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Revert "Fix #230: Add BiconnectivityAugmentation model" #690

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47 changes: 0 additions & 47 deletions docs/paper/reductions.typ
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Original file line number Diff line number Diff line change
Expand Up @@ -66,7 +66,6 @@
"MinimumVertexCover": [Minimum Vertex Cover],
"MaxCut": [Max-Cut],
"GraphPartitioning": [Graph Partitioning],
"BiconnectivityAugmentation": [Biconnectivity Augmentation],
"HamiltonianPath": [Hamiltonian Path],
"UndirectedTwoCommodityIntegralFlow": [Undirected Two-Commodity Integral Flow],
"LengthBoundedDisjointPaths": [Length-Bounded Disjoint Paths],
Expand Down Expand Up @@ -538,52 +537,6 @@ Graph Partitioning is a core NP-hard problem arising in VLSI design, parallel co
caption: [Graph with $n = 6$ vertices partitioned into $A = {v_0, v_1, v_2}$ (blue) and $B = {v_3, v_4, v_5}$ (red). The 3 crossing edges $(v_1, v_3)$, $(v_2, v_3)$, $(v_2, v_4)$ are shown in bold red; internal edges are gray.],
) <fig:graph-partitioning>
]
#problem-def("BiconnectivityAugmentation")[
Given an undirected graph $G = (V, E)$, a set $F$ of candidate edges on $V$ with $F inter E = emptyset$, weights $w: F -> RR$, and a budget $B in RR$, find $F' subset.eq F$ such that $sum_(e in F') w(e) <= B$ and the augmented graph $G' = (V, E union F')$ is biconnected, meaning $G'$ is connected and deleting any single vertex leaves it connected.
][
Biconnectivity augmentation is a classical network-design problem: add backup links so the graph survives any single vertex failure. The weighted candidate-edge formulation modeled here captures communication, transportation, and infrastructure planning settings where only a prescribed set of new links is feasible and each carries a cost. In this library, the exact baseline is brute-force enumeration over the $m = |F|$ candidate edges, yielding $O^*(2^m)$ time and matching the exported complexity metadata for the model.

*Example.* Consider the path graph $v_0 - v_1 - v_2 - v_3 - v_4 - v_5$ with candidate edges $(v_0, v_2)$, $(v_0, v_3)$, $(v_0, v_4)$, $(v_1, v_3)$, $(v_1, v_4)$, $(v_1, v_5)$, $(v_2, v_4)$, $(v_2, v_5)$, $(v_3, v_5)$ carrying weights $(1, 2, 3, 1, 2, 3, 1, 2, 1)$ and budget $B = 4$. Selecting $F' = {(v_0, v_2), (v_1, v_3), (v_2, v_4), (v_3, v_5)}$ uses total weight $1 + 1 + 1 + 1 = 4$ and eliminates every articulation point: after deleting any single vertex, the remaining graph is still connected. Reducing the budget to $B = 3$ makes the instance infeasible, because one of the path endpoints remains attached through a single articulation vertex.

#figure(
canvas(length: 1cm, {
import draw: *
// 6 vertices in a horizontal line
let verts = range(6).map(k => (k * 1.5, 0))
let path-edges = ((0,1),(1,2),(2,3),(3,4),(4,5))
// Candidate edges: (u, v, weight, selected?)
let candidates = (
(0, 2, 1, true), (0, 3, 2, false), (0, 4, 3, false),
(1, 3, 1, true), (1, 4, 2, false), (1, 5, 3, false),
(2, 4, 1, true), (2, 5, 2, false), (3, 5, 1, true),
)
let blue = graph-colors.at(0)
let green = graph-colors.at(2)
let gray = luma(180)
// Draw path edges (existing graph)
for (u, v) in path-edges {
g-edge(verts.at(u), verts.at(v), stroke: 2pt + black)
}
// Draw candidate edges as arcs above the path
for (u, v, w, sel) in candidates {
let mid-x = (verts.at(u).at(0) + verts.at(v).at(0)) / 2
let span = v - u
let height = span * 0.4
let ctrl = (mid-x, height)
bezier(verts.at(u), verts.at(v), ctrl,
stroke: if sel { 2.5pt + green } else { (dash: "dashed", paint: gray, thickness: 0.8pt) })
// Weight label
content((mid-x, height + 0.25),
text(7pt, fill: if sel { green.darken(30%) } else { gray })[#w])
}
// Draw nodes
for (k, pos) in verts.enumerate() {
g-node(pos, name: "v" + str(k), label: [$v_#k$])
}
}),
caption: [Biconnectivity Augmentation on a 6-vertex path with $B = 4$. Existing edges are black; green arcs show the selected augmentation $F'$ (total weight 4); dashed gray arcs are unselected candidates. The resulting graph $G' = (V, E union F')$ is biconnected.],
) <fig:biconnectivity-augmentation>
]

