{"paper":{"title":"Target PageRank: Matching Prescribed PageRank Scores via Budgeted Edge Additions","arxiv_id":"2611.06782","primary_cat":"cs.SI","submitted_at":"2026-11-04T16:55:52+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"PageRank is widely used to quantify the importance of nodes in directed networks.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.03,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.98,"id":"s1","own":false,"role":"background","text":"In applications such as recommendation systems, it is increasingly important that the PageRank distribution provides a fair representation of node exposure.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.05,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.02,"method":0.0,"result":0.0,"background":0.98,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.89,"id":"s2","own":false,"role":"background","text":"This motivates the problem of making minimal changes to a graph so that the PageRank values of a given set of target nodes $T$ match a desired vector $\\boldsymbol{t}$.","hedge":{"p":0.93,"label":"asserted"},"own_p":0.08,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.01,"method":0.0,"result":0.0,"background":0.89,"limitation":0.0,"future_work":0.0,"contribution":0.1,"interpretation":0.0}},{"i":3,"p":0.61,"id":"s3","own":false,"role":"contribution","text":"In this paper, we study this problem under an edge-addition budget $B$, where exactly $B$ edges may be added to the graph.","hedge":{"p":0.95,"label":"asserted"},"own_p":0.35,"main_claim_p":0.04,"quantitative":true,"quantitative_p":0.65,"role_probabilities":{"gap":0.0,"method":0.18,"result":0.0,"background":0.21,"limitation":0.0,"future_work":0.0,"contribution":0.61,"interpretation":0.0}},{"i":4,"p":0.97,"id":"s4","own":true,"role":"result","text":"We show that deciding whether a multiset of exactly $B$ added edges can make the target nodes attain their desired absolute PageRank scores is NP-complete.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.2,"quantitative":false,"quantitative_p":0.29,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.97,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.0}},{"i":5,"p":0.85,"id":"s5","own":true,"role":"contribution","text":"After this, we define the $\\ell_1$ \\textsc{Target PageRank} problem in which we seek to minimize the $\\ell_1$ distance between the target vector and resultant vector.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.9,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.13,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.85,"interpretation":0.0}},{"i":6,"p":0.98,"id":"s6","own":true,"role":"result","text":"We show that this optimization problem admits no polynomial-time multiplicative constant-factor approximation unless $P=NP$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.16,"quantitative":true,"quantitative_p":0.64,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.01,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":7,"p":0.66,"id":"s7","own":true,"role":"contribution","text":"Motivated by these hardness results, we propose two greedy heuristics for approaching the target PageRank vector.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.92,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.37,"role_probabilities":{"gap":0.0,"method":0.33,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.66,"interpretation":0.01}},{"i":8,"p":0.66,"id":"s8","own":true,"role":"method","text":"We additionally propose a Random Walk Hungarian (RWH) heuristic that addresses the addition of edges between dissimilar nodes by incorporating a penalty for such edges.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.66,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.34,"interpretation":0.0}},{"i":9,"p":0.52,"id":"s9","own":true,"role":"method","text":"Finally, we evaluate the proposed heuristics on several real-world and synthetic datasets and compare their performance in terms of PageRank accuracy, 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