networking & algorithm classes

src/notes/class_notes/csci651.md

@@ -11,6 +11,17 @@ flow: same source&destination (IP&port) & protocol
 
 NABC for research: need, approach, benefit, competition
 
+## *Some Reflections on Innovation and Invention*, George H. Heilmeier
+
+- think about where field is going, not where it is
+- involve researcher throughout deployment & business
+- technology transfer: focus on what people "care about", what help people,
+    not mathematical beauty
+    - overcome existing benefit haver; marketing
+    - everything need to work, or else fail
+- catechism for DARPA funding/ startup: goal, existing solution,
+    improvement & novelty, expected outcome, cost estimate
+
 ## *The design philosophy of the DARPA Internet protocols*, David D. Clark
 
 - Internet: multiplexed utilization of existing interconnected networks
@@ -79,16 +90,28 @@ NABC for research: need, approach, benefit, competition
 
 ## *BBR: Congestion-Based Congestion Control*, Neal Cardwell, Yuchung Cheng, C. Stephen Gunn, Soheil Hassas Yeganeh, Van Jacobson
 
-- avoid timeout
+- better for WAN, cellular, large bandwidth+delay link
+    - adapt to larger queue routers have now
+    - avoid timeout & retransmission
+    - CUBIC struggle to keep many packet in flight because of
+        long feedback loop
+    - BBR try to run at performance knee not cliff
 - TCP need to measure ideal window size: bandwidth-delay product (BDP)
     = bottleneck bandwidth (BtlBw) × RTT (RTprop)
 - measure RTT: exponential weighted moving average
     (EWMA)—ACK time - sent time
-- measure bandwidth: window size & packet loss & ACK rate
-- TCP keep probing at equilibrium → oscillation
-- router has larger queue now
-    - clear queue periodically
-- pacing: additional to ACK clocking
+- measure bandwidth periodically: window size & packet loss & ACK rate
+    - pacing: additional to ACK self-clocking
+    - try-faster (ProbeBW state, 98%): send 5/4 pace to
+        probe bandwidth (multiplicative increase), then send 3/4 to drain queue
+        - CUBIC keep probing at equilibrium → oscillation
+        - BBR more aggressive ⇒ dominate bandwidth when sharing
+    - try-slower (ProbeRTT state): send few packet to clear queue;
+        probe RTprop by taking minimum
+- startup state (slow start)
+    - exit startup when BtlBw stay same for 3 RTT
+    - drain mode to clear queue
+- converge to fair share
 
 ## *BGP Routing Policies in ISP Networks*, Matthew Caesar, Jennifer Rexford
 
@@ -97,6 +120,9 @@ NABC for research: need, approach, benefit, competition
     community
 - manual & unscalable configuration
 - trick to enhance security, no systematic solution
+- when can avoid BGP: connect to single network, default routing
+- BGP multihoming goal: reachability, cost, performance, latency,
+    reliability, load balancing
 
 ## *How the Great Firewall of China detects and blocks fully encrypted traffic*, Wu, Mingshi, Jackson Sippe, Danesh Sivakumar, Jack Burg, Peter Anderson, Xiaokang Wang, Kevin Bock, Amir Houmansadr, Dave Levin, Eric Wustrow
 

src/notes/class_notes/csci670.md

@@ -18,6 +18,11 @@ P space: $∃x_1, ∀x_2, ∃x_3, \cdots\text{ s.t.
 - P time $\in$ P space (equal?)
 - PPAD
 
+\#P: account #solution to NP problem
+
+- each NP problem has \#P problem
+- \#P-complete $\subseteq$ P space
+
 linear programming: proved P
 
 learning problem
@@ -196,18 +201,17 @@ given $G=(V,E,d)$ w/ metric $d$, $k$, want $(S_1,\cdots,S_k)$ s.t.
         c_G(i_t)=\frac{w_{i_t}}{|S_{i_t}\cap U_t|} ≤ H(|S_{j_t}|)w_{j_t}
         $$
 
-        where
-        [harmonic series](../mathematics/sequence_series.html#harmonic-series)
-        $H(k)=∑_{i=1}^k\frac{1}{i}$
-
+        - [harmonic
+            series](../mathematics/sequence_series.html#harmonic-series)
+            $H(k)=∑_{i=1}^k\frac{1}{i}$
         - when $h$th (starting from 0) element $V_{\pi_h}$ in
             $S_j$ is covered,
             $\displaystyle c_G(\pi_n)≤\frac{w_j}{|S_j|-h}$ because at most
             $h$ element is covered in $S_j$
 
