Delay-Constrained Unicast: Improved upper bounds Sudeep Kamath - PowerPoint PPT Presentation

Delay-Constrained Unicast: Improved upper bounds Sudeep Kamath Joint work with Chandra Chekuri Sreeram Kannan Pramod Viswanath DIMACS workshop on Network Coding, 17 December 2015 0 / 10

Intra-fmow coding has fewer security and privacy concerns Practical constraint - eg. video streaming, fjnancial data Implementation aligned with self-interest 1 / 10 Delay-constrained unicast [Wang-Chen '14]

Practical constraint - eg. video streaming, fjnancial data Intra-fmow coding has fewer security and privacy concerns Implementation aligned with self-interest 1 / 10 Delay-constrained unicast [Wang-Chen '14] Single flow with delay constraint D

Practical constraint - eg. video streaming, fjnancial data Intra-fmow coding has fewer security and privacy concerns Implementation aligned with self-interest 1 / 10 Delay-constrained unicast [Wang-Chen '14] Single flow with delay constraint D

Practical constraint - eg. video streaming, fjnancial data Intra-fmow coding has fewer security and privacy concerns Implementation aligned with self-interest 1 / 10 Delay-constrained unicast [Wang-Chen '14] Single flow with delay constraint D For this network with D=6, Capacity = 4 Flow 3

Practical constraint - eg. video streaming, fjnancial data Intra-fmow coding has fewer security and privacy concerns Implementation aligned with self-interest 1 / 10 Delay-constrained unicast [Wang-Chen '14] Single flow with delay constraint D For this network with D=6, Capacity = 4 Flow 3

Practical constraint - eg. video streaming, fjnancial data Intra-fmow coding has fewer security and privacy concerns Implementation aligned with self-interest 1 / 10 Delay-constrained unicast [Wang-Chen '14] Single flow with delay constraint D For this network with D=6, Capacity = 4 Flow 3

Practical constraint - eg. video streaming, fjnancial data Intra-fmow coding has fewer security and privacy concerns Implementation aligned with self-interest 1 / 10 Delay-constrained unicast [Wang-Chen '14] Single flow with delay constraint D For this network with D=6, Capacity = 4 Flow 3

Practical constraint - eg. video streaming, fjnancial data Intra-fmow coding has fewer security and privacy concerns Implementation aligned with self-interest 1 / 10 Delay-constrained unicast [Wang-Chen '14] Single flow with delay constraint D For this network with D=6, Capacity = 4 Flow 3

data Practical constraint - eg. video streaming, fjnancial Intra-fmow coding has fewer security and privacy concerns Implementation aligned with self-interest 1 / 10 Delay-constrained unicast [Wang-Chen '14] Single flow with delay constraint D For this network with D=6, Capacity = 4 Flow 3 How large can this ratio be?

1 / 10 Implementation aligned with self-interest concerns Intra-fmow coding has fewer security and privacy data Practical constraint - eg. video streaming, fjnancial Delay-constrained unicast [Wang-Chen '14] Single flow with delay constraint D For this network with D=6, Capacity = 4 Flow 3 How large can this ratio be? Capacity 2 ≤ sup ≤ D + 1 Flow graphs

1 / 10 Implementation aligned with self-interest concerns Intra-fmow coding has fewer security and privacy data Practical constraint - eg. video streaming, fjnancial Delay-constrained unicast [Wang-Chen '14] Single flow with delay constraint D For this network with D=6, Capacity = 4 Flow 3 How large can this ratio be? Capacity We improve 2 ≤ sup ≤ D + 1 over this Flow graphs

2 / 10 Network Combinatorial Information Optimization Theory This work

2 / 10 Multi-commodity flow problem Network Combinatorial Information Optimization Theory This work

2 / 10 Multi-commodity Multiple-unicast flow problem problem Network Combinatorial Information Optimization Theory This work

Multi-commodity fmow / Multiple-unicast Flow: Maximum total commodity fmow EdgeCut: Fewest edges whose removal disconnects all paths from to Capacity: Maximum information fmow EdgeCut Cutset bound Capacity Cutset bound However, we may have EdgeCut Capacity 3 / 10 Given a directed graph and k source-destination pairs { ( s i , d i ) }

Multi-commodity fmow / Multiple-unicast EdgeCut Capacity EdgeCut However, we may have Cutset bound Cutset bound Capacity Capacity: Maximum information fmow to disconnects all paths from EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow 3 / 10 Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } d 2 d 1

