Draw the cable layout to efficiently connect various blocks within the Amritsar University Campus.

Computer Networks

Efficient Cable Layout Design

Official Answer

The most efficient layout connects all four blocks using the three shortest possible links, giving a total cable length of 180 m.

Layout (direct cable connections):

ACADEMIC — HOSTEL : 40 M
ADMIN — ACADEMIC : 60 M
ADMIN — SPORTS : 80 M

This connects ADMIN, ACADEMIC, HOSTEL and SPORTS with the minimum possible total cable ( $40+60+80 = 180 \text{ M}$ ), avoiding the longer direct links such as ADMIN-HOSTEL (160 M) or HOSTEL-SPORTS (150 M).

cable layoutminimum distanceACADEMIC-HOSTELADMIN-ACADEMICADMIN-SPORTStotal cable lengthefficient network design

Marking Scheme

11 mark: correct minimum layout shown/described — ACADEMIC-HOSTEL, ADMIN-ACADEMIC and ADMIN-SPORTS (or any equivalent diagram giving the same 180 M minimum total, with justification).

Hint

Sort all six inter-block distances ascending and pick the shortest links that connect all four blocks without forming a loop.

Quick Oral Answer

I connect ACADEMIC-HOSTEL (40 M), ADMIN-ACADEMIC (60 M) and ADMIN-SPORTS (80 M), which links all four blocks using only 180 M of cable — the minimum possible total.

Analysis & Explanation

This is a minimum-cost connectivity question: all four blocks must be linked using the least total cable.

Concept: List every block-pair distance, then keep adding the shortest remaining link that does not create a loop (Prim's/Kruskal's idea, taught intuitively at Class 12 level): ACADEMIC-HOSTEL (40), ADMIN-ACADEMIC (60), ADMIN-SPORTS (80) already connect all four blocks — no more links are needed.

Exam trap: Students often connect blocks in the order they are listed in the question (ADMIN-ACADEMIC-HOSTEL-SPORTS in a chain) without checking whether a shorter combination exists; here, using ADMIN-SPORTS (80 M) instead of ACADEMIC-SPORTS (120 M) or HOSTEL-SPORTS (150 M) saves real cable cost.

Real-world application: This mirrors how network engineers design real campus backbones — always choosing the layout with the least total cable/fibre length while still keeping every building connected, since cabling is one of the most expensive parts of a wired network installation.

Common Mistakes

1Connecting blocks in a simple chain following their listed order instead of checking actual distances for the minimum total.
2Including a redundant fourth link (creating a loop), which wastes cable without adding connectivity.
3Choosing HOSTEL-SPORTS (150 M) or ADMIN-HOSTEL (160 M) links which are far longer than necessary.

Interesting Facts

This distance-minimisation approach is the real-world Minimum Spanning Tree problem, formally solved by Prim's and Kruskal's algorithms in computer science.

The chosen 180 M layout saves at least 60 M of cable compared to naive alternatives such as connecting via HOSTEL-SPORTS instead of ADMIN-SPORTS.

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Frequently Asked Questions

Why is ADMIN-SPORTS (80 M) chosen over ACADEMIC-SPORTS (120 M)?

Once ADMIN, ACADEMIC and HOSTEL are already connected via the first two links, SPORTS only needs one more connection; the shortest available link to any already-connected block is ADMIN-SPORTS at 80 M, which is cheaper than the 120 M or 150 M alternatives.

Is there only one correct cable layout?

Any layout connecting all four blocks with total cable length 180 M using non-redundant links is acceptable; the specific 40+60+80 combination shown is the standard minimum answer.