 1 rat. NK 1 fly. NK fly. NPY mus. GIR rat. CCKA mus. EP 2 dog. CCKB dog. Ad 1 hum. D 2 hum. A 2 a ham. A 1 a rat. D 1 ham. B 2 bov. H 1 hum 5 HT 1 a hum. M 1 rat. NTR mus. TRH mus. Gn. RH mus. GRP rat. V 1 a bov. ETA
Discovering New Proteins herpes. EC ? ? crnv. HH 2 hum. RSC cmv. HH 3 humf. MLF hum. IL 8 rat. G 10 d rat. ANG bov. LOR 1 chk. GPCR RBS 11 hum. SSR 1 gp. PAF dog. RDC 1 musdelto mus. P 2 u hum. C 5 a chk. P 2 y rat. BK 2 rat. ODOR rat. LH rat. RTA hum. MRG hum. MAS bov. OP hum. EDG 1 rat. CGPCR rat. POT hum. ACTH hum. MSH mus. EP 3 hum. TXA 2 rat. CCKA mus. EP 2 dog. CCKB hum. THR dog. Ad 1 hum. D 2 hum. A 2 a ham. A 1 a rat. D 1 ham. B 2 bov. H 1 hum 5 HT 1 a hum. M 1 rat. NPYY 1 rat. NK 1 fly. NK fly. NPY mus. GIR rat. NTR mus. TRH mus. Gn. RH mus. GRP rat. V 1 a bov. ETA
Landmine Detection
Lets Collaborate! • What we offer: • Brainpower & ideas • Skills and experience • UVa’s infrastructure • Faculty ® students ® employees • What we need: • Practical problems to solve • Some support
UVa Computer Science 24
“I think you should be more explicit here in step two. ”
- Slides: 25