Multi-commodity fmow / Multiple-unicast EdgeCut Capacity EdgeCut However, we may have Cutset bound Cutset bound Capacity Capacity: Maximum information fmow to disconnects all paths from EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow 3 / 10 Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } d 2 d 1

Multi-commodity fmow / Multiple-unicast EdgeCut Capacity EdgeCut However, we may have Cutset bound Cutset bound Capacity Capacity: Maximum information fmow to disconnects all paths from EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow 3 / 10 Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } d 2 d 1 Flow = 1

Multi-commodity fmow / Multiple-unicast Cutset bound Capacity EdgeCut However, we may have Capacity Cutset bound EdgeCut Capacity: Maximum information fmow EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow 3 / 10 Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } disconnects all paths from s i to d i ∀ i d 2 d 1 Flow = 1

Multi-commodity fmow / Multiple-unicast Cutset bound Capacity EdgeCut However, we may have Capacity Cutset bound EdgeCut Capacity: Maximum information fmow EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow 3 / 10 Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } × disconnects all paths from s i to d i ∀ i d 2 d 1 Flow = 1

Multi-commodity fmow / Multiple-unicast Cutset bound Capacity EdgeCut Cutset bound Capacity However, we may have EdgeCut Capacity: Maximum information fmow EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow 3 / 10 Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } × × × disconnects all paths from s i to d i ∀ i d 2 d 1 Flow = 1 EdgeCut = 1

Multi-commodity fmow / Multiple-unicast Cutset bound Capacity EdgeCut Cutset bound Capacity However, we may have EdgeCut Capacity: Maximum information fmow EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow 3 / 10 Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } × × × disconnects all paths from s i to d i ∀ i d 2 d 1 Flow = 1 EdgeCut = 1

Multi-commodity fmow / Multiple-unicast Cutset bound Capacity EdgeCut However, we may have Cutset bound Capacity 3 / 10 EdgeCut Capacity: Maximum information fmow EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } b a a ⊕ b a b disconnects all paths from s i to d i ∀ i a ⊕ b a ⊕ b d 2 d 1 Flow = 1 EdgeCut = 1

Multi-commodity fmow / Multiple-unicast Cutset bound Capacity EdgeCut However, we may have Cutset bound Capacity 3 / 10 EdgeCut Capacity: Maximum information fmow EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } b a a ⊕ b a b disconnects all paths from s i to d i ∀ i a ⊕ b a ⊕ b d 2 d 1 Flow = 1 EdgeCut = 1 Capacity = 2

Multi-commodity fmow / Multiple-unicast Capacity Capacity EdgeCut However, we may have Cutset bound 3 / 10 EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow Capacity: Maximum information fmow Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } b a a ⊕ b a b disconnects all paths from s i to d i ∀ i a ⊕ b a ⊕ b d 2 d 1 EdgeCut ̸ = Cutset bound Flow = 1 EdgeCut = 1 Capacity = 2

Multi-commodity fmow / Multiple-unicast Capacity: Maximum information fmow Capacity EdgeCut However, we may have 3 / 10 EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } b a a ⊕ b a b disconnects all paths from s i to d i ∀ i a ⊕ b a ⊕ b d 2 d 1 EdgeCut ̸ = Cutset bound Flow = 1 EdgeCut = 1 Capacity ≤ Cutset bound Capacity = 2

Multi-commodity fmow / Multiple-unicast Capacity: Maximum information fmow However, we may have 3 / 10 EdgeCut: Fewest edges whose removal Flow: Maximum total commodity fmow Given a directed graph and k s 1 s 2 source-destination pairs { ( s i , d i ) } b a a ⊕ b a b disconnects all paths from s i to d i ∀ i a ⊕ b a ⊕ b d 2 d 1 EdgeCut ̸ = Cutset bound Flow = 1 EdgeCut = 1 Capacity ≤ Cutset bound Capacity = 2 EdgeCut < Capacity

4 / 10

4 / 10 Flow = EdgeCut = Capacity For k = 1: (Max-Flow Min-Cut Theorem)

4 / 10 Flow = EdgeCut = Capacity For k = 1: (Max-Flow Min-Cut Theorem) For k ≥ 2:

4 / 10 Flow = EdgeCut = Capacity For k = 1: (Max-Flow Min-Cut Theorem) For k ≥ 2: Flow ≤ EdgeCut Flow ≤ Capacity EdgeCut ≶ Capacity