On the polynomial time computability of abstract ray-tracing problems

Shuji Isobe, Tetsuo Kuriyama, Masahiro Mambo, Hiroki Shizuya

Research output: Contribution to journalArticlepeer-review


The abstract ray-tracing problem asks, for a given scene consisting of a light source, a light receiver and finitely many obstacles in a space, and a given positive integer ε +~ 0, whether a ray going out from the light source could reach the light receiver with intensity at least ε. The problem is known to be PSPACE-hard, and it is very unlikely that there exists an efficient algorithm to solve the problem without adding any restriction. In this paper, we show that the problem can be solved in polynomial time under some weak practical restrictions.

Original languageEnglish
Pages (from-to)1209-1213
Number of pages5
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number5
Publication statusPublished - 2005


  • Abstract ray-tracing problem (ARTP)
  • PSPACE-hard/complete
  • Ray-tracing problem
  • Scene


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