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. ”