#problem-def("BoundedComponentSpanningForest")[
Given an undirected graph $G = (V, E)$ with vertex weights $w: V -> ZZ_(gt.eq 0)$, a positive integer $K <= |V|$, and a positive bound $B$, determine whether there exists a partition of $V$ into $t$ non-empty sets $V_1, dots, V_t$ with $1 <= t <= K$ such that each induced subgraph $G[V_i]$ is connected and each part satisfies $sum_(v in V_i) w(v) <= B$.
Expand Down
51 changes: 0 additions & 51 deletions problemreductions-cli/src/cli.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -236,7 +236,6 @@ Flags by problem type:
X3C (ExactCoverBy3Sets) --universe, --sets (3 elements each)
SetBasis --universe, --sets, --k
BicliqueCover --left, --right, --biedges, --k
BiconnectivityAugmentation --graph, --potential-edges, --budget [--num-vertices]
BMF --matrix (0/1), --rank
SteinerTree --graph, --edge-weights, --terminals
CVP --basis, --target-vec [--bounds]
Expand Down Expand Up @@ -272,7 +271,6 @@ Examples:
pred create MIS/KingsSubgraph --positions \"0,0;1,0;1,1;0,1\"
pred create MIS/UnitDiskGraph --positions \"0,0;1,0;0.5,0.8\" --radius 1.5
pred create MIS --random --num-vertices 10 --edge-prob 0.3
pred create BiconnectivityAugmentation --graph 0-1,1-2,2-3 --potential-edges 0-2:3,0-3:4,1-3:2 --budget 5
pred create FVS --arcs \"0>1,1>2,2>0\" --weights 1,1,1
pred create UndirectedTwoCommodityIntegralFlow --graph 0-2,1-2,2-3 --capacities 1,1,2 --source-1 0 --sink-1 3 --source-2 1 --sink-2 3 --requirement-1 1 --requirement-2 1
pred create X3C --universe 9 --sets \"0,1,2;0,2,4;3,4,5;3,5,7;6,7,8;1,4,6;2,5,8\"
Expand Down Expand Up @@ -440,12 +438,6 @@ pub struct CreateArgs {
/// Directed arcs for directed graph problems (e.g., 0>1,1>2,2>0)
#[arg(long)]
pub arcs: Option<String>,
/// Weighted potential augmentation edges (e.g., 0-2:3,1-3:5)
#[arg(long)]
pub potential_edges: Option<String>,
/// Total budget for selected potential edges
#[arg(long)]
pub budget: Option<String>,
/// Deadlines for MinimumTardinessSequencing (comma-separated, e.g., "5,5,5,3,3")
#[arg(long)]
pub deadlines: Option<String>,
Expand Down Expand Up @@ -581,46 +573,3 @@ pub fn print_subcommand_help_hint(error_msg: &str) {
}
}
}

#[cfg(test)]
mod tests {
use super::*;

#[test]
fn test_create_parses_biconnectivity_augmentation_flags() {
let cli = Cli::parse_from([
"pred",
"create",
"BiconnectivityAugmentation",
"--graph",
"0-1,1-2",
"--potential-edges",
"0-2:3,1-3:5",
"--budget",
"7",
]);

let Commands::Create(args) = cli.command else {
panic!("expected create command");
};

assert_eq!(args.problem, "BiconnectivityAugmentation");
assert_eq!(args.graph.as_deref(), Some("0-1,1-2"));
assert_eq!(args.potential_edges.as_deref(), Some("0-2:3,1-3:5"));
assert_eq!(args.budget.as_deref(), Some("7"));
}

#[test]
fn test_create_help_mentions_biconnectivity_augmentation_flags() {
let cmd = Cli::command();
let create = cmd.find_subcommand("create").expect("create subcommand");
let help = create
.get_after_help()
.expect("create after_help")
.to_string();

assert!(help.contains("BiconnectivityAugmentation"));
assert!(help.contains("--potential-edges"));
assert!(help.contains("--budget"));
}
}
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