 ### set function
 
-$f:\{S|S\subseteq V\} → R$
+$f:\{S|S\subseteq V\} → \R$
 
 - salary for group in society
 - hypergraph: indicator set function determine if each subset is hyperedge
@@ -216,17 +220,56 @@ property:
 
 1. grounded: $f(∅)=0$
 1. monotone: $∀ S\subseteq T,f(S) ≤ f(T)$
-1. submodular: $∀ S\subseteq T,∀ v\notin T$
+1. submodular
 
-    $$
-    \nabla f_S(v) ≥ \nabla f_T(v)
-    $$
+#### submodular function
+
+$∀ S\subseteq T,∀ v\notin T$
+
+$$
+\nabla f_S(v) ≥ \nabla f_T(v)
+$$
+
+- diminishing return: less happier when having more and more chocolate
+- discrete derivative: $\nabla f_S(v)=f(S\cup \{v\})-f(S)$
+    - how much value can $v$ add to $S$
+- complementarity: $1 + 1 > 2$
+- $f,g$ submodular $⇒ ∀\alpha\in[0,1], \alpha f+(1+\alpha)g$ submodular
+
+problem
+
+- input: submodular $f:\{S|S\subseteq V\} → \R^*$, $k$
+- output: $S\subset V$, s.t. $|S|=k$, $\max f(S)$
+- oracle model: can get $f(T)$
+
+- example: max cover: for mapping $f:V → B$ choose $k$ element from $V$ to
+    maximize $|f(S)|$
+- greedy algorithm $S'$: at time $t$, add $u_t$ that maximize
+    $\nabla f_{u_t}(S_{t-1}')$
 
-    - diminishing return: less happier when having more and more chocolate
-    - discrete derivative: $\nabla f_S(v)=f(S\cup \{v\})-f(S)$
-        - how much value can $v$ add to $S$
-    - complementarity: $1 + 1 > 2$
-    - $f,g$ submodular $⇒ ∀\alpha\in[0,1], \alpha f+(1+\alpha)g$ submodular
+theorem: $∀f$ monotone & submodular, $∀k$, $f(S')≥(1-\frac{1}{e})f(S^*)$
+
+proof:
+
+$$
+S^*=:\{v_1,\cdots,v_k\};\\
+f(S^*)≤f(S^*\cup S_t')=f(S_t')+[f(S^*\cup S_t')-f(S_t')];\\
+f(S^*\cup S_t')-f(S_t')=
+∑_{i=1}^k[f(\{v_1,\cdots,v_i\}\cup S_t')-f(\{v_1,\cdots,v_{i-1}\}\cup S_t')]\\=
+∑_{i=1}^k\nabla f_{v_i}(\{v_1,\cdots,v_{i-1}\}\cup S_t')≤
+∑_{i=1}^k\nabla f_{v_i}(S_t')=
+k\nabla f_{v_i}(S_t')\\≤
+k\nabla f_{u_{t+1}}(S_t')=
+k[f(S_{t+1}')-f(S_t)]\\
+⇒ \delta_t:=f(S^*)-f(S_t')≤k[f(S_{t+1}')-f(S_t)]\\=
+k[(f(S_{t+1}')-f(S^*))+(f(S^*)-f(S_t))]\\=
+k[-\delta_{t+1}+\delta_t]\\
+⇒ \delta_{t+1}≤\frac{k-1}{k}\delta_t≤\cdots≤
+\left(1-\frac{1}{k}\right)^{t+1}\delta_0\\=
+\left(1-\frac{1}{k}\right)^{t+1}f(S^*)≤
+e^{-\frac{t+1}{k}}f(S^*)\\
+⇒ f(S'_k)=f(S^*)-\delta_k≥\left(1-e^-\frac{k}{k}\right)f(S^*)
+$$
 
 ### reachability
 
@@ -239,3 +282,25 @@ $f(S)=|\text{Reach}(S)|$
     $$
     \nabla f_S(v)=|\{x|\text{can reach }x\text{ from }v\text{ but not }S\}|
     $$
+
+### network influence
+
+input $G=(V,E),p_e;t=1,\cdots,T$
+
+- dynamic & complex compared to traditional static graph
+- network influence maximization: often submodular
+
+#### independent cascade (IC)
+
+each node has probability $p$ to influence
+
+- stochastic network influence; e.g., pandemic
+- $S_t=S_{t-1}\cup N(S_{t-1})$
+- influence spread $\sigma(S)=∑_{W\in 2^V}\Pr_W[S → W]|W|$
+    - generally \#P-complete
+
+#### threshold model
+
+each node $v$ has threshold $\theta_v$ to be influenced by neighbor
+
+- deterministic/ stochastic by $\theta_v$, e.g., idea